Hence, the nociceptor’s temperature threshold must be estimated, which in turn will depend on the depth at which transduction happens in the skin. Since the temperature at the receptor cannot be accessed experimentally, such an estimation can currently only be achieved through modeling. However, the current state-of-the-art model to estimate temperature at the receptor suffers from the fact that it cannot account for the natural stochastic variability of neuronal responses. We improve this model using a probabilistic approach which accounts for uncertainties and potential noise in system. Using a data set of 24 C-fibers recorded in vitro, we show that, even without detailed knowledge of the bio-thermal properties of the system, the probabilistic model that we propose here is capable of providing estimates of threshold and depth in cases where the classical method fails.The subjective experience of thermal pain follows the detection and encoding of noxious stimuli by primary afferent neurons called nociceptors. However, nociceptor morphology has been hard to access and the mechanisms of signal transduction remain unresolved. In order to understand how heat transducers in nociceptors are activated  Therefore, to obtain an accurate estimate of threshold temperature of the receptor neurons, the first step has been to model the propagation of the temperature in several layers of the skin from the surface to the receptor depth. Several models have been developed to estimate nociceptor depth and threshold by using neurophysiological recordings of nociceptors or behavioral measurements to parameterize the heat diffusion equation to model the ability of the skin to conduct heat energy23303132Tillman et al.To mitigate these shortcomings, mathematical models were used to estimate the threshold temperature as a parameter212829An accurate estimation of the time at which the threshold temperature was reached is essential for the classical approaches. Small inaccuracies in spike time measurement, internal random process which could result in a delay between reaching the threshold and generation of first action potential, and trial-to-trial variability of neural responses, can result to big inaccuracies in depths, and sometimes even make depth estimation impossible. Additionally, there are many sources of uncertainty in the estimation method. For example, the bio-thermal skin parameters  are difficult to estimate accurately, since they vary with the age, gender, recording area and even the hair cycle of the specimenIn this contribution, we reformulated the established model for temperature propagation in a probabilistic way. We thus open up the way to account for natural variability on receptor response and uncertainties in other model parameters, enabling a statistical approach to the problem of inferring receptor depth from spike times and associated surface temperature. We introduce two modifications to the previous approach. First, we allow for a small, variable delay that can account for the variability of spike latency arising from deterministic properties of the system and/or ‘noise’, e.g. generated by random processes inside the neuron. Second, we use Monte-Carlo methods to deal with the uncertainty in bio-thermal parameters of skin model. To demonstrate the reliability of the new probabilistic model we applied both the classical approach and the probabilistic approach on a data set of extracellular recordings from 24 C-MH nociceptors. We then estimated the receptor parameters, depth and threshold temperature of all neurons and evaluated the probabilistic model using model evidence tests. The proposed method succeeds in producing realistic estimates of both threshold and depth for all measured neurons, although previous methods failed to provide such estimates for all neurons.Towards our aim to improve the classical model for depth and threshold estimation we first investigated the factors that rendered previous approaches unstable. We assumed that the instability of the classical model was mainly due to uncertainties of the threshold time and an incomplete skin model. Here, we use the term ‘threshold time’ to refer to the (not directly measureable) time at which the neuron reaches its firing threshold and action potential initiation. In the classical approach, threshold time is assumed to be equal to the time of the first spike. However, the first spike after stimulation onset may be generated with a small delay (latency noise), or it may be caused by spontaneous sub-threshold activity, especially in cases where the spike latency is very short compared to stimulus onset. To deal with these uncertainties and variability in spike times we (i) introduce a delay between threshold time and first spike (latency), (ii) allowing for some responses to be outliers that are not driven by the presented stimulus, and (iii) introduce a probabilistic model for the skin.in vitro skin preparationsWe first assessed the performance of the classical model to estimate receptor depth and threshold, based on the analytical solution of the heat diffusion equation. An attractive feature of the analytical approximation is that the solution at any point in the skin can be obtained independently from the skin model, which is particularly useful when the skin model is not completely determined, or when the skin is stimulated from the corium side to facilitate electrical stimulation and pharmacological manipulation of the primary afferents in T = 38.8 °C at a depth of D = 0.3 mm. Each curve hence refers to a different time point after stimulus onset, i.e. the latency of the first action potential. All curves intersect in a single point: the estimated depth of the receptor.Assuming a fixed temperature threshold of a neuron at a fixed depth, it is possible to infer this depth from the time until this threshold is reached after applying a constant supra-threshold temperature to the surface. This idealized example illustrates how the classical approach to depth and threshold estimation depends on reliable spike latency. Neuronal “noise” that causes variability in spike timing unfavorably affects the performance of this method. Real-world measurements affected by noise thus often fail to intersect in a single point, as illustrated in We studied the capability of the classical approach to predict receptor threshold and depth in recordings from 24 C-MH neurons. Our experimental protocol consisted of three heat stimuli with three ramp rate durations of long: 16 s, middle: 4 s, and short see .t = t* and the attenuated threshold temperature x of the receptor can be entered in the solution of heat equation as formulated by HenriquesFor a given threshold time D and We assume the skin has uniform temperature lane see . For the results . AssuminTo solve the equation Only 2 out of 24 neurons intersected in a single point . For 12 For the 2 neurons with a single intersection point distinct depth and threshold temperature were directly obtained by the intersection. For 5 neurons that the intersections span a small triangle we generated an average over the intersections. For cases where the intersections span wider ranges, generation of an average over stimulations induces a high variance in the estimated depth, leading to an expected large estimation error for threshold and depth.The mean average receptor threshold temperature for the 2 neurons with a single intersection was 39.44 °C and standard deviation of 5.7 °C, consistent with values found in the literatureThe main limitation of the classical approach lies in its assumption that parameter constellations are either fully consistent with the experimental outcome (i.e. they are on the curve) and can be included in the estimation or they are completely inconsistent with the experimental outcome (not on the curve) and might be discarded. In the following sections we will use equation The classical method for inferring depth and temperature threshold assumes that the latency of the response is exactly equal to the time when the temperature threshold was reached. Here, we weaken this assumption by introducing a delay, i-th measurement and n = 3 equations with the same parameter γ but n = 3 different i as a function of γ, by inverting equation In this equation, This allows us to write the log likelihood function;The parameters We can view the negative of the right side of equation In example neuron C-MH1 the classically estimated normalized depth is Note that in In the case of neuron C-MH4 the classical method failed to find an intersection of all three ramp stimuli see  and thertion see . Note thγ. We divided all 24 C-MH neurons into two main groups: The group ‘Single intersection’ that includes 7 neurons for which the classical model successfully resulted in a single intersection or the intersections span a small triangle like neurons C-MH1 and C-MH2 of Tthreshold = 33.3 °C and mean depth of D = 12.5 mm. Previous studies have shown that the majority of C-MH fibers display a threshold of 43 °C2283039Tthreshold = 32.36 °C and a mean depth D = 0.9 mm. Hence this model likely failed to estimate Tthreshold (because it is implausibly low), but the estimated depth was consistent with the reported depth from the previous studies in range of 20-570 μm30De = 100 μm (assuming that the skin is approximately 1 mm thick).Tthreshold = 32.36 °C were lower than previously reported thresholds in range of 36–47 °C283039As a brief summary, in this section we showed that using a statistical model to estimate the parameters gives a successful parameter combination of depth for all neurons even when the classical model fails to give any parameter estimate. Yet, in the case of estimated threshold temperatures the values with a median of The major contribution of the probabilistic model is to incorporate noise by allowing for delay in first spike time. However, we didn’t cover the possibility that the first spike recorded after stimulus onset might be an ‘outlier’ which was not triggered by the stimulus, but rather generated by the (low) resting state activity of the receptor. Next we therefore addressed the question of how our results would change under the assumption that the first spike after stimulus onset may have been triggered by a probabilistic random process.Every stimulus that is taken into account for the estimation of depth and threshold adds a certain amount of information and reduces the uncertainty of the estimation. But since there is also a certain probability that the first spike is not a response to the stimulus, every stimulus also adds a certain amount of noise to the estimation. Hence, there exists a potential tradeoff in adding as many recordings as possible to the estimation, or rejecting some of them as outliers. For example in our data for 12 out of 24 neurons in We extended this idea to the maximum likelihood framework described in the previous section. We introduced multiple probabilistic models that could describe the data and then decided which one provides a more concise description.To discriminate between the models we employed a Bayesian testing procedureThe main reason for adopting a Bayesian approach for model comparison is that Bayes factors provide a way of including other information as prior knowledge when assessing the evidence for a hypothesis. This is a strong advantage for data with lots of uncertainties, such as a small number of recorded neurons and no repetition of recordings for each stimulus, or an incomplete skin model. We can incorporate histological and bio-thermal information and results reported by other investigators as prior knowledge and use this to improve the estimation of receptor parameters. Furthermore, by integrating over the full parameter space, marginal likelihoods penalize complex models in a very natural way42Bayes Factors can only be calculated for pairwise comparisons. Yet, here we are interested in selecting the best out of multiple models. We therefore used the marginal likelihoods directly and chose the model that maximizes the marginal likelihood. For simplicity, we will refer to any of the models that exclude one or more stimuli from the determination of the neuron’s parameters as the ‘Selection model’.n different experimental conditions, e.g. ramped stimuli, where for all responses the first spikes have been triggered by the stimulus. More specifically, the first model assumes that the corresponding delays i = 1,2,3 number of stimuli) have a probability distribution with free parameters The first model is the full probabilistic