Analysis of fluids in porous media is of great importance in many applications. There are many mathematical models that can be used in the analysis. More realistic models should account for the stochastic variations of the model parameters due to the nature of the porous material and/or the properties of the fluid. In this paper, the standard porous media problem with random permeability is considered. Both the deterministic and stochastic problems are analyzed using the finite volume technique. The solution statistics of the stochastic problem are computed using both Polynomial Chaos Expansion (PCE) and the Karhunen-Loeve (KL) decomposition with an exponential correlation function. The results of both techniques are compared with the Monte Carlo sampling to verify the efficiency. Results have shown that PCE with first order polynomials provides higher accuracy for lower (less than 20%) permeability variance. For higher permeability variance, using higher-order PCE considerably improves the accuracy of the solution. The PCE is also combined with KL decomposition and faster convergence is achieved. The KL-PCE combination should carefully choose the number of KL decomposition terms based on the correlation length of the random permeability. The suggested techniques are successfully applied to the quarter-five spot problem. Fluid flow in porous media is a subject of great interest due to its wide range of applications such as water/oil flow in underground reservoirs, modeling the underground spreading of toxic, and biological applications such as the transport in lungs and arteries . When deUncertainty quantification (UQ) methods are used for analyzing the system using a model by the parameterization of the uncertain input data (such as permeability) using a set of independent random variables. Then, the model is solved to determine the response of the system to the given random input data . Most of the numerical models used for uncertainty quantification are based on the Monte Carlo (MC) sampling method ,6,7,8,9.Another method is the polynomial chaos expansion (PCE) , where tom space ; howeverom space , where tom space . Howeverom space . To overom space ,17, wherWhen dealing with Gaussian processes, the convergence of the KL expansion is optimal , howeverThe purpose of this paper is to solve one of the standard porous media problems, namely, the quarter-five spot problem after imposing uncertainty to the problem. The quarter five sport problem is used to model the case when a regular set of injection and production wells is present in the reservoir; as this problem already illustrates the features and difficulties of the general problem . The proThe remainder of this paper is organized as follows. First, in Consider the problem of fluid flow in porous medium for a single-phase flow with an incompressible rock and fluid under isothermal conditions .The problem is presented by the following partial differential equation (PDE):Let As gravity forces are approximately constant inside a reservoir domain, we getTherefore,If we assume water phase with Equation (6) is a second order linear PDE. Additionally, Equation (6) is elliptic as the eigenvalues of its coefficient matrix are all negative.Due to our incomplete knowledge about the medium properties, subsurface flow involves some degree of uncertainty, and therefore we need a stochastic description of the medium properties . We can Thus, Equation (6) becomes an SPDE stated asThe PCE method can be used to represent a second order process essed as  u=To simplify writing the equations, we can eliminate the arguments when there is no ambiguity. If For Gaussian random variables, Hermite polynomials are the most suitable orthogonal basis . For othFor computational purposes, if we have a random vector  the PCE .(11)P+1The functions relation (12)ψi,ψIn case that the polynomial chaos basis are the Hermite polynomials, The mean square error of the truncated PCE expansion,For the case of univariate Gaussian stochastic germ, the following theorem provides an error bound.Theorem 1 . Given uThe KL expansion can be viewed as a special case of the PCE where only first-order polynomials have non-zero coefficients . The KL definite .We can represent The KL expansion is effective when the correlation function is known, as it is characterized by an optimal convergence in the mean square sense . HoweverRecall Equation (6):To have a complete solution, we need to specify the boundary conditions. Closed flow systems where there is no fluid flow across the external boundaries are modeled by specifying homogeneous Neumann boundary conditions:There are several numerical methods used to solve (4), three of these methods were discussed in . The firTo compute the flux The integral can be approximated asSimilarly, we have for cellBy imposing the continuity of fluxes, we have Finally, when substituting Therefore we get the following system of equations,lgorithm .Equation (4) is solved on aThe concentration of a tracer is given by a continuity equationWe define the time-of-flightApplying the time flight to a tracer, the communication patterns of the reservoir can be studied effectively. Therefore, in order to estimate the speed of flow inside the reservoir, we solve equation (6) subject to We now proceed to solve Equation (7) while considering the uncertainty of the permeability field First: Using PCELet permeability tensor Accordingly,Which can be simplified to becomeApplying inner product d priori . We can Second: Using KL expansionAs the realizations of a Gaussian distribution may take negative values, it is more practical to assume a log normal distribution forthe form ,31(41)CThe permeability To obtain the coefficients After computing the coefficients We compare the differences in solutions obtained using MC and PCE methods. In the second case, we apply the KL expansion to the input, in order to reduce the dimension of the input space and then use PCE. The permeability field First, we compare the convergence of the eigenvalues of the correlation function The problem is solved using PCE of order , PCE witIn this paper, we studied the quarter-five spot problem. We solved both the deterministic problem and the stochastic problem after imposing uncertainty to the problem. We considered two cases for the stochastic problem: The first case is solved using both MC and PCE methods and the results are compared. It was shown that for the given problem, assuming a PCE with order


This paper compares methods for measuring selected morphological features on the surface of thin metallic layers applied to flexible textile substrates. The methods were tested on a silver layer with a thickness of several hundred nanometers, which was applied to a textile composite with the trade name Cordura. Measurements were carried out at the micro scale using both optical coherent tomography (OCT) and the traditional contact method of using a profilometer. Measurements at the micro-scale proved the superiority of the OCT method over the contact method. The method of contactless measurement employs a dedicated algorithm for three-dimensional surface image analysis and does not affect the delicate surface structure of the measured layer in any way. Assessment of the surface profile of textile substrates and the thin films created on them, is important when estimating the contact angle, wetting behavior, or mechanical durability of the created metallic structure that can be used as the electrodes or elements of wearable electronics or textronics systems. Textronics and flexible electronics are rapidly developing fields of science. Common areas of interest in these fields include the creation of metallic layers with optimal electrical properties on flexible substrates. Such structures can be implemented in items requiring flexible electronics or in clothing with textronic elements and sensors as well. Good quality thin layers, acting as passive elements or electrically conductive paths , are a kThe sensor market is developing rapidly. According to Zion Market Research, the sensor market will be worth $11.2 billion in 2025 , pressurAccording to the literature, the higher the roughness parameters, the smaller the nominal contact surface between the surfaces, and adhesion to the rough surface is reduced ,19,20,21The original ways of creating textronic structures and flexible electronics involve weaving thin wires with low