model described above, assuming a data set consisting of m < n responses the first spikes have been triggered by the stimulus and would therefore contribute meaningfully to the estimate of depth and threshold. For the remaining responses the first spikes are the result of a stationary background process, e.g. spontaneous discharges or in any other way not triggered by the stimulus. Thus the second model assumes that only the first delays i = 1,…,m, and m < n have the same probability distribution with parameters In the ‘Selection models’ only for the first 1 have the same probability distribution with the parameter space 2 only two delays out of three have the same distribution with the parameter space In the case of our data the delays of three ramped stimuli in first model MTo compare the models, we use the marginal likelihood,k. This term provides a way to include other information about plausible values of parameters. Our first concern is thus how to choose prior densities to represent the available information.In equation The prior densities offer an appropriate way of adding biologically meaningful constraints from the literature into a statistical model. In 2,i (i-th stimulus was omitted) with the highest evidence and compared the estimates with the results of full probabilistic model M1 and with the classical model. γ. The selection model shows for the ‘Group II’ a mean threshold of D = 0.8 mm. In contrast to the full probabilistic model, the selection model approached successfully to a mean threshold temperature, which is consistent with the previous studies.We applied the ‘Selection models’ on the 24 neurons. To demonstrate the performance of the selection models, we chose the model MfullL  was larger for the ‘Group I’ for which the classical model had been successful than it was for the ‘Group II’ for which the classical model had failed to find a consistent parameter estimate. Put another way, this indicates that for many neurons in ‘Group II’, one of the selection models provided a better description than the full model. As the selection models accounted for outliers, while the full model did not, we conclude that statistical outliers might have contributed to the failure of the classical method on the neurons in ‘Group II’.We supposed that the main reason why the classical model failed was its inability to account for neural noise and for statistical outliers in the responses. Thus, one might expect that a working stimulus selection model would mainly detect outliers, and thus exclude the response to one stimulus from the parameter determination for those neurons for which the classical model failed. To test this idea, we normalized the sum of the marginal likelihoods for each neuron across all candidate models to 1. We then plotted the normalized marginal likelihood for the full model that does not exclude any stimuli see . ClearlyThus, the results from our method suggested that for ‘Group II’, selection models that accounted for statistical outliers were more successful at describing the data, suggesting that outliers had indeed contributed to the failures of the classical method in these neurons.in vitro context where skin is absentin vivo.In this study we have shown that considering variability, noise and stochastic processes in study of primary afferent pain receptors improved the classical deterministic models to estimate the depth and threshold of C-fiber nociceptors. We have shown that allowing for a small delay in the first response of C-MH nociceptors modified the localization of the receptor neurons. Moreover, assuming some stochastic activities which were not triggered by stimulus and discarding the outlier responses caused by these stochastic activities further improved the estimation of activation threshold of C-MH neurons. We demonstrated the reliability of our general framework on a challenging data set, in which the stimulus electrode was placed on the corium and dermal side of the skin, the thickness of measured skin was unknown and each stimulus condition was applied only once. Our approach provides a unique insight into how temperature impinges on heat transducers in their native, complex environment. Most studies have hitherto focused on activation of channels by membrane heating in an Introducing delay in response time allows us to weaken the assumption that latency and the threshold time should be the same. However, a delay is justified only if the probabilistic model converges to the classical model in boundary condition. Because in classical model all delays are neglected it describes an ideal, noise-free case and thus represents the boundary condition for the probabilistic model when delays are zero. Hence in the boundary condition the classically estimated model parameters should maximize the log likelihood function of delays. Our results confirmed that for negligibly small delays, the probabilistically estimated parameters converge towards the classically estimated results. Hence, the probabilistic model improves the results in cases where the classical model failed and converges to the classical model in boundary condition.An alternative way to account for noise in the system might be to add white noise into equation a priori density function. For some parameters, there were multiple possibilities for choosing the prior density. This could have influenced our computation of model evidenceIn fact, while the probabilistic model improved the estimation of depth, it did not improve the estimate of the mean threshold temperature. The low average threshold temperature around the baseline temperature for some results estimated by probabilistic model suggests that for some responses, a small delay in threshold time might not be sufficient to deal with the noise. Indeed, the estimation of depth and threshold temperature was improved by discarding these outlier responses in the ‘Selection models’. In addition, the marginal likelihood ratios suggested that the ‘Selection models’ described the observed latency better than the initial probabilistic model that used all stimuli to estimate the neuron’s parameters. Using marginal likelihoods also offered a way of adding prior information about model parameters from the literature by choosing an Localization of sensory endings is particularly interesting for quantitative models that describe the responses of a neuron to stimulation and for attempts to uncover the neurons encoding strategy. For instance, in mathematical modeling of touch sensitive A-fibers several investigators have used the histologically measured depth to model the somatosensory responses4546Experiments were performed in strict accordance with the recommendations in the Guide for the Care and Use of Laboratory Animals of the Max Delbrück Centre for Molecular Medicine. The protocol was approved by the Committee on the Ethics of Animal Experiments of Animal Welfare German authorities .2 inhalation for 2–4 min followed by cervical dislocation. The saphenous nerve and the shaved skin of the hind limb of the mouse were dissected free and placed in an organ bath at 32 °C. The chamber was perfused with a synthetic interstitial fluid (SIF buffer) the composition of which was (in mM): NaCl, 123; KCl, 3.5; MgSO4, 0.7; NaH2PO4, 1.7; CaCl2, 2.0; sodium gluconate, 9.5; glucose, 5.5; sucrose, 7.5; and HEPES, 10 at a pH of 7.4. The skin was placed with the corium side up in the organ bath. The saphenous nerve was placed in an adjacent chamber on a mirror to aid and under microscopy fine filaments were teased from the nerve and placed on the recording electrode. Electrical isolation was achieved with mineral oil.The skin-nerve preparation was used to record from single primary afferents484950Single mechanically sensitive units were characterized by probing the skin with a glass rod for mechanically responsive receptive fields. For heat stimulation, a Peltier element–based contact probe (4 × 3 mm surface) applied thermal stimuli  to the receptive field of identified C fibers.The stimulation protocol sent as a pre-programmed series of commands to the Peltier element were applied to all C-fibers. The thermal stimulation protocol consisted of 3 stimuli (32–48 °C) with different ramp durations  and the hold phase of 10 seconds. The interstimulation interval was 60 seconds. The order of stimulation was first heat and then mechanical from the slowest to fastest ramps. After the thermal stimulation we carried out a mechanical stimulation protocol, the results of which are not part of this manuscript. Data were obtained from 11 C57Bl6/N wildtype mice.Heat energy flows through the skin to the nociceptive terminals due to the temperature gradients. According to the second law of thermodynamics, heat flows from warmer location to colder location. With no heat source, these thermodynamical effects will let the skin relax to one homogeneous temperature. In an experimental set using a Peltier device, the stimulus acts as a heat source, inducing heat at one location which then flows through the skin and eventually results in a temperature increase at the receptor site of neuron. Because the stimulus temperature varies over time, the resulting heat flow will vary over time as well. In addition, it varies in space because skin is not an ideal conductor and locations further from the stimulus receive lower heat energy and at a later time. Directly measuring the exact temperature profile in the skin at the depth of nociceptor is difficult. Therefore, heat transfer in the skin is typically modeled using thermodynamical laws32Here, When solving equation 303031Several investigators measured the epidermal and dermal thickness and their thermal properties. In γ would compose of epidermis and dermis layersIf the estimated De is the depth of the epidermis, and Dd is the depth of dermis. To estimate D in equation Deand thermal diffusivities and solve the equation for Dd.Where, 8 and in the end averaged over the computed D.In our data set, however, the heat electrode was placed on the dermal and subcutaneous site of the skin and the thickness of the skin wasn’t measured. This experimental redundancy prevented using a direct multilayer model of the skin. Therefore we reduced a two layer model with separate layers for epidermis, and dermis to a one layer model, which accords properties of both epidermis and dermis. Next step is to set the skin of a one layer model. To this end, we took the maximum and minimum reported values of thermal conductivity, density, and specific heat of epidermis and dermis from literature see . We thena priori density function of the depth and all parameters of the thermal diffusivity. According to histological studies most C-MH fibers end in the epidermal to dermal layers of the skinIn order to express the prior assumptions about the value of i-th draw from sampling population).To define an explicit density function γ from these assumptions. Therefore, we approximated the distribution of the sampled γ by a mixture of 3 Gaussian distributions with unknown parameters (estimated using expectation-maximization (EM) algorithm for fitting mixture-of-Gaussian models implemented in scikit-learn, the number of components was determined by minimizing Bayesian Information Criterion (BIC).).We chose uniform distribution U  for the thermal diffusivity parameters. To this end 2. In order to create a meaningful marginal likelihood, the prior should be a proper probability density functionA more complicated case is the prior In k,Typical strategies to estimate the marginal likelihood (4) are sampling (i.e. Monte-Carlo integration) or analytical approximations like the Laplace approximation, Variational Inference, or Expectation Propagation. For low dimensional parameter spaces (2-4 dimensions), numerical integration may work as well. In equation 1: 2: 2, however, we assumed the outlier first spike has a fixed value, so that we can formally write the likelihood for the outlier components as a dirac function 2 were treated in the same way as in M1.and used numerical integration according to trapezoidal rule to compute the expected value. The prior densities are for model M2, we estimated the ratio of the marginal likelihood for the full model M1 over the marginal likelihood for the model M2 without the excluded stimuli.For every potentially excluded stimulus in selection model MHow to cite this article: Dezhdar, T. et al. A Probabilistic Model for Estimating the Depth and Threshold Temperature of C-fiber Nociceptors. Sci. Rep.5, 17670; doi: 10.1038/srep17670 (2015).


Personalised treatment of heart disease requires an understanding of the patient-specific characteristics, which can vary over time. A newly developed implantable surface acoustic wave pressure sensor, capable of continuous monitoring of the left ventricle filling pressure, is a novel device for personalised management of patients with heart disease. However, a one-size-fits-all approach to device sizing will affect its positioning within the pulmonary artery and its relationship to the interrogating device on the chest wall on a patient-specific level. In this paper, we analyse the spatial orientation and morphology of the pulmonary artery and its main branches in patients who could benefit from the device and normal controls. The results could optimise the design of the sensor, its stent, and importantly its placement, ensuring long-term monitoring in patient groups. Heart failure is one of the leading causes of morbidity and mortality worldwide –4. The dSeveral implantable devices have been developed to monitor LV filling pressures noninvasively, either indirectly or directly –13. The The only device which can provide continuous monitoring of the filling pressure at rest and during exercise is the implantable surface acoustic wave pressure sensor (SAWPS)  currentlThe goal of this study is to analyse spatial orientation and morphology across different patient populations. While studies on the measurements of the PA diameter at the level of the bifurcation have been performed , the exaThe surface acoustic wave pressure sensor (SAWPS) is a novel wireless transponder used in conjunction with a miniature communication system for continuous evaluation of PA pressure in patients with severe heart failure and those with pulmonary hypertension. It allows for accurate measurements to be taken on a continuous basis, and then transmitted remotely, allowing for blood pressure to be continuously monitored throughout waking and sleeping activities . The impPrevious studies by Murphy et al. , 18 were2 for NYHA Class II patients, 51 ± 8/1.86 ± 0.20 m2 for NYHA Class III, 62 ± 10/2.07 ± 0.25 m2 for NYHA Class IV and 30 ± 5/1.84 ± 0.37 m2 for PH and 32 ± 3/1.92 ± 0.05 m2 for normal subjects.The study includes normal subjects and a representative sample of the patients who could potentially benefit from the SAWPS device Table . 15 hearFor each patient, images of the PA and chest wall structure were acquired. Selected heart failure and pulmonary hypertension patients had archived computed tomography (CT) images, scanned using a dual-source 128-slice FLASH Siemens CT scanner. The acquisition for heart failure patients followed a breath-hold, cardiac-gated scanning protocol with a slice thickness of 0.6 mm. Pulmonary hypertension patients had breath-hold, non-gated CT scans with a slice thickness of 1 mm. For the controls, gated scans were used.All subjects’ data utilised in this study were based on data previously acquired for clinical purposes after approval from the Ethics Committee.To determine the range of PA sizes and orientations the SAWPS device must accommodate, 3D analysis of the PA was performed to extract the necessary parameters to ensure that the final device(s) will fit in the majority of patients. The workflow is shown in Fig. The DICOM images were imported into Mimics  for segmentation of the PA (including left and right pulmonary arteries) and the chest wall. The models of the structures were then exported as triangular meshes in STL format. In addition, the centrelines of the PA models were automatically produced by Mimics and exported. The STL models were imported into MeshLab  to removThe proximal section of the PA was divided into two main segments. The first was the main pulmonary artery (MPA) leading to the left pulmonary artery (LPA), as shown in Table Pi is the ith point in the centreline, was used as the normal to the ith orthogonal cutting plane. There was one orthogonal cutting plane for each point in the centrelines.To attempt to normalise PA centreline lengths, the centreline for each MPA-LPA structure was linearly interpolated and the MPA and LPA were sampled to 50 points each, both separated by the bifurcation that leads to the RPA. Likewise, the centreline for each RPA structure was linearly interpolated and sampled to 40 points, with the number of points chosen empirically. These points were ordered and the lengths along the PA segments  for the ages of the different patient cohorts. Height and weight of patients from the groups were not statistically significant (p > 0.1).Statistical analysis of the basic data of the study population Table  showed sp = 0.02). However, when examining the entire length of the MPA through to the LPA .In Fig. LPA Fig. , this enp > 0.05).Figure 2/m) while the bottom row shows the average diameters of the same contours. The general trend over the average is greater cross sectional area and diameters for the PH group and lower parameters for the Controls. The average diameter from the MPA to the LPA, i.e. after the bifurcation, lowers by approximately 6 mm, indicating that the stent, if it is to straddle the bifurcation, needs to be flexible enough to adapt to the two diameters.Figure p < 0.05). No statistical significance was found at the start of the LPA across the patient groups. These measurements will affect the diameter required of the stent.From Table p > 0.05).Figure Regarding the orientation of the PA segments with respect to each other, the angles between the RPA and LPA did not change much across the patient groups Fig. . The aveIt is proposed that at least two separate stent sizes will be required to take into consideration the measurements found in this study. In particular, the length of the stent is recommended to be 45 mm for the NYHA Class 4 patients while 40 mm is sufficient for the HF patients. This is shown in Fig. The data presented in this paper was analysed to optimise the design of the SAWPS Device and could be used to select a range of different stent sizes to fit patient groups with similar PA morphology and spatial orientation. It will also guide clinicians to determine the most suitable position of the device within the PA and its branches.The SAWPS device is a permanent implant and therefore consideration of the progression of the morphology of the PA is essential. The first design decision was that the whole device should rest against the PA wall and become endothelialised to reduce the risk of thromboembolism. An alternative approach has been taken by CardioMems  where a The longitudinal aspect and low profile of the device are well suited to lying against the inner wall of a tube. The antenna is flexible and will naturally rest against the wall if the vessel has a concave longitudinal surface, which is the case on the anterior surface of the MPA. The distal part of the antenna will be further held against the wall by the flowing blood; the proximal part needs to be held against the wall during endothelialisation to avoid generating vortices in the blood flow and the risk of emboli.The stent can extend into the LPA or RPA—but given the significant discrepancy in size between the main PA and its branches it must be designed with different segmental radial sizes and strengths. The sharp angulation of the RPA means that the LPA is an easier choice for placement of the distal part of the device. The anterior wall from the MPA into the LPA is essentially a single concave surface. Extension across the bifurcation is permissible if the stent struts are spaced widely enough (open-cell design) to allow for unobstructed flow into the partially jailed right branch, as shown in Fig. Given the importance of placing the antenna as close as possible to the chest wall to enhance signal transmission, the antenna should be radiopaque to allow for optimal positioning and orientation within the pulmonary artery during implantation. For better wave propagation and RF signal noise reduction, positioning the device in the MPA segment is preferable. This is due to the fact that the MPA is the nearest segment to the sternum and chest wall and is not covered by other anatomical structures . With optimal placement of the implant, there will be much greater tolerance on the optimal location of the ID antenna on the chest wall and more freedom to make an ergonomically-driven decision on placing the external antenna—for instance, within clothing.At a recent initial preclinical test, an implantable SAWPS was delivered by an 18 F catheter into the main PA of a 75-kg swine via the femoral vein. The position and orientation of the device were adjusted using fluoroscopy and transoesophageal echocardiography before final deployment. The implanted sensor was interrogated and the signal quality was evaluated. The transmitting power and the received signal quality confirmed the previously measured performance of the implantable antenna with respect to the main PA orientation. The sensor orientation was observed to be parallel to the chest wall and the implantation depth was measured at 5 cm using the acquired images. The implanted sensor was interrogated for 30 min and the received signal was monitored in real time. The received signal quality was consistently good for about 25 min but started to deteriorate afterwards before the signal was completely lost at 30 min. The autopsy confirmed that migration of the implant into the LPA was the cause of signal loss. The migration occurred because the stent was undersized; the signal loss was due to the non-ideal orientation and depth of the LPA with respect to the chest wall in swine.Analysis has been performed on PA orientation and morphology from four patient groups and a control group and results show variance in PA segment lengths that will affect device placement. Initial preclinical tests confirmed the need for correct sizing and positioning of the device to ensure good received signal quality. These measurements will aid in stent design for future iterations of the SAWPS device and will ensure better management of patients with heart disease.