electrical resistance into a textile product during the manufacturing process. These types of techniques are usually complex, and at the same time they do not allow for diverse product functionalization such as surface techniques, printing, sputtering, chemical vapor deposition, and physical vacuum deposition (PVD). These more modern techniques enable the production of metallic conductive layers on the surface of flexible substrates. In each case, however, the metallic layer has a different structure and surface morphology .Surface metrology is the analysis of surface irregularities—i.e., all deviations of the real surface relative to the nominal surface. The real surface is what is obtained as a result of applying a layer on a specific substrate, while the nominal surface is a geometrically perfect product with a specific shape, most often specified in the technical documentation. Unfortunately, the real surface is very difficult to measure, and the nominal surface is impossible to achieve, which means that the measured surface should be analyzed, i.e., observed using a specific measuring method. The purpose of surface description is thus to characterize its geometrical structure . It provTraditionally, determining surface morphology involves examining its structure at individual cross-sections using contact methods. Obtaining surface topography on the entire plane by these methods is therefore time-consuming, as it requires information from many parallel measuring sections collected with contact profilometers. They are easy to use, resistant to industrial conditions, able to measure any selected fragment of the surface, and have low sensitivity to vibrations. Contact methods have both advantages and disadvantages , which aContact measurements provide good presentation of surface morphology, but the time needed to gather data is much longer than that required by the contactless methods . ContactRoughness tests using a profilometer relate to a micrometer scale. Confocal microscopy measures unevenness in the sub-micrometer and nanometric scale with a resolution of up to 0.1 µm/px. Therefore, the confocal microscope measurement is not an alternative to profilometer measurement. Optical coherent tomography, due to its resolution, also measures roughness parameters in a micrometric scale. For this reason, it can be an alternative method to contact measurement using a profilometer. In addition, due to the flexibility of the measured substrate, the optical method using optical coherent tomography (OCT) has been select by the authors. The choice of the OCT method is made for economic reasons, when no nanometer resolution of the profile is required. In this application, confocal systems are usually very expensive. Real-time measurement is also possible for OCT, due to flexible positioning of its scanning head over the surface of the material moving at a low speed . DependiOCT is a high-resolution imaging technique, which provides depth profiles of inhomogeneous and turbid materials in a contactless and non-destructive manner . The genOCT is suitable for testing both biological structures and artificial materials, but in the initial period of development of this method, the focus was almost exclusively on organic systems research.For over 15 years, the OCT has increasingly been used for the study of the structures of materials. It tenders an approach to quantify both surface and internal  properties of paper , siliconOCT is used not only to study deep structures, but, due to the ability to carry out accurate three-dimensional mapping the topology of the samples, can be used to carry out a visual quality inspection of the surface layer or study surface phenomena, such as the wettability of materials ,39.The first study demonstrating the application of OCT in printed functional materials and printed electronics was published by Czajkowski et al. in 2010 . The autModern OCT tools offer speed-enabling online monitoring of printed devices. Alarousu et al. 2013  used speThe purpose of this article is to evaluate the surface profile of a metallic layer applied to a flexible textile composite through which light cannot pass. The optical method proposed in the paper uses optical coherent tomography, and the authors proved that it could offer an alternative to profilometric contact measurements. Z(x)) within the measuring surface inside the elementary segment lr.The parameters used for quantitative assessment of the analyzed surface profile are as follows ,44 Figu:Ra—arithMost of the parameters and functions used in three-dimensional analysis are marked with the letter “S,” as the equivalent of the letter “R” in the profile parameters. Hence, the parameters This paper presents the results of measurements of 2 was used as both the raw material and the substrate for a thin silver layer. This composite textile material consists of nylon threats which are laminated with a polyurethane layer . . 49]. Topography measurement of the surface of the sample top layer was carried out for 41 lines on a 5 × 5 mm surface with intervals of 125 µm.Wasatch Photonics Inc., NC, USA) [The infrared tomographic system HR Spark OCT 800 nm   presenteThe OCT setup contains a Fourier domain (FD) Michelson’s interferometer. In this device, the signal of light interference between the sample and the reference arms at different depths below the fabric surface corresponds to different frequencies of the scanning source spectrum, distinguished by the internal diffraction grid. The sample arm of the interferometer was equipped with both a scanning MEMs mirror and a CMOS camera, which provided fundus images of a material surface. A Computational Engine (PC) containing an image acquisition card was connected to the OCT Engine via a Camera Link interface. The card registered 3D images of the infrared signal, reflected from the material surface or in the semi-transparent subsurface layers. The HR-Spark apparatus creates an array of  1.79 μm . The scaXZ-plane) inside the registered OCT image. A typical perspective view of the scanned material covered with the silver layer and a single cross-section (B-scan) are presented in The sample of measurement material was glued to the glass substrate and then placed horizontally, under the OCT scanning head. The tilt of the OCT head was adjusted to provide horizontal orientation of the material surface cross-section in each B-scan  , and conThe tested Cordura material covered with a silver layer strongly scatters the OCT scanning beam even on the border of the layer. This gives a bright edge to the material surface in each B-scan image, as shown in Due to the distortions and changes in the material structure that can occur during OCT scanning, the bright material edge may disappear at some locations inside the view field. Thus, the surface boundary values N-rank tensor: To obtain a regular grid of voxels evenly distributed on the material surface, the fast-smoothing spline method described in  was selelable in .(14)p11The difference in height of the surface base plane The surface profile outliers of Two-dimensional and perspective views of the final depth map In order to assess the accuracy of each presented measurement method, the roughness parameters of reference sample No. 178–601, serial no. 318411402  were anay, and The operation of waviness removal in the image domain can be written as:aR parameter calculated by the OCT method are averaged for the lines in individual measurement fields covered by the frames shown in maxR value given in maxR value determined in the contactless method is clearly overestimated compared to the given standard, probably due to impurities and reflections from the shiny metallic surface. Reflective surfaces can cause OCT image distortions over metal surface visible in the air layer in the form of bright vertical streaks. This phenomenon can be partially reduced by shifting the focus range towards the material surface. Then, however, the material border is slightly blurred. Individual, small reflections of IR light can appear over different surfaces and affect maxR value.Values for the Measurements of the Cordura surface profile were made in relation to the reference profile realized by the device rails. After leveling the profile, i.e., separating the mapped slope from the profile, which results from the lack of parallelism of the object surface to the measurement line, the original surface profile