A domain decomposition technique is proposed which is capable of properly connecting arbitrary non-conforming interfaces. The strategy essentially consists in considering a fictitious zero-width interface between the non-matching meshes which is discretized using a Delaunay triangulation. Continuity is satisfied across domains through normal and tangential stresses provided by the discretized interface and inserted in the formulation in the form of Lagrange multipliers. The final structure of the global system of equations resembles the dual assembly of substructures where the Lagrange multipliers are employed to nullify the gap between domains. A new approach to handle floating subdomains is outlined which can be implemented without significantly altering the structure of standard industrial finite element codes. The effectiveness of the developed algorithm is demonstrated through a patch test example and a number of tests that highlight the accuracy of the methodology and independence of the results with respect to the framework parameters. Considering its high degree of flexibility and non-intrusive character, the proposed domain decomposition framework is regarded as an attractive alternative to other established techniques such as the mortar approach. Modern engineering applications require sophisticated simulation techniques which deal with increasing complexity and refinement of the computational models. Consequently, detailed finite element discretizations are commonly used in nowadays structural analysis and a number of practical situations are emerging in which special techniques are indispensable to handle non-matching discretizations. In this introduction we focus on engineering applications and computational techniques concerning the assembly and resolution of models involving non-overlapping meshes.Typical scenarios arise when independent mesh discretizations are applied to different parts of a structure and when large models are divided and distributed among different working teams. A common situation is encountered when particular structural components are reused in evolving designs such as the wings among diverse aircraft models with changing fuselages. The meshes of the structural components are most likely non-matching and need to be assembled along common edges using special techniques that account for the non-conforming interfaces , 35.The field of contact mechanics  has signAn emerging set of techniques intimately related with computational material design are the so-called multiscale and multiresolution methods , 17, 27.Most of the above mentioned applications involve complex models which upon discretization, e.g. using finite elements, lead to large systems of equations. It is then not surprising that most of the existing methodologies to connect different meshes are frequently encountered in domain decomposition techniques . These tIn most of the domain decomposition applications the geometrical compatibility of the interface g meshes  meaning mentclass2pt{minimg meshes , 51. DomStrong coupling constraints refer essentially to collocation techniques where one constraint is assigned to each degree of freedom (DOF) while weak coupling techniques refer to constraints enforced in an integral or average sense along portions of the interface surface assigning one constraint per group of DOFs belonging to the interface portion. In the contact domain literature these techniques are often referred to as node-to-segment techniques and segment-to-segment techniques, respectively.h or p refinement of the coarse mesh at the interface for the strong coupling case. For this reason, weak coupling techniques are preferred in the context of a general non-conforming interface since they relax the constraint such that stiffening and locking effects do not occur. Mortar methods and their formulation in terms of finite elements constitute the most general technique for non-conforming interfaces in which geometrical incompatibilities can be handled [Generally, a reference displacement field entclass1pt{minima handled . The mosinf-sup condition) [The enforcement of constraints at a non-conforming interface is typically done with the introduction of Lagrange multipliers . Basicalndition)  in orderndition)  for an ondition)  which candition) . In ordendition) . Althougndition) , 38 and a priori satisfy the constant stress patch condition. The technique can be viewed as a general and optimal node-to-segment approach applied to the connection frame but still arbitrary highly irregular grids and geometrically incompatible interfaces are not addressed.Domain decomposition frameworks typically found in literature that account for non-conforming interfaces are based on the introduction of Lagrange multipliers to weakly enforce the compatibility constraints. This is the case for the mortar approach  which isIn contrast with the above mentioned techniques we propose a general and flexible methodology to account for the most complex interface situations, i.e. geometrically incompatible and arbitrary non-conforming. The main idea in the domain interface method (DIM) is to explicitly discretize the interface through a Delaunay triangulation. In all previously introduced techniques one slave node or segment belonging to a domain interface was somehow projected on the other domain interface or on an auxiliary one. Therefore, the interface constraints were formulated in a domain which is one dimension lower than the subdivided domains. In the DIM, the interface constraints are formulated on an intermediate interface of the same dimension as the adjacent decomposed domains cf. Fig. . ConsequIn this section the necessary geometrical aspects of the methodology are introduced and strong and weak forms of the problem are outlined. The solvability of the resulting system is discussed in terms of its stabilization and possible resolution choices including a parallel scheme. The main idea behind the DIM method concerns an explicit meshing of the interface between domains and is inspired in the methodology introduced in , 38 for s and q. Discretizations of the two bodies, e.g. using finite elements (FE), leads to a number of Consider the structure assembly depicted in Fig. k. The result will be independent on the chosen magnitude k but in our analyses The interface generation cf. Fig.  starts wD using triangular linear elements Note that, upon discretization of the domain interface r method , where oD at time n.Consider the assembly of two non-overlapping domains cf. Fig.  undergoiIt is important to note that fined in .As depicted in Fig. n for a given point p) and not only defined at the interface nodes as other methodologies would consider. For future use into the variational statement it is convenient to express the gap in terms of the displacement field and, to this end, a Taylor series expansion of The initial normal gap cf. Fig.  is definduced in , 38 is nThe expressions of the gap match the ones obtained in node-to-segment techniques  when \dor et al. , the expIn order to formulate the variational principle in Sect. It is important to note that the gap intensity results singular when a perfect connection is fulfilled at the previous configuration, i.e. entclass1pt{miniman and the normal vector Inserting  in  16)16) the fcf. Fig. . Displaccf. Fig. .Fig. 5LaFor the case of tied contact within the present domain decompositon framework there is no need for a splitting between normal and tangential contributions. However, this splitting is introduced for the sake of completeness presenting a methodology that serves as a basis to tackle, if needed, more complex phenomena in which a different treatment can be considered for the tangential and normal interface components. Such scenarios may involve, for instance, sliding between domains. Additionally, the imposition of particular boundary conditions utilizing the Lagrange multiplier framework can be considered as well in which the tangential component is treated differently due to friction or sliding. Specific cases involving fluid structure interaction could in this manner be treated as well. The case of normal tying along an interface segment between fully tied limit corners has been studied already within a multiscale Domain Decomposition framework  to avoidn, The strong form of the equilibrium problem at domain Note that the compatibility constraints are enforced to nullify the normal cated in . The gaprding to . In addiThe weak form of the problem stated in –28 is exloped in , 38 the Finally, the variational statements of the constraint equationsThe equilibrium equation in  and impoa denotes the discrete nodes corresponding to the displacement interpolation. In a similar fashion, the displacements D are discretized as:b stands for the the discrete nodes corresponding to the Lagrange multipliers interpolation using the shape functions Consider a Galerkin-based discretization in which the displacement solution field and its variations are interpolated using the shape functions It should be noted that a piece-wise constant interpolation of the Lagrange multipliers might not lead to optimal spatial convergence rates. We have not observed any critical convergence behaviour in any of our simulations. However, it is observed in our analyses that the theoretical convergence rates might not be fully recovered due to use of piece-wise constant Lagrange multipliers. A more theoretical and practical study regarding convergence rates with respect to the choice of the Lagrange multiplier space is out of the scope of this work and could be considered as a future research topic for a more mathematically oriented contribution.The FE approximation of the virtual work expression in  can be wFollowing an analogous procedure for the variational expression of the interface constraints , 3555\doL stands for the base-side length of the interface domain element in the previous configuration   \documen methods , 45, thes method . The rigThe mechanical work developed by the domain boundary forces tituting  in the stituting 85\documeThe local problems in  are solvmentclasspt{minimator   91) is gcf. Fig. . In ordeTo this end, we consider the stabilization expressions , 64. Theual Eqs. , 68 can tituting , 98 we ocf. Fig.  correspowidth in  is kept width in –80.Equations , 114 areelations , 114 canIn all our computations we considered all interface patches ected in  and, theThe linearized set of equations in  obtainedmentclasspt{minimaent}Ω(s) .Assuming a fix domain decomposition and a given Delaunay interface discretization, the iterative scheme for the non-linear DIM framework is summarized in Box 1.In the following we present a number of academic examples which highlight the accuracy and convergence properties of the framework. Attention is focused on the continuity of the solution at the interface, the convergence rate upon mesh refinement and a qualitative comparison of the advantages and eventual pitfalls against existing formulations. Infinitesimal strain theory is utilized in all examples except from the one reported in Sect. cf. Eqs. –68 is seThe so-called ‘patch test’ is specially selected to verify the correct transference of information throughout the interface. A compression analysis is performed on a two-dimensional homogeneous quadrilateral specimen. Plane strain conditions are assumed and a linear elastic constitutive law is considered with Young’s modulus The quadrilateral specimen is submitted to an homogeneous strain state whereDisplacement contours for both discretizations are shown in Fig. Since the maximum relative error is order c used to overcome the appearance of RBMs  is monitored and compared to the one obtained with a reference monolithic approach considering a similar spatial discretization. As it can be observed in the contour plots in Fig. The kernel of the proposed DIM to be used in domain decomposition methods and presented in this contribution resides in an explicit discretization of the interface by means of a zero-thickness Delaunay triangulation. This is accomplished through a fictitious contraction of the subdomains at the interface which allows for a proper discretization between the shrunk domain boundaries. The fictitious contraction has no impact on the solution of the problem since all calculations are performed using the original coordinates. Moreover, it is shown that the integrals over the zero-thickness interface are bounded despite the fact that the integrand is not bounded. The method is grounded in the so called Nitsche methods in which a stabilization term is added at the constraint equations. In this manner, zero diagonal terms are not present at the global system and instabilities are avoided if the LBB condition is not fulfilled by the chosen discretization. This process is viewed as a consistent penalty method since the stabilization term vanishes with progressive mesh refinement and the penalty factor can be made significantly small without affecting the results.The methodology is inherited from the field of contact mechanics and, for this reason, is regarded as more general than existing domain decomposition strategies since there is no need for a fixed interface geometry that needs to be shared by the decomposed domains at both sides of the interface. This is for instance the case of some dual domain decomposition techniques in which the limit DOFs at the interface need to be common in both adjacent domain discretizations. Moreover, the generation of interface patches is independent of the choice of slave and master sides in contrast with early mortar methods and, for this reason, the methodology is regarded less prone to errors related with such choice. More evolved mortar methodologies are able to automatically handle these situations by considering, for instance, an extra interface surface from which a particular distribution of DOFs serves to construct an optimal set of interface constraints between adjacent meshes. However, such an intermediate surface involves calculations over extra DOFs which could increase the computational cost and complexity of the approach.A new non-intrusive strategy to handle floating domains is outlined which adds an extra stabilization term to the energy functional with contributions of all adjacent interface patches. This avoids the calculation of a pseudo-inverse at floating domains and does not destroy the band structure of the global system. For this reason, it does not spoil a possible parallel solution as done with existing dual domain decomposition methods.The DIM method passes the patch test also for the case of floating subdomains providing continuity of the stress field across the interface which indicates that all new ingredients do not affect the accuracy of the solution when compared to other established techniques. Remarkable continuity of the displacement field across the interface is shown in all reported experiments. A comparable accuracy degree has been observed with independence of the shape of the interfaces. In addition, good convergence rates are reached upon mesh refinement similar to other accurate techniques for non-conforming interfaces although theoretical convergence rates could not be obtained exactly due to the piece-wise constant interpolation of the Lagrange multipliers.The algorithmic treatment of the subdomains allows for a parallel solution scheme analogous to well established techniques such as dual domain decomposition techniques. In this manner the local factorizations can be tackled by direct solvers and the resulting interface problem can be assembled in a matrix-free fashion and solved with the use of iterative solvers. A full parallel version of the framework involves the construction of adequate preconditioners for the interface problem which was out of the scope of this contribution and it is left as a future research line. In the same spirit, a 3D extension of the method is left as a topic for further research. Preliminary 3D works have been successfully performed for the contact domain case  and it iThe framework presented in this contribution provides the basis to study complex deformation phenomena involving large strains, e.g. bulk metal forming, and shows a clear potential to tackle multifield applications, e.g. mixed formulations for incompressible and thermo-mechanical problems. In this view, the field of Lagrange Multipliers needs to be extended in order to account for the temperature and pressure fields and it is planned for a future contribution.The explicit Delaunay triangulation of the interface is expected to positively impact the field of multiresolution problems and adaptive multiresolution analysis. Since arbitrary discretizations can be handled at non-conforming interfaces, adaptive multiresolution analyses can be performed employing an independent ‘on-the-fly’ refinement at particular domains of interest without meshing restrictions. In the same spirit, existing independent discretizations of particular domains can be easily reused and incorporated to the calculations.Due to its versatility and generality the DIM method is viewed as an attractive alternative to mortar methods and other established dual domain decomposition methods in which the interface geometry and its limits are restricted to the boundary discretization of the connected domains.


The aim of this study was to explore the influence of the characteristics of Japanese patients on the long-term outcomes after aortic valve replacement with either mechanical or biological prostheses by means of a microsimulation.A microsimulation model was used to simulate the lives of patients living in Japan and in the United States after aortic valve replacement. The background mortality data taken from the 21st complete life table of Japan and the bleeding hazard determined from a meta-analysis of long-term results in Japanese institutions were used to simulate Japanese patients. The life expectancy, event-free life expectancy, and lifetime risk of structural valve degeneration were calculated. A sensitivity analysis for various bleeding hazards was performed.Regarding the event-free life expectancy, the age crossover points between the two valve types were 64–65 and 57–58 years for Japanese and American patients, respectively. Regarding the life expectancy, the age crossover points were 88–89 and 64–65 years, respectively, for Japanese and American patients. The lifetime risk of structural valve degeneration was higher in Japanese patients than in American patients. The sensitivity analysis showed that the age crossover points were sensitive to the hazard of bleeding complications.The long-term clinical outcomes after aortic valve replacement were simulated with a microsimulation model. The results indicated that the age crossover points in the advantages and disadvantages between mechanical valves and bioprostheses may be higher in Japanese patients than in American subjects. The decision regarding whether to choose a mechanical or biological prosthesis to replace diseased aortic valves is a complex problem. It generally can be considered as the tradeoff between the risk of reoperation for a bioprosthesis due to structural valve degeneration (SVD) and the risk of bleeding complications associated with long-term anticoagulation for mechanical prostheses . We usuaThe Japanese Circulation Society Guidelines for Surgical and Interventional Treatment of Valvular Heart Disease recommend the use of a bioprosthesis for patients older than 65 years old for the aortic position . HoweverWe also found in our previous study that the incidence of bleeding complications associated with mechanical valves was considerably lower in Japan than in other countries by performing a comprehensive systematic review . Since tThe aim of this study was to explore the influence of these variables on the long-term results of patients who undergo aortic valve replacement by either mechanical or biological prostheses by performing a microsimulation.A microsimulation model is a kind of Monte Carlo simulation which simulates a representative population at the individual patient level . This caA microsimulation model was used to simulate the lives of patients living in Japan and in the United States after AVR. We used a previously described microsimulation model by Rotterdam group . This miIn brief, after aortic valve replacement, a patient either dies as a result of the procedure or survives. If the patient survives, then they remain at risk of developing valve-related events for the rest of their life. The hazard estimates for all valve-related events in the original model have been explained in detail elsewhere , 9, 11. The EFLE, LE and lifetime risk of SVD for patients in Japan and the United States for various ages were calculated in this study. In this study, we changed several variables from the original model to simulate contemporary Japanese and American patients, as described below.For residents in the United States, we calculated the background mortality, which is the mortality experienced by the normal population, using American life tables derived from the Vital Statistics of the United States in 2009 reported by the Centers for Disease Control and Prevention to update the data . The staIn the original model, the bleeding hazard increased with age, and was given by a Gompertz function, where lambda was −8.71. Based on this assumption, the bleeding hazard in the original model was 0.23 % per patient-year in patients aged 35 years, 1.58 % per patient-year in patients aged 60 years and 4.9 % per patient-year in patients aged 75 years [For the Japanese population, we changed two probability distributions from the original model. These were the background mortality and bleeding hazard. In the present analysis we used the background mortality for Japanese patients from the 21st life table made by the Ministry of Health, Labor and Welfare of Japan based on the census conducted in 2011 .We obtained the bleeding hazard of mechanical valves for Japanese patients based on our previous meta-analysis. In this meta-analysis, we included studies that reported the long-term results of valve replacement with bileaflet mechanical valves reported from institutions located in Japan between 1988 and 2010 . In thatFor the bleeding hazard in Japanese patients, we used the same Gompertz function as was used for the US population, but at a lower bleeding rate, and we substituted −9.40 for lambda. The bleeding hazard was 0.54 % per patient-year in patients aged 55 years, 0.79 % per patient-year in patients aged 60 years, 2.5 % per patient-year in patients aged 75 years and 3.6 % in patients aged 80 years based on this assumption. These numbers are compatible with the results of another meta-analysis of the results of mechanical valves in the elderly population .We explored three level of hazard for bleeding events with mechanical valves as a sensitivity analysis. These were using lambda values of −9.40, −8.99 and −8.71 in the Gompertz function. The values of −9.40 and −8.71 have been already explained above. The value of −8.99 was assigned as the number in the middle of these two numbers. We performed this analysis because it is theoretically possible that the bleeding hazard derived from our meta-analysis might be somewhat lower than the true hazard because of the nature of the retrospective studies that had been included in the meta-analysis.The microsimulation model calculates the EFLE and LE following aortic valve replacement with mechanical valves and bioprostheses for patients of either sex and of different ages. The EFLE in Japanese and US females is shown in Fig. Regarding the EFLE, for a 70-year-old Japanese female, for example, the average EFLE was 9.64 and 10.30 years, respectively, after implantation with a mechanical valve and a bioprosthesis, whereas these were 7.06 and 8.69 years for an American female (Fig. The age crossover points between the two valve types were 65 and 58 years, respectively, for Japanese and American females Fig. . SimilarRegarding the LE, for a 70-year-old Japanese female as an example, the average LEs were 12.47 and 12.04 years, respectively, after implantation with a mechanical valve and a bioprosthesis, whereas the average LEs were 9.59 and 9.87 years, respectively, for an American female (Fig. The lifetime risks of structural valve degeneration are depicted in Fig. The results of the sensitivity analysis for the three bleeding hazards on the EFLE in Japanese females are shown in Fig. The aim of this study was to explore the effects of the characteristics of Japanese patients on the clinical outcomes after aortic valve replacement with the aid of a microsimulation.A microsimulation is a useful tool, especially when evidence is scarce and the decision to be made is complex . This isIn this study, the microsimulation model predicted the age crossover point between the valve types in Japan to be 64–65 years with regard to the EFLE and 88–89 years for the LE. These age crossover points were significantly older compared to the results of the simulations calculated for patients in the United States. The age crossover points were 58–57 years for the EFLE and 65–66 years for the LE for the patients in the United States. These results suggest that the appropriate age to recommend implantation of a bioprosthetic valve may be older in Japan compared to the United States.As far as the EFLE is considered, the age crossover point was 65–66 years old. This is the age that the current Japanese guidelines recommend, and the recommendation is compatible with our results. However, the age crossover points were much higher when the LE was considered. Several researchers have expressed their opinion that the age recommendation for the use of a bioprosthesis should be raised from 65 years for Japanese patients based on their follow-up data . Our resIn this study, we explored the effect of two different probabilities. One was the background mortality in Japanese populations. Japan has been known to have long life expectancies, even among developed countries . The othRegarding the background mortality, there is little doubt about the accuracy of numbers, because these data were extracted from reliable official government sources from Japan and the United States. However, the difference in this study may be a little exaggerated as an example of the differences among Japan, North America and Europe. First, the United States has a relatively short life expectancy among developed countries, being ranked 31st in the world . Many reWe found an incidence of 0.41 %/patient/year of bleeding complications in our previous meta-analysis  and usedTranscatheter aortic valve implantation has been introduced in clinical practice. This undoubtedly is a significantly different way of treating aortic valve disease compared to surgical aortic valve replacement, and may have a significant impact on the decision-making with regard to the choice of prosthetic valve. Although we were aware of this, we did not take this treatment modality into account in the current study. We believe this procedure is still immature, and it is not yet possible to estimate the accurate hazard of prosthesis-related complications and the procedure-related mortality and morbidity for a wide range of patient ages.This study is associated with several other potential limitations that we would like to clearly state. First, we used the data from Japan for two variables. The other variables were taken from the original model, and are from a meta-analysis of papers written in English, which likely means that most of the data were from North America and Europe. It is natural to think that variables other than the two selected variables may also be somewhat different from the numbers in contemporary Japanese practice, although we did not see large differences in the incidence of other valve-related complications in our meta-analysis. We are planning to make our own original model and to update all of the variables based on a large dataset from Japanese subjects. In the meantime, the results of this study should be informative as they provide the results of a sensitivity analysis of an established model to better understand the relationships between the characteristics of Japanese patients and the balance of advantages and disadvantages for the different valve types.Second, although this model took into account all of the valve-related complications and their sequences, a microsimulation still is a simplified model of the real world, and has its own methodological limitations, as described elsewhere .The long-term clinical outcomes of Japanese subjects implanted with mechanical valves and bioprostheses were simulated using an established microsimulation model with variables changed to reflect the current status in Japan. The results showed that the age crossover points of the LE and EFLE were higher than those calculated for the US general population.