was obtained. The measurement results, showing the appearance of the real surface without Gaussian filtration, are presented in On the surface of the clean composite, pits with high values can be observed. These result in a higher surface roughness value, which is confirmed by the measurement results presented in aS and vS parameters. The maximum roughness profile height for the coated layer was 46 µm, while a value of about 95 µm was obtained for the raw surface.Presented views of the surface roughness and structure of the base material indicate high values for the The results presented in XY plane of each OCT image, as illustrated in Based on the surface profile standard  in five The results of roughness measurements obtained with both a profilometer and optical coherent tomography relate to measurements on a micrometric scale. We observed the differences between the values obtained using the contact and contactless methods. These differences related both to the profile of the clean textile composite substrate and to the profile of thin metallic layer applied to the substrate. The values obtained using the optical sensor (OCT) were higher than those obtained using the stylus method, which has also been reported as being the case for surface structures of composites with an aluminum layer tested using contact and non-contact  methods . For rawThe roughness parameters of the metallic layer measured by the non-contact method were also higher . The experiments confirm the usefulness of the OCT method for assessing surface parameters of layers applied on flexible substrates, as an alternative to contact measurements. In contact profilometry, the stylus profiler mechanically touches the surface, which can cause damage to the surface of the flexible sample when the contact pressure cannot be precisely adjusted to the hardness of a deposited layer on a composite material. On the other hand, OCT can be regarded as an approximate method because of its own limitations. OCT extreme parameters often are overestimated and have poor repeatability, due to the influence of unwanted infrared light reflections from the surface during measurements. The lateral resolution of High Resolution (HR) Spark OCT device used in tests is about two times worse than in the contact method, which also affects the measurement results. However, the OCT method does not influence the tested metal layer, and thus delivers results unchanged by mechanical factors. Furthermore, it provides higher acquisition speed compared to mechanical scanning of the sample area. The studies have been conducted on samples without cracks or delaminations to assess the profile of a uniform surface. Nevertheless, the measurement algorithm can take into account the location of defects in the case of their occurrence. Using this method, it is possible to assess the quality of the created layers by measuring the number and size of discontinuities, but only these extending from the metal surface to the textile substrate. This problem will be studied in the future.The OCT method can be applied not only for conductive layers, but also for other surfaces, with particular emphasis on flexible materials. Due to the ability of the IR light beam to penetrate semi-translucent or turbid layers, the OCT method can be applied to analyze the profiles of internal surfaces covered by thin polymer or textile layers. This feature enables the inline quality validation of textronic sensors in the industry production conditions.


A forward head and rounded shoulder posture is a poor posture that is widely seen in everyday life. It is known that sitting in such a poor posture with long hours will bring health issues such as muscle pain. However, it is not known whether sitting in this poor posture for a short period of time will affect human activities. This paper investigates the effects of a short-duration poor posture before some typical physical activities such as push-ups. The experiments are set up as follows. Fourteen male subjects are asked to do push-ups until fatigue with two surface electromyography (sEMG) at the upper limb. Two days later, they are asked to sit in this poor posture for 15 min with eight sEMG sensors located at given back muscles. Then they do the push-ups after the short-duration poor posture. The observations from the median frequency of sEMG signals at the upper limb indicate that the short-duration poor posture does affect the fatigue procedure of push-ups. A significant decreasing trend of the performance of push-ups is obtained after sitting in this poor posture. Such effects indicate that some parts of the back muscles indeed get fatigued with only 15 min sitting in this poor posture. By further investigating the time-frequency components of sEMG of back muscles, it is observed that the low and middle frequencies of sEMG signals from the infraspinatus muscle of the dominant side are demonstrated to be more prone to fatigue with the poor posture. Although this study focuses only on push-ups, similar experiments can be arranged for other physical exercises as well. This study provides new insights into the effect of a short-duration poor posture before physical activities. These insights can be used to guide athletes to pay attention to postures before physical activities to improve performance and reduce the risk of injury. Poor posture is regarded as prolonged deviations from the neutral spine, and it usually can be characterized by the forward head posture, rounded shoulders, and increased thoracic kyphosis  was used to collect sEMG signals for analysis. Two sources of sEMG signals were used during the experiment, (1) the sEMG signals were collected from biceps brachii and triceps brachii during push-up exercises in the two sessions. (2) During the poor posture sitting, sEMG signals were collected from eight upper back muscles, including the right upper fibers of trapezius , left upper fibers of trapezius , right middle fibers of trapezius , left middle fibers of trapezius , right lower fibers of trapezius , left lower fibers of trapezius , right infraspinatus , and left infraspinatus . Locations of the eight sensors was illustrated in t-test or Wilcoxon signed rank test was performed to compare the frequency changes of push-up exercise in the two experiment sessions. One-way Analyses of Variance (ANOVA) with repeated measures or Kruskal-Wallis test was employed to measure frequency changes among different levels  during the poor posture sitting. The Tukey post hoc test was used to investigate the significant difference between different levels. The significance value was set at 0.05, and the data was presented as mean value ± standard deviation.Standard statistical analysis was performed on the collected data. Prior to the statistical analysis, data normality was checked with the Shapiro-Wilk test. Depending on whether the data distribution is normal or not, paired The signal processing procedures for the sEMG signal collected from upper limb muscles during the push-up protocol are shown as The MDF and MNF are then calculated for each burst, the Hamming window with length of 100 ms is used to obtain each segment in sEMG signal, the envelope of the windowed signal is illustrated as p = 0.025) smaller than those after poor posture. The statistical analysis of the difference value between the start and the end frequency is shown as p = 0.002), which indicates that the muscle fatigue process has a smaller decreasing percentage after poor posture.The fatigue analysis with the mean MDF for push-up before and after the poor posture protocol is demonstrated as p = 0.007; p = 0.020) smaller than those obtained after poor posture. The similar comparison can be found in Similar results were obtained by calculating the mean MNF values of the triceps brachii. It can be seen from section 3.1 that significant differences are observed for the push-up before and after the short-time poor posture sitting in terms of the frequency change in mean MDF and MNF, which indicates the poor posture has influence on the performance of physical exercise of the group. In this section, a detailed investigation of upper back muscles related to the poor posture is presented to evaluate the changes and sensitive frequencies of upper back muscles during the poor posture sitting.As described in the experiment setup, eight wireless sensors are employed to collect sEMG signal from upper back muscles during the poor posture sitting. An illustration of the raw sEMG signals collected from the LLFT muscle during the 15 min poor posture sitting is demonstrated in As indicated in previous studies  wavelets, the Symlets (sym) wavelets, the Biorthogonal (bior) wavelets, and the Coiflets (coif) wavelets. The decomposition level was set as 7 to obtain a fine resolution in the frequency domain  was calculated for all windows. p = 0.024). As demonstrated in p = 0.023) than the value of level 2 around 37 Hz. The similar frequency differences can be observed in p = 0.0095).It can be seen from p = 0.025), the frequency differences between the start and the end of the push-up (p = 0.025), and the rate of the frequency differences (p = 0.017). Second, it is confirmed from experiments and data analysis from sEMG sensors, some parts of back muscles are affected during the short time of poor posture with a clear indication of fatigue, which has not been observed in literature. As indicated in There are two major findings in this study, first, the short-time poor posture indeed has an effect on the performance of physical exercise. Comparing the subjects' performance of push-ups before and after poor posture, the median frequencies of the two sessions have significant differences after 10 push-ups in terms of the slope of the trend  after the poor posture. People should be mindful of their postures if they will undertake physical activities in the near future.The current study has some limitations. First, only male subjects were recruited for the study, as the experiment requires placing eight sensors on the back muscles, due to the privacy issue and lack of female team members to collect data from female volunteers. We will further investigate whether there has gender difference for the results. Second, due to the limitation of available data, the current study does not include the results from natural posture. The next step research will recruit more subjects to evaluate the effect of poor and natural postures, and investigate the prevention to the immediate and latent effects of muscle fatigue from the poor posture, which will provide know-how and awareness to prevent during sports and most importantly the activities of daily living (ADLs).This study contributed to the understanding of a particular short-duration poor sitting posture on the effect of the performance of physical exercise and the fatigue of back muscles. From statistics of 14 subjects, it was observed that the median frequencies of the sEMG signal of the triceps brachii has significant differences after poor sitting posture, and the median frequencies collected from the RI muscle in the upper back have been shifted in different time levels. The results suggest that the poor posture will lead to a quicker fatigue procedure of the following physical exercise as shown in the median frequency of the corresponding muscles. The results also demonstrated that the proposed frequency analysis techniques were able to identify the frequency range of the individual muscle, which can be used to show a clear shift of median frequencies of noisy sEMG signals in order to represent fatigue.The datasets that support the findings of this study are available from the corresponding author upon reasonable request.The studies involving human participants were reviewed and approved by the Human Research Ethics Committee of the University of Melbourne (#1954575). The patients/participants provided their written informed consent to participate in this study.LL, XG, MR, KG, and YT contributed the experiment design and data collection. LL and YT contributed the data analysis and drafting the manuscript. LL and MR performed the statistical analysis. KG, IM, and DO contributed the manuscript revision and results interpretation. All the authors read and approved the manuscript.IM is employed by the IBM Research - Australia. KG is a sport physiotherapist for the Melbourne University Elite Athlete Unit, and CEO of the Elite Akademy Sports Medicine. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.


Lung sounds acquired by stethoscopes are extensively used in diagnosing and differentiating respiratory diseases. Although an extensive know-how has been built to interpret these sounds and identify diseases associated with certain patterns, its effective use is limited to individual experience of practitioners. This user-dependency manifests itself as a factor impeding the digital transformation of this valuable diagnostic tool, which can improve patient outcomes by continuous long-term respiratory monitoring under real-life conditions. Particularly patients suffering from respiratory diseases with progressive nature, such as chronic obstructive pulmonary diseases, are expected to benefit from long-term monitoring. Recently, the COVID-19 pandemic has also shown the lack of respiratory monitoring systems which are ready to deploy in operational conditions while requiring minimal patient education. To address particularly the latter subject, in this article, we present a sound acquisition module which can be integrated into a dedicated garment; thus, minimizing the role of the patient for positioning the stethoscope and applying the appropriate pressure. We have implemented a diaphragm-less acousto-electric transducer by stacking a silicone rubber and a piezoelectric film to capture thoracic sounds with minimum attenuation. Furthermore, we benchmarked our device with an electronic stethoscope widely used in clinical practice to quantify its performance. Lung-related diseases such as pneumonia, chronic obstructive pulmonary disease (COPD), and asthma impose heavy societal and economic burdens. To date, the health state of patients with respiratory diseases is monitored intermittently only, during visits to a doctor. Therefore, it is difficult to align the medical treatment with the individual development of the disease. More frequent or even continuous observation of respiratory functions during patients’ daily life has the potential to improve the therapeutic outcome. Recent years have seen the development of a number of devices for remote recording of respiration-linked body signals. In the context of respiratory diseases, signals of interest are, among others, blood oxygen saturation, respiration frequency, body activity, and importantly, sounds produced by the respiratory organs. Sound-based remote monitoring can, for example, be done by training patients in the use of digital stethoscopes which transmit the recorded sounds to a health care professional for further analysis . This apThe wearable stethoscope presented in this paper was designed in the frame of the European project WELMO, which aims at developing and validating a new generation of low-cost and low-power miniaturized sensors. The sensors are integrated in a comfortable vest, enabling the effective and accurate monitoring of the lungs. The goal of the WELMO vest is to measure activity, bioimpedance and chest sounds with a high spatial resolution. The key to improve the wearing comfort of systems with many sensors, is to reduce the cabling between sensors. In WELMO, this challenge was tackled by employing cooperative sensor technology , which aIn this article, we focus on the design and characterization of the sensor module which acquires thoracic sounds. The central element of the sensor module, the acoustic transducer, can either be realized by using an air microphone ,7,8 or aThis section reports the design of the thoracic sound acquisition module. The module serves to capture the pressure waves, originating from the (turbulent) airflow in the respiratory tract, and to convert these to electrical signals which can then be communicated to the central unit as digital data. The signal flow path begins with the coupling of pressure waves to the module’s physical interface with the body, and continues with the conversion of vibration signals to electrical signals via a piezoelectric transducer, conditioning of the analog signals, and finally ends with on-site quantization of these signals. Accordingly, the sound acquisition module consists of a piezoelectric transducer and read-out electronics. Coherent with the signal flow path, first the transducer design is presented and in the second part of the section, the design of the electronics is detailed.Sound waves emanating from airflow in the respiratory organs