A numerical study on the response of steel beams to fire and explosion is presented in this paper. First, a unified computing model, which can be used to simulate the behaviour of beams under four loading scenarios that involve fire and explosion or impact, is constructed. The proposed technique allows complete transparency of the influence of the various parameters on the structural behaviour. Second, the effects of load level on critical temperature are analyzed for various static and explosion load ratios. Two cases of explosion and fire loading sequences are compared, it is shown that the critical temperature of the beam subjected to fire followed by an explosion is lower than that of the beam subjected to an explosion followed by fire. The influence of temperature on the p–i diagram is investigated, an iso-damage surface is introduced to distinguish safe and unsafe regions. Third, the limiting temperature criteria are further examined. That is, the first and second limiting temperatures can be determined when the dimensional catenary force is equal to zero or to one, which corresponds to the bending or stretching plastic hinge, respectively. After the 9/11 attacks in 2001, the response and failure of structures under the combined loads of impact, explosion, and fire has become a major concern in building design  blast or impact load, (b) fire load, (c) blast or impact load followed by fire, and (d) blast or impact load during fire.The load and response process for scenario (a) is short (time is measured in ms). An effective explicit integration technique has been developed to simulate the behavior of structures in current finite element programs  is regarded as a static problem because a fire load is not short-lived (the unit of time is h). The experimental results have shown that the fire resistance of an isolated steel beam with simple supports at its ends differs from that of a beam restrained by surrounding structures. One of the main causes of this difference is the effects of catenary action. Current studies on beams under the effects of fire have also shifted toward this direction , the blast results in fire. The behavior of the structure under fire is near explosion, and the entire course—from blast to fire—can be regarded as a dynamic behavior because it has time and inertial effects. Related studies on this subject have been published  is more complex than that in scenario (c). In addition, coupling response occurs between thermal and impact effects if structural temperature changes during the course of the blast or impact load and the dynamic response phase. However, even if temperature does not change during the blast or impact response course, and the coupling behavior does not manifest, the dynamic response in the second phase will still be related to material degradation and expansion deformation caused by the elevated temperature during the first phase. Furthermore, although the dynamic properties of a material are also affected by current temperature, experimental data on the relationship between these two factors remain lacking and related literature is scarce. In addition to the study just completed recently   6) can bThe preceding motion equation can also be applied to the case of concentrated loads but only by using the Dirac function   12) compTo solve the proposed computing model, the following discrete equations, which are obtained by applying the central finite difference technique to the velocity and acceleration at each node, must be used:This computing model can be called the dynamic finite difference method (abbreviated as FD).Herein several numerical examples are presented. Based on the numerical results, several response features and the limiting temperature of the beam are analyzed, and the interaction effects of structural behavior under two types of loads are discussed.For example, the response of the steel beam with an H cross section shown in Fig. L = 1.14 mSpan of beam: H = 0.08 mHeight of cross section: B = 0.046 mWidth of flange: tf = 0.0052 mThickness of flange: tw = 0.0038 mThickness of web: Material constants of steel at normal temperature:3, Density and Thermal expansion coefficient: Young’s modulus, yield stress and Poisson ratio: D = 40.4 s−1, q = 5Strain rate constants: Geometric dimensions of the beam with an H cross section:P/Pc, in which Pc = 4MP/L, MP is the plastic limiting bend moment.The load ratio is defined by The deformation behavior of a beam under fire may be seriously affected by the restraining action of the surrounding structures because of thermal expansion. As a reduced beam model in practice, a hinged–hinged beam has been demonstrated to have the best fire-resistant capability  Eurocode . The criAccording to the aforementioned criteria for limiting temperature and critical temperature, the corresponding temperature against the load ratio can be presented, as shown in Fig. Based on the preceding numerical results, a suggestion for a fire-resistant design for a hinged–hinged steel beam can be provided. If a large deformation is permitted and the influence of the reaction force at the ends of the surrounding structures can be ignored, then the criterion that the maximum deflection is equal to span/10 [as indicated in Yin and Wang , this diand Luan .It should be stressed that some results obtained herein are quite already known in the fire community, this indicates that the minimum principle of acceleration can be used to effectively analysis the large deflection static behavior of structures subjected to fire loading. Compared with the method of Newton–Raphson commonly used in the response analysis of structures under fire, the proposed method is more straightforward and simple, and the iterative computation is not need.①P is applied at the mid-span, First, a transverse dead load ②t0 = 0.25 s, is applied at the mid-span. The Explosion Load Ratio (ELR in short) is Next, an explosion load, which is a rectangular pulse with intensity ③Fire is applied. Temperature is assumed to be distributed uniformly along each direction of the beam.The beam discussed earlier is then subjected to the following loads in succession.Undoubtedly, the response of the steel beam under these combined loads is complicated. At present, the influence of blast loads on failure limiting temperature is examined in particular.For the four cases of load ratio (To analyze variations in critical temperature, the L/20 and L/10 horizontal lines are also depicted in the figure. The maximum permanent deflections exceed the L/20 horizontal line for the two cases of ELR (The four curves on each figure tend to be superimposed as temperature increases, thus indicating that the influence of blast load has been exceeded by the serious deterioration of the strength and stiffness of the material caused by the elevated temperature. Thus, the deformation of the beam induced by the blast load no longer has a leading role. This effect is striking when the blast load is small, such as when ①P is applied at the mid-span, First, a transverse dead load ②Next, the fire load is applied until a given temperature is reached.③An explosion load with a rectangular pulse is then applied. ELR and duration are The hinged–hinged beam is subjected to the following loads in succession:D and q of the Cowper–Symonds equation are related to temperature. However, such test data are lacking. In a recent study on the behavior of a steel beam subjected to fire and subsequent impulsive loading (Xi et al. Obviously, the response of the steel beam under these combined loads is complicated, particularly because the blast or impact load is applied on the steel beam that is subjected to the fire load. The sensitivity of the strain rate of the materials is different from that when temperature is normal. Thus, both parameters For load case T < 400 °C. This phenomenon can be attributed to the increase in the axial thermal expansion deformation of the beam as temperature increases to 400 °C, thus indicating that the deformation mechanism is dominated by axial thermal expansion. When temperature exceeds 400 °C, the strength of the material starts to deteriorate and the deformation mechanism assumes a leading role in bending deflection. Then, deflection rapidly increases as temperature continues to rise. Obviously, the failure limiting temperature can be easily determined for such deformation mode.Based on the curves of the deflection–time history shown in Fig. Compared with the three curves that correspond to the case with no blast load, the three curves of For The L/20 and L/10 horizontal lines are also depicted in Fig. In Fig. To evaluate the effects of temperature on the pressure–impulse diagram, Fig. The criteria that can determine the limiting temperature of a large deflection steel beam under fire are further confirmed, i.e., the first and second limiting temperatures that correspond to the bending and stretching plastic hinges, respectively. Both temperatures can be obtained from the curve of the dimensionless axial force against temperature when the dimensionless catenary force is zero and one, respectively.The numerical results also show that the limiting temperatures determined by the first criterion are closer to the critical temperature determined by the L/20 line, whereas the limiting temperatures determined by the second criterion are slightly higher than the critical temperature determined by the L/10 line.For beams subjected to explosion followed by fire, the blast load affects the limiting and critical temperatures. The critical temperatures are related to ELRs, and the difference of both critical temperatures corresponding to two low ELRs is related to the static load ratio. Such difference increases as The influence of the blast load decreases as temperature rises, and the deformation induced by the blast loads no longer has a leading role. These effects are obvious in low ELRs, and the key factor that affects the critical temperature is static ratio.T < 400 °C. However, when temperature exceeds 400 °C, the influence of the reduction in material strength on permanent deflection is significant, and deflection rapidly increases as temperature rises. High temperatures also seriously influence the pressure–impulse diagram of a beam. An iso-damage surface on temperature, ELR and impulse space is introduced to distinguish safe and unsafe regions, which could be used in the structural design for the resistance of fire and blast loads.For beams subjected to fire followed by an explosion, the numerical results show that the influence of thermal expansion deformation and the reduction of stiffness caused by temperature change in the permanent deflection of the beam are minimal. Moreover, no serious deformation is observed within the scope of Two cases of explosion and fire loading sequences are compared. The displacement response and the critical temperatures are different for the two cases. The critical temperature of the beam that is subjected to fire followed by an explosion is lower than that of the beam that is subjected to an explosion followed by fire.Explosion limit load do not exist because the effects of strain and inertia when the material failed are not considered. The area of the safety zone in the pressure–impulse diagram decreases as temperature rises, whereas the influence of the static load ratio is insignificant.Based on the minimum principle of acceleration in the dynamics of elastic–plastic continua at finite deformation, an FD computing model to simulate the large deflection behavior of a steel beam that is subjected to the combined loads of static, fire, and explosion is presented. Response analysis for a hinged–hinged steel beam is conducted for several load cases by using the proposed model. The innovations of this study are listed as follows.In summary, a method for analyzing the large deflection behavior of restrained steel beams under the combined loads of explosion and fire is presented. The conclusions obtained through numerical results are conducive to further understanding on structural response and failure. Undoubtedly, this study is beneficial to designing fire- and explosion-resistant structures.