propagate omnidirectionally, though not necessarily with the same frequency response, towards the outer surface of the body. These waves, although being within the frequency range humans can perceive, cannot be captured like speech or any other airborne sound. This is essentially due to the incompatibility of the two media, body and air, or more precisely due to the acoustic impedance mismatch between these two media. Impedance matching is a well-known concept that is applied in different physical domains  to maximize the energy transfer from one point to another and particularly from a source to a load. In the case of an impedance mismatch, a fraction of the incoming wave is reflected back towards the source; thus, limiting the signal power on the receiving end. For instance, in conventional acoustic stethoscopes, this problem manifests itself at each junction, i.e., at the chest wall and the stethoscope’s diaphragm, at the tube and the earpiece, etc. . Bell (oRecent work reported a silicone membrane filled with water (or hydrogel) to acquire phonocardiogram signals . AlthougIn this work, we present a method which does not involve air as a propagation medium since the introduction of electronic stethoscopes has eliminated the necessity to guide the thoracic sounds all the way through from the chest wall to the ear. Today’s electronic stethoscopes work on the principle of on-site signal acquisition and digitization—thus improving the noise immunity in the subsequent stages. Although conventional tubes and earpieces are generally preserved in most of the electronic stethoscopes in the market, mainly to be compliant with the habits of clinicians, the sound is actually regenerated by means of a speaker driven by the input signals acquired at the stethoscope head piece. On top of that, for applications involving acquisition of thoracic sounds from multiple points at the same time, preserving the hearing experience becomes less important—or a feature than can be considered as nice-to-have.An important disadvantage of an air layer between the chest wall and the sensing unit is the high sensitivity of such systems to ambient noise. Unless a very rigid wall or multi-layer sound absorption solutions are incorporated, the ambient noise will penetrate through the sidewalls into the “air chamber” and decrease the signal quality. Considering the wavelength of the sound signals at the frequencies of interest (100–2000 Hz), the absorption layer needs to be impractically thick for the presented application.Based on the arguments listed above, in this work, we have implemented a diaphragm-less acousto-electric transducer by stacking a silicone rubber and a piezoelectric film—which is also known as contact microphone. The silicone rubber plays two roles: (1) providing the physical interface with the skin and (2) supporting and shaping the piezoelectric film. In conventional acoustic stethoscopes, a diaphragm is employed to interface with the skin. When the diaphragm, conforming to the skin, moves up and down, the pressure inside the cavity of the stethoscope changes and this pressure difference is transmitted to the listener’s ear . In the A piezoelectric thin film, conforming to the surface of the silicone rubber, converts the pressure wave impinging on the material to an electrical signal whose amplitude is proportional to the strain. Polyvinylidene difluoride (PVDF or PVF2) is employed to realize the sensing unit. Since the demonstration of the piezoelectric characteristics of PVDF, the material has been widely used in acoustic applications, particularly for underwater acoustics thanks to its specific acoustic impedance quite close to that of the water. Thanks to this property, no impedance matching layer between the two media is necessary. Considering that the acoustic impedance of the body is quite close to that of water (mainly due to high water content), PVDF makes a perfect candidate for the presented application.PVDF can be manufactured in the form of a thin flexible film. This quality differentiates PVDF from the widely used piezoelectric ceramics. Although the piezoelectric coefficients of PVDF are lower than those of ceramic parts, its ability to be bent or curved compensates for this disadvantage.31 and g33, respectively) of a mono-oriented PVDF hints that for a higher sensitivity, it makes more sense to use it in thickness (or transverse) mode, i.e., backing one side of the planar surface with a rigid surface and applying the pressure on the other side to modulate the thickness of the PVDF film. However, Naono et al. [31) mode than in thickness mode (g33) if one curves a PVDF film along its poling direction (1-axis) and clamps the non-curved sides  to a rigid frame. This approach provides a mechanical amplification as a function of the radius of curvature (R). More precisely, the sensitivity is proportional to R. This property comes along with a trade-off; as the sensitivity increases, the resonance frequency of the sensor decreases—thus limiting its linear operation region, i.e., the resonance frequency is inversely proportional to R. A simplistic model to calculate the resonance frequency is given by [Y is Young’s modulus and ρ is the density of the PVDF film. It should be noted that this equation neglects the backing material and effects of clamps. Nevertheless, it is useful to understand how the resonance frequency could be controlled by tuning the design. As it is desired to acquire signals in a given bandwidth with flat frequency response, it is preferable to set the resonance frequency high enough to ensure the specified flatness in the bandwidth of interest. The flatness in audio applications is generally defined as ±2 dB (or ±3 dB) as the human ear can hardly detect a 2-dB difference.Comparing the longitudinal and transversal direct piezoelectric voltage coefficients f02 (10 mm × 12 mm) which approximately corresponds to 120 pF sensor capacitance.Later Toda et al.  have intThis section reports the design of the electronics of the sound acquisition module. The section is organized in two subsections, first the signal conditioning for high-impedance sensors is detailed and then filtering and quantization aspects are explained.S (with a linear voltage-strain behavior) in series with a capacitance Cs . Cs and the input resistance of the impedance converter  form a first order high-pass-filter (HPF).To deal with the high source impedance, we have opted for a common-source junction field effect transistor (JFET) amplifier acting as an impedance converter. JFETs are characterized by high input impedance, very low gate bias current, and low flicker (1/f) noise. Furthermore, the negative threshold voltage allows simplifying the biasing scheme by connecting the gate to the source (or to ground (GND) in the case of a common-source amplifier). As shown in gd will be seen as multiplied by (1 + gain) due to the Miller effect, which reduces the signal gain from the sensor to the drain of the JFET). For higher bias resistance values (which results in less noise), the input bias current value becomes more important and decisive for the total output noise (or input-referred noise) as well as the offset voltages. Taking into consideration that the noise voltage increases with the resistance value, it may seem at first glance that the bias resistance RB should be reduced to such a value, and that the lower cut-off frequency of the amplifier (resulting from the time constant defined by the bias resistance RB and capacitance of the piezoelectric sensor CS) is equal or slightly below the lowest frequency of interest. However, it should be noted that the network constituted by the bias resistance and capacitance of the piezoelectric sensor acts as a high-pass filter with respect to the signal to be measured, while it acts as a low-pass filter with respect to the noise generated by the bias resistance. While the time constant of the mentioned low-pass filter is proportional to the resistance, the noise voltage increases with the square root of the resistance value. As a result, noise properties of the amplifier should improve with the input resistance value. Therefore, it is preferable to have a bias resistance as large as possible to minimize the noise. Similarly, [A noise analysis of this first stage shows the importance of the current noise associated with the transistor and its biasing resistor as well as the channel thermal