The ability to decide which of the two stimuli is presented first can be probed using a temporal order judgment (TOJ) task. When the stimuli are delivered to the fingers, TOJ decisions can be confounded by the fact that the hands can be moved to different locations in space. How and where this confounded information is processed in the brain is poorly understood. In the present set of experiments, we addressed this knowledge gap by using single-pulse transcranial magnetic stimulation (TMS) to disrupt processing in the right or left posterior parietal cortex (PPC) during a vibrotactile TOJ task with stimuli applied to the right and left index fingers. In the first experiment, participants held their hands in an uncrossed configuration, and we found that when the index finger contralateral to the site of TMS was stimulated first, there was a significant increase in TOJ errors. This increase did not occur when stimuli were delivered to the ipsilateral finger first. In the second experiment, participants held their hands in a crossed configuration and the pattern of errors was reversed relative to the first experiment. In both the first two experiments, significant increases in TOJ error were present with TMS over either hemisphere, regardless of arm configuration; however, they were larger overall following TMS over the right PPC. Control experiments using sham TMS indicated the systematic modulation in error was not due to nonspecific effects of the stimulation. Additionally, we showed that these TMS-induced changes in TOJ errors were not due to a reduced ability to detect the timing of the vibrotactile stimuli. Taken together, these results demonstrate that both the right and left PPC contribute to the processing underlying vibrotactile TOJs by integrating vibrotactile information and proprioceptive information related to arm position in space. A vital aspect of human behavior is the ability to keep track of time. Despite the clear need for temporal discrimination, the neural mechanisms underlying time processing are poorly understood. In laboratory settings, temporal processing can be probed using temporal order judgment (TOJ) tasks. In such tasks, two stimuli are presented in quick succession, typically in the visual or auditory domain, and the participant makes a decision as to which arrived first. Such tasks are simple when the interstimulus interval (ISI) is long in duration, but become increasingly difficult as the ISI approaches zero.Unlike with stimuli presented in the visual or auditory domain, when vibrotactile stimuli are used in a TOJ task, it is possible to alter their spatial location by changing the configuration of the limbs, for example, by applying the stimuli to each index finger and varying the relative position of the hands with respect to the midline of the body. Yamamoto and Kitazawa  demonstrA number of brain imaging studies have examined the cortical sites at which this spatial remapping is carried out in the context of a vibrotactile TOJ task. Each of these studies demonstrated that the posterior parietal cortex (PPC) showed greater activity associated with the remapping process when the arms were in a crossed posture  aged 19–35 years (mean age = 23.4 ± 4.0 year) participated in the experiment. Exclusion criteria included no previous history of sensorimotor deficits or personal or family history of seizure. All participants signed an informed consent form which explained the nature of the procedure and the small but potential risks of the application of TMS. The research was approved by the Committee for the Protection of Human Subjects at the University of Oregon and the Behavioural Ethics Research Board at the University of British Columbia and was conducted in accordance with the Declaration of Helsinki guidelines. Participants were paid $10 for each session in which they participated.2) so as to touch the surface of the skin.The participant sat comfortably in a chair with their eyes open and their arms resting palms down ~15 cm apart on a table. A piezoelectric vibrotactile stimulator was attached to the underside of the distal segment of the extended index finger pad of each hand with Velcro straps. Stimulation was achieved by applying a single rectangular voltage pulse  to the piezoelectric device producing a small displacement (1 mm) of the contact point  of 100 ms Fig.  when theA 2T Magstim Mono pulse 200 was used to deliver single TMS pulses via a figure eight coil. Stimulation was delivered at 110 % of the resting motor threshold for reliably eliciting an observable twitch of the first dorsal interosseus (FDI) of the contralateral hand at the motor hot point. The motor threshold from the right hemisphere M1 was used to calculate the stimulation intensity for the right PPC and that of the left M1 was used for the left PPC. During each experimental condition, the stimulating coil was moved 7 cm posterior to the motor hot point to a position that was an average of 17.44 ± 5.1 mm superior and 6.72 ± 1.96 mm anterior to the P3 and P4 sites in the international 10–20 EEG system . Figure The PPC TMS sites were confirmed in one participant using the Brainsight system . For this purpose, a whole-brain anatomical scan was obtained from the participant using a T1-weighted magnetization-prepared rapid gradient-echo sequence , hemisphere stimulated (right vs. left), and type of TMS stimulation  were held constant. Subjects had full vision of his or her hands in each experiment, and the room was illuminated. By keeping each of these aspects constant, we effectively controlled for the known influence of vision on TOJ errors  = 4.942, p < 0.001) as has been demonstrated previously  compared to uncrossed 18.63 %) configuration  or hemisphere to which TMS was applied ; however, there was a main effect of delay . Additionally, there was a significant interaction between the PPC hemisphere stimulated and the hand stimulated first , such that TMS applied to the left PPC led to significantly higher normalized error rates when the right hand was stimulated first relative to when the left hand was stimulated first . This pattern was reversed when TMS was applied to the right PPC, such that in left-first trials, there was a significantly higher normalized error rate than in right-first trials . All the above-mentioned results should be interpreted with caution because we also observed a quite intuitive significant 3-way interaction between hand stimulated first, TMS delay, and the hemisphere to which TMS was applied . To facilitate the understanding of these results, this interaction was broken down and further analyzed with Bonferroni-corrected pairwise post hoc comparisons within each of the combinations of conditions represented in the panels in Fig. In experiment 1, we observed no significant main effect for the hand that was stimulated first , hemisphere stimulated , or delay ; however, several significant interactions were present. In particular, we observed significant 2-way interactions between the hand stimulated first and the hemisphere to which TMS was applied  and between the hand stimulated first and TMS delay . As in Experiment 1, there was also a significant 3-way interaction between the hand stimulated first, TMS delay, and the hemisphere to which TMS was applied . Bonferroni-corrected pairwise post hoc comparisons revealed that, similar to Exp. 1, there were significant differences between the hands at all the delays except +100 ms and also 0 ms in the right PPC condition. Counter to Exp. 1, the effect was absent in any of the delays in the left PPC condition. This is consistent with the fact that the effects of TMS were greater during the period leading up to the first finger stimulation and were larger overall in the right compared to left PPC ). Nevertheless, there was also a significant 3-way interaction between the hand stimulated first, sham TMS delay, and the hemisphere given sham stimulation , demonstrating that real TMS had a larger impact on TOJ decisions than sham TMS. Furthermore, a significant interaction was observed between hemisphere, hand stimulated first, and arm configuration . This interaction captures the fact that the effects of TMS over the right PPC on normalized error rate were more substantial overall than TMS over the left PPC, and this effect was modulated by the arm configuration and the hand stimulated first. Moreover, the effect sizes  were larger for real TMS compared to sham TMS.A subsequent 5-way ANOVA allowed us to directly compare the impact of real versus sham TMS on this task and revealed a significant main effect of stimulation type  but a significant difference between the distal and proximal stimulation , possibly suggesting a difference in sensitivity of the regions stimulated . The results from this control experiment suggest that the PPC does not play a direct role in timing perception at least in the context of TOJ decisions.In experiment 5, we examined whether the right PPC contributes more directly to timing processes by characterizing the effects of TMS on the ability to determine the timing of two vibrotactile stimuli delivered to the same finger. Results indicated no significant effect of TMS delay . Yamamoto and Kitazawa  took advreduced relative to the non-TMS control trials. Thus, under this combination of conditions, participants’ performance improved with the TMS, suggesting that the processing underlying the detection of the initial vibrotactile stimulus to the left hand was more effective. It is unclear why this occurred; however, it could be due to at least two factors: (1) the use of a forced-choice task—participants that perceive stimulation arriving more frequently on one side during TMS are less likely to choose that side on non-TMS trials; or (2) a TMS-induced increase in sensitivity to the ipsilateral hand  was stimulated first. Under these circumstances, the error rates were actually The asymmetry between left and right PPC contributions to TOJ processing was apparent in the range of TMS delays. With right PPC TMS, differences were observed across a much broader range of delays prior to the hand stimulation than with left PPC TMS. By contrast, when the TMS arrived coincident with or in between the two vibrotactile stimuli, the differences across hands were markedly reduced. We suggest that this pattern of results is consistent with the critical involvement of the right, and to a lesser extent, the left PPC in the spatial remapping required to successfully perform the TOJ task  as opposed to an allocentric response  has the potential to allow participants to explicitly avoid remapping in their decisions. In other words, in the crossed con in particular, participants may ignore the allocentric information and focus instead on the somatotopic signals to drive their decisions. While this possibility cannot be completely discounted, we suggest that it is the interaction between the somatotopic information signaling the configuration of the arm and the vibrotactile stimulation that requires the spatial remapping to which the PPC appears to be vital in the current study. It is also important to keep in mind that this mode of responding has been used in most of the previous studies that have investigated the behavioral and neural characteristics of this issue (Hermosillo et al. In conclusion, we have shown that the human PPC plays a prominent role in vibrotactile TOJ tasks especially in the context of the spatial remapping required when the hands are in a crossed configuration. Furthermore, the right PPC appears to play a more substantial role than the left PPC in the processing underlying TOJ tasks when assessed across a wide time period prior to the vibrotactile stimulation. Taken together, this evidence provides fresh insight into the neural mechanisms underlying spatiotemporal processing and how it interacts with different bodily configurations.


Its application for prostate cancer requires intravenous infusion of TOOKAD® Soluble and the illumination of the targeted area by transperineal optical fibers inserted under trans-rectal ultrasound guidance under general anesthesia.This mini-invasive technique destroys targeted tissues using a photosensitizer [TOOKAD® Soluble defined during the phase II and III trials.Based on the experience gained through hundreds of procedures, we describe here the standardized technique of vascular-targeted photodynamic therapy with TOOKAD The photosensitizer absorbs light and transfers energy to oxygen molecules creating reactive oxygen species inducing local vascular occlusion resulting in cell destruction [Vascular-targeted photodynamic therapy (VTP) with TOOKADreatment –3. VTP dtruction . It is itruction . It indutruction  and bloctruction . Damage truction –10.® Soluble VTP procedure is indicated in patient suffering from localized prostate considered eligible for focal treatment. Optimal results are obtained for prostate volume between 25 and 70 cc.TOOKADThe absolute contra-indications are as follows: a prior prostate surgery, an acute urinary retention in the last 6 months, and history of urethral stricture disease. This procedure was first performed in 2004 by John Trachtenberg in the Princess Margaret Cancer Center in Toronto on a series of patients presenting recurrent prostate cancer following radiation failure. It was then imported in Europe by Mark Emberton at the University College Hospital, London.® Soluble VTP procedure and how it has been standardized during the phase II and III trials in Europe, North America and Latin America.The aim of this article was to report the technical aspects of the TOOKADAn alpha-blocker was advised a week before the procedure for a period of 1 month in order to ease the lower urinary tract symptoms (LUTS) due to prostate swelling during the immediate postoperative period (2–3 weeks).A rectal preparation was performed the day before surgery.® (Stebabiotech) which optimizes the parameters of treatment: number of optical fibers, accurate position of the fibers into the prostate and the length of the light diffusing of each optical fiber (Steba-Biotech) [The treatment guidance by imagery (either by MRI or by ultrasound) permitted to define the target volume to treat, the safety margin regarding the urethra, posterior, lateral capsula and rectal wall. The integrity of these anatomical structures had to be strictly respected during the procedure. It was performed with a software called TOOGUIDEBiotech)  Fig. 1)® . The Anesthesiologist was informed of this requirement before the procedure, and a zero movement rule was mandatory.The patient was placed in lithotomy position at the edge of the operating table with enough hip flexion in order to expose the perineum without being hindered by the pubis. As in brachytherapy, the legs had to be spread to avoid a conflict between the pubic arch and the insertion of the FIC.Conventionally, the ultrasound machine was on the left of the surgeon, the nurse, her table and the laser, on the right Figs. , 3.Fig. The prostate and the adjacent structures were visualized by the biplane trans-rectal ultrasound probe attached to a standard brachytherapy stepper  with an attached transperineal prostate template (i.e. Mic Radio Nucelar Instruments Inc 0308-02-13 B&K or compatible). Biplane vision was mandatory in the choice of the TRUS scan machine. Before the insertion of the TRUS probe, it was capital to make the rectum perfectly clean with no residual feces. A feeding syringe with saline solution can be used. This point was capital since the image had to remain optimal during the whole procedure especially because there is no opportunity to correct it once started Fig. .Fig. 4ClThe probe was covered by a protective endo-cavity balloon previously filled with urethral gel. The urethral gel was more appropriate than ultrasound gel because it contains fewer bubbles and facilitates the introduction of the probe in the balloon Fig. . Thus, tBefore introducing the TRUS probe in the rectum, the brachystepper had to be set on a neutral position to allow movements in all directions. Pointing the stepper toward the floor while inflating the balloon removed spontaneously the residual bubbles Fig. . Ten to When the probe was introduced into the rectum, it was advised to remove it two or three times in order to empty the remaining saline trapped into the rectum after its cleaning. Once the TRUS probe was in position, an optimal picture was sought by adjusting: the frequency to 5–6 MHz, the width by focusing the ultrasounds on the prostate, the depth to increase the size of the prostate at its maximum on the screen, and the resolution of the image. Once an optimal image was obtained, the stepper device was locked, and only longitudinal (superior–inferior) movements were permitted thereafter.® software (Steba-Biotech), the US images of the prostate were acquired by steps of 5 mm from the basis to the apex by mobilization of the stepper. The pictures were saved on the ultrasound machine and transferred to the software. The Urologist had to delineate the prostate limits and to launch the software in order to produce the treatment guidance within 2 min . These two drapes were fixed to the transparent drape to completely close the sterile operative area. The keyboard of the ultrasound machine was also covered with a transparent sterile drape to allow the urologist to independently manage the US measurements.The bladder was drained through a Foley catheter placed in the urethra, and the balloon was inflated with 10 cc saline. The catheter had to be pushed far in the bladder and fixed to the glans with a sticky tape in order to avoid blowing up the balloon during the procedure. The catheter was clamped with a spigot during the whole procedure in order to keep the bladder full which will improve the visualization of the limits of the prostate by ultrasound.The Anesthetist should avoid excess fluid supply as a full bladder could trigger movements and even waken the patient, as well as it could alter the shape of the prostate by compressing its base.The patient was integrally protected from light exposure. The only exposed zone was the perineum.®. The virtual template grid on the screen increased the accuracy of the FIC placement. Using FICs with metallic tips facilitated their penetration through the skin and the prostate. The best way to introduce the FIC was to do it swiftly. A slow movement would make the skin more difficult to pass through and displace the prostate leading to a wrong position of the FIC into the targeted area. Conventionally, the FICs were inserted from anterior to posterior and from right to left. By using this method, the visualization of the posterior FICs during the introduction was not disturbed by the artifacts due to the FICs already in place. The right to left convention was very helpful to label each FIC and its corresponding optical fiber in a right and reproducible order.Once the installation was achieved, transparent hollow FICs were positioned into the prostate transperineally through the template Figs. , 8, usin3 of necrosis with more than 90 % of necrosis of the targeted volume [2. Above this threshold, the first measure taken was to deflate the balloon in order to increase the distance between the posterior part of the prostate and the anterior rectal wall. If it was insufficient, the endorectal probe was moved posteriorly by using the Z-axis of the brachystepper in order to obtain an acceptable light intensity level into the anterior rectal wall. Once the adequate light level was obtained, the US probe should not be moved anymore in order to keep the light monitor in place.Once all the FICs were in place, the accurate measurement of each corresponding optical fiber was performed. The positions of the optical fibers into the FICs must respect a safety margin of 5 mm to the urethra, the rectal wall, the sphincter and the capsula Fig. . The difd volume . At the d volume . Before ® Soluble was then initiated through opaque syringe and line.Once all FICs and optical fibers were in position, the light of the room was dimmed and the patient was entirely protected from light exposure and wear goggles. The infusion of TOOKAD® Soluble. The activation of the TOOKAD® Soluble was achieved by continuous illumination of the prostate gland through the optical fibers with a 753-nm laser light at a power of 150 mW/cm and light energy of 200 J/cm delivered by a multichannel diode laser  and depended on the volume of the targeted area and the number of optical fibers to be placed Fig. . At the The patient was kept under medical surveillance under dimmed light for at least 6 h and may be discharged on the day of the procedure as a day-case surgery. The patient was informed that he had to avoid direct exposure to sunlight during 48 h after the injection. Dimmed light was recommended the day of the procedure. The urinary catheter could be removed 3–4 h after the procedure or on the following day. An alpha-blocker was prescribed because of the increased risk of LUTS during the first month after the procedure.® Soluble (WST11) is a standardized procedure for localized prostate cancer treatment. It is relatively simple, easy to learn and easy to perform. It is minimally invasive and requires a short anesthesia (approximatively 2 h), therefor it can be done in ambulatory conditions. The evolution of the technical procedure has been the result hundreds of cases in various environments such as public or private sectors, university or general hospitals. The shared experience on various continents with different medical cultures of the surgeons involved in the studies improved the technique in a way to adapt itself to a vast majority of surgical centers with an optimal safety and efficacy of the treatment.Vascular-targeted photodynamic therapy with TOOKAD