noise. milarly,  formulatv) is not introduced at the impedance converter stage is the capacitive nature of the source impedance. The gate-to-drain capacitance (Cgd) of the JFET is multiplied with a factor of (Av + 1) where Av is the small-signal gain of the impedance converter. The resulting capacitance is seen as a shunt capacitance from gate to ground. In the model of a piezoelectric sensor in its linear range this additional input capacitance  creates a capacitive voltage divider. Therefore, the effective gain at the output of the impedance converter is scaled with a factor ofThe output of the impedance converter is connected to a gain- and filtering-stage realized by an operational amplifier. In the previous section, the trade-off between transducer gain (sensitivity) and resonance frequency has been explained. As we are interested in capturing lung sounds that cover a frequency span up to 2 kHz, the signal level at the output of the impedance converter cannot reach sufficient amplitude to exploit the entire input range of the analog-to-digital converter (ADC). Therefore, a gain stage is needed between the impedance converter and the ADC. This gain stage also reduces the input-referred noise of the ADC. The answer to the imminent question why more voltage gain  noise of the electronics. Again, this filtering operation could also be realized at the impedance converter stage, by reducing the bias resistance RAmplified and filtered signals are quantized with a successive-approximation-register (SAR) analog-to-digital converter (ADC) providing 16-bit resolution and at a sampling rate of 5 kSamples/second . The digital output stream is sent to a central unit via an SPI communication protocol. The central unit collects the data from all the six modules present in the wearable sensor system and transmits them to an external post-processing unit for offline signal processing.A simplified schematic of the sound acquisition module comprising (i) the impedance converter, (ii) gain and filtering stage, and (iii) analog-to-digital converter is shown in PVDF film has a Curie temperature of about 125 °C ; thus, sIn order to characterize the sound acquired from the sensor, two typical auscultation points were considered to record respiratory sounds (positions 7 and 18 in ® Electronic Stethoscope Model 3200 (henceforth abbreviated as Littmann 3200) electronic stethoscope (benchmark) next to the sensor, using a tight strap around the person’s torso. The recorded signals contained tidal breathing, deep breathing, one fit of two coughs, and speech segments. All these instants were manually annotated to perform a comparative analysis.The respiratory sounds were simultaneously recorded with a 3M™ LittmannSpectral rolloff estimates the amount of high frequency in the signal by finding the frequency below which a defined percentage of the total spectral energy is contained .Spectral brightness estimates the amount of high frequency in the signal by measuring the amount of energy above a cut-off frequency .Spectral centroid is the center of mass of the spectrum.Spectral spread indicates the spread of the spectrum around its mean value.To compare the signals obtained with the sensor and the benchmark electronic stethoscope, the magnitude spectra of each signal acquired for the different auscultation points were determined. Moreover, four relevant audio descriptors were extracted to perform a descriptive and comparative analysis, namely spectral rolloff, brightness, centroid, and spread.atlab’s MIR Toolbox [The spectral features were extracted using M Toolbox .The magnitude spectra, as well as the described features, were extracted for the full signals, breathing, cough, and speech segments separately, as presented in A qualitative evaluation of the magnitude spectra shows for both auscultation points and different segments considered that the sensor’s amplitude decays rapidly, but remains almost constant from 400 Hz to 2000 Hz see . This beThis work reports the design and characterization of a wearable stethoscope module which is intended to be integrated in a vest for multi-channel lung sound acquisition. The sensing unit is made of a contact microphone based on a piezoelectric sensor. The physical interface materials as well as the piezoelectric film itself are optimized to minimize the acoustic impedance mismatch at different junctions.Based on a mechanical amplification approach that was introduced in , we haveAssembled modules have been benchmarked with a commercial electronic stethoscope which is widely used in clinical settings. Spectral analysis of the signals acquired under different conditions such as breathing, coughing shows that the information content can be positioned between two different modes of the commercial stethoscope. Considering that this stethoscope has built-in digital filters, mainly to provide a hearing experience similar to that of the acoustic stethoscopes, we expect that the manifested differences between our device (which does not have any filters within its flat band) and the benchmarking device can substantially be minimized by the introduction of digital filters. For instance, in the case of speech for both positions it is observed that the form of the magnitude spectra acquired by the presented sensor and the benchmark stethoscope  are significantly similar except that for certain frequency windows the signal acquired with the benchmark stethoscope are further highlighted or suppressed. The frequency windows where the signals are amplified or attenuated are in agreement with the literature  which inThe extracted features , do not In general, the sensor characteristics are in between the Littmann 3200′s bell and diaphragm filters, but closer to the bell one. This means that the sensor emphasizes lower frequency sounds, as reported in the analysis of the extracted features. Moreover, the wideband noise of the sensor is relatively high, which demonstrates the necessity to develop and implement of relevant digital filters.Future work will focus on applying high-pass filters on hardware level to suppress low frequencies, which may saturate the recording due to their high energy or may cause a reduction in the signal headroom; thus, compressing the response at higher frequencies . Except


This work discusses methods and experimental results on passive radar detection of moving ships using navigation satellites as transmitters of opportunity. The reported study highlights as the adoption of proper strategies combining target motion compensation and track-before-detect methods to achieve long time integration can be fruitfully exploited in GNSS-based passive radar for the detection of maritime targets. The proposed detection strategy reduces the sensitivity of long-time integration methods to the adopted motion models and can save the computational complexity, making it appealing for real-time implementations. Experimental results obtained in three different scenarios  comprising maritime targets belonging to different classes show as this combined approach can be employed with success in several operative scenarios of practical interest for this technology. Passive radar sensors are a very promising alternative to conventional systems exploiting dedicated transmitters. As is well known, the lack of the transmitting section lowers the costs of the system and its maintenance and enables covert operations, noticeably without the need of frequency allocations. Moreover, as the passive radar sensors do not emit any electro-magnetic radiation, the system is totally ‘green’ and hence installable in places where heavy active radars are undesired for their harmful radiations. While numerous studies focused on the exploitation of terrestrial-based illuminators, such as FM radio, analog/digital television, cell phone, and Wi-Fi signals, see for example ,2,3,4, mOne of the fields of application that can more enjoy the availability of signal sources in remote areas is the maritime surveillance. Maritime areas far from land, such as international waters and economic exclusive zones, cannot be reached by the radio waves emitted by ground-based transmitters, but are in the scope of few satellite sources. Suitable candidates are communication satellites such as Inmarsat and Iridium ,14, broaThe works ,17 are aFrom a conceptual point of view, the signal energy can be strengthened by extending the integration time. Open literature reports a number of approaches to realize long time coherent integration to improve the radar detection capability in spite of the migration of the moving target through the resolution cells . NeverthAlternative strategies to handle energy integration over multiple frames belong to the class of track-before-detect (TBD) methods. The TBD paradigm consists in not declaring detections at each integration window, but rather feeding the tracker with unthresholded datastreams, operating integrations over possible trajectories, and finally declaring detections for those trajectories with high merit functions . This tyIn this work, we address the ship detection problem in the GNSS-based passive radar by combining the TMC with this type of two-stage TBD strategy. The idea is operating a TMC procedure over a limited number of frames, such that the motion model has higher chances to hold. Although the integration gain achieved over few frames could not suffice for strengthening the returns enough, setting a low decision threshold allows increasing the probability of their detection. Obviously, the false alarm rate will increase consequently, making the detections not reliable. The subsequent TBD processing will exploit the space-time correlation among the plots to discard the not reliable detections. In other words, the TBD processor acts as a filter to separate the false from the true target detections. The main goal of this paper is to give experimental evidences of the possibility of fruitfully exploiting such a combined detection strategy for the detection of maritime targets with the GNSS-based passive system . To thiThis paper is organized as follows. The operative conditions are given by navigation satellites as illuminators of opportunity and a passive receiver to observe remotely the sea area of interest. The receiving hardware could be mounted on the land, for littoral traffic monitoring or for supporting port operations; it could be also mounted on a moored buoy for offshore surveillance such as sea boarder monitoring or marine trade route controls. As the GNSS signals are continuous-wave, a reformatting according to an equivalent pulse repetition interval (PRI) is previously performed. Usually, this is selected equal to 1 ms, i.e., the typical length of the PRN code. Let In passive radar, the goal of the detection processing is identifying the moving target (or multiple targets) and extracting its (their) bistatic range and Doppler position(s). The classical approach to detect the target is applying a Doppler filtering over a short time interval of the range-compressed data. In practice, this corresponds to apply a Fast Fourier Transform (FFT) over an individual frame of duration 2 and with carrier frequency 1176.450 MHz [−4, and probability of detection 2. To extend the detection range, longer integration times can be considered. Nevertheless, as aforementioned, extending the CPI is not practical due to the unpredictable fluctuations of the complex reflectivity. To overcome this limitation, a non-coherent combination can be considered, by performing a quadratic integration of the RD maps pertaining N successive frames.Let us consider a receiving system operating with a surveillance antenna with gain .450 MHz . For a tfound in ). As it 2 has been selected as example). For example, for To reduce the number of filters, the common practice is selecting a subset of values by making simplified assumptions on the variety of the observable motions. This can cause significant losses if the actual target motion sensibly deviates from the model, which can likely occur in the case of long integration times , therefore the frame to frame Doppler migration is given by -Range migration compensation—this step is fed by the data in the fast-frequency and Doppler domain. Therefore, after the Doppler migration compensation, a slow time FFT and a fast time FFT are implemented. While range migration inside each frame can be neglected due to the coarse range resolution , the frame to frame migration must be compensated. Form (4), the frame-to-frame range migration is composed by a range walk and a range curvature component, respectively described as -Motion-compensated RD map formation—a fast time inverse FFT allows finally achieving the motion compensated RD map.The basic-plane technique described in  implemenIt should be noticed that the procedure described above is completely adaptive except for the target Doppler rate. Therefore, a bank of M filters according to a grid of possible Doppler rates has to be considered. For the The design of the bank obviously requires a proper setting of the Doppler rates to be tested. In order to guarantee that the uncompensated Doppler variation among the integrated frames is completely contained in the Doppler cell, the sampling of the Doppler rate axis must respect the following rule:Each map of the stack is finally subject to a thresholding procedure according to a desired level of (i)As the procedure is based on a modelling of the motion, the performance can degrade in the case of model mismatches. Moreover, the model implicitly assumes the target as point-like. It should be noted that the sizes of ship targets of interest could be greater than the range resolution cell and that, depending on the particular motion conditions, the target energy could spread over multiple Doppler cells . Because(ii)For given bounds of the Doppler rate to test, the sampling rule (6) implies that the number of filters in the bank increases with the number of integrated frames, entailing a direct increase of the computational load.This approach has been proved able at increasing the ship detection capability of the GNSS-based passive radar system . NeverthA straightforward solution to overcome these issues is limiting the integration at few frames, so that the motion model has higher chances to hold and the number of filters in the bank is such that the computational load is still affordable. As low Let us consider the TMC and multi-frame integration performed over By performing the procedure over successive scans, the TBD processor receives in input the current plot-list and correlates it with the past The basic structure of the TBD processor implements the dynamic-programming algorithms defined in , but herThe track formation stage correlates the plots taken from The formation of admissible tracks requires the definition of physical constraints on its evolution. Let As no measurement of the Doppler rate variation is provided in the plot list, the expected Doppler rate can be defined as a value belonging to an interval defined according to the maximum expected target velocity and acceleration. Denoting these as Therefore, the current plot Each track is also scored by a vector storing the intensities of the individual plots. In the case of a missed detection, such a vector is filled with a null entry in the corresponding position.After the track formation, it could happen that some plots belong to multiple tracks. To solve this ambiguity, a pruning of the track is implemented, which assigns the common plots only to the track exhibiting the highest score defined as the sum of the intensities of the individual plots belonging to the track.The pruned tracks formed by a number of plots lower than (1)It could be noticed that the kinematic rules for plots correlation are still based on a linear Doppler model, as in the TMC. However, this model has to hold only inside each scan, while the technique allows to integrate returns from plots having different Doppler rates (because of (11) and as depicted in (2)The integration is no more constrained by the resolution cells, as the TBD processor links plots having the highest intensity within an admissible RD area.(3)The inclusion of proper margins in range and Doppler further relaxes the impositions on the target kinematics, so that the processor can handle deviations between the theoretical and actual motion model, including the presence of multiple scattering centers in the case of extended targets.Some final considerations are now in order:In this section, it is shown as the proposed strategy can be fruitfully exploited in scenarios of practical interest. To this purpose, real data collected during three experimental campaigns have been used. The receiving hardware used during the acquisition was a superheterodyne receiver mounted onto a van, which was also equipped with an automatic identification system (AIS) receiver to register in real time the actual locations of ship targets of opportunity. (The photographs and the information about the size of the ships of opportunity reported in this section have been taken from .) DuringA first acquisition campaign was carried out near the Marghera port, Italy. The receiver was placed at the entrance of the port area, with the radar antenna pointed toward the terminal area, as depicted in −4, 10−3, or 10−2. The corresponding plot lists are sent to the TBD processor that uses L = 8 scans to confirm the detections. As the interval between two scans is set equal to 5 s, the overall dwell to get the final decision is 45 s. It should be also pointed out that, in this particular scenario, the targets move along an a priori known direction, as all the ships follow the route to entry/exit the port area. As the receiving antenna boresight is aligned onto this direction, it is expected that all the targets exhibit a dominant radial motion, namely a negligible Doppler rate. Therefore, in these particular conditions, the TMC has been performed by considering a priori known and equal to zero the value of the Doppler rate.The experimental and signal processing parameters are listed in −4, 10−3, and 10−2, respectively. The greater number of alarms achieved lowering the threshold is easily observed. In these figures, the red markers denote the plots confirmed after the TBD processing: It can be observed as the false measurements have been correctly discarded, while the surviving plots form tracklets that are compared with the AIS ground truths in -−4, 10−3, and 10−2, respectively.Fairpartner has been correctly detected in almost all the epochs in which it was in the FOV for all the considered -−2 and evaluating the detection rate as the number of scans in which it gave rise to a confirmed detection over the overall scans, we move from 33% and 58% for −4, 10−3, respectively, up to 89% when −2.The use of the lower threshold allowed detecting Tailwind (which is at a higher distance than Fairpartner) for a longer interval, as it can be easily observed by comparing the tracklets in -−3 and 10−4, it has not been detected. Nevertheless, using the proposed approach with a lower detection threshold (−2), it was nicely detected.Neptun is a small target, which has small chances to be detected. In fact, with conventional processing involving A second acquisition campaign was carried out at the Venice lagoon, Italy. The receiver was placed on the West side of the Venice Lido Island with the surveillance antenna pointed toward the waterway crossing the lagoon see a,b. Duri−4 and 10−2.The experimental and signal processing parameters for this acquisition are listed in sholding d, the weA last experimental campaign has been carried out near Bonn, Germany. In this case, the receiver was placed on the shore of the Rhine observing the river traffic, mainly composed by barges and inland cruise ships. During a two mins acquisition, four targets were in the FOV. They were the passenger ships Godesia (38.6 m by 8.6 m) and Filia Rheni (42 m by 11 m), moving away from the receiver, and the two motor tankers Oranje Nassau II (110 m by 13.5 m) and Marsja (110 m by 11.44 m), approaching, whose AIS ground truths are shown as full lines in −2. The remainder of the processing parameters are listed in Two Galileo satellites were simultaneously tracked so that the detection processing was performed for both the resulting bistatic geometries. For the TMC the full Doppler rate bank has been used and the It is worth to point out that in the case of multistatic acquisitions the system is potentially able to localize the targets. Usually, this is obtained via multilateration methods, consisting in intersecting bistatic range ellipsoids obtained at each epoch . HoweverThis paper explored as using a two-stage detection strategy relying on target motion compensation and track-before-detect processor could be fruitfully exploited to enable maritime surveillance with a GNSS-based passive radar. The unfavorable power budget provided by navigation satellites requires in fact proper detection techniques to improve the detectability of ship targets of interest. The multi-frame integration performed over a limited number of motion compensated frames potentially allows target actual kinematic to fit to the motion model for the compensation of the range and Doppler migration. Although the integration gain achieved over such limited dwells could not suffice to strengthen the target energy sufficiently, the use of a low threshold can ameliorate this problem and allow the target detection. Exploiting the space-time correlation among successive plot lists, the subsequent TBD processor can filter out the false alarms, providing in output high reliable detections, furthermore with their temporal evolution.The effectiveness of the approach has been tested in a number of experimental case studies, including different scenarios and targets belonging to different dimensional classes and undergoing different types of motion. The achieved results have shown as this detection strategy may increase the detection capability of the system under a variety of situations of practical interest.Next stage of this research is exploring as the proposed framework can be used in the multistatic configuration  to ameliorate the localization performance of multilateration algorithms.


Mimicking angiogenetic processes in vascular territories acquires importance in the analysis of the multi-scale circulatory cascade and the coupling between blood flow and cell function. The present work extends, in several aspects, the Constrained Constructive Optimisation (CCO) algorithm to tackle complex automatic vascularisation tasks. The main extensions are based on the integration of adaptive optimisation criteria and multi-staged space-filling strategies which enhance the modelling capabilities of CCO for specific vascular architectures. Moreover, this vascular outgrowth can be performed either from scratch or from an existing network of vessels. Hence, the vascular territory is defined as a partition of vascular, avascular and carriage domains  allowing one to model complex vascular domains. In turn, the multi-staged space-filling approach allows one to delineate a sequence of biologically-inspired stages during the vascularisation process by exploiting different constraints, optimisation strategies and domain partitions stage by stage, improving the consistency with the architectural hierarchy observed in anatomical structures. With these features, the aDaptive CCO (DCCO) algorithm proposed here aims at improving the modelled network anatomy. The capabilities of the DCCO algorithm are assessed with a number of anatomically realistic scenarios. Manifestation of abnormal signals in mid- and large-sized vessels and in whole-organ function is a consequence of the two-way coupling between growth and remodelling, and even loss of functional response of arterioles and capillaries, and the global systemic hemodynamic environment15. This interplay between peripheral and central vascular mechanics, mediated by proper chemical balances at the cell level and by blood pressure, blood flow and wall shear stress at the systemic level, is a clear example of the multi-scale nature of the circulation.In the field of cardiovascular research, many circulatory diseases found in global or regional circulations begin with a dysfunctional chemo-mechanical pairing that governs the interaction between peripheral (arteriolar and capillary) blood flow and cellular functions20. Experimental approaches to answering questions involving such intricate mechanisms have a limited range of spatial scales. Therefore, mathematical models and computational simulations of the circulation and its coupling with cellular function provide powerful tools to push the boundaries of cardiovascular research26. However, the realisation of the domain of definition at a microvascular level is required for the blood flow models and cell coupling. This can be achieved by resorting to imaging techniques, which are capable of delivering high resolution images of small vessels in animal models. However, even with the power of these tools, their applicability to different vascular territories is rather constrained, as is the translation to humans30.Because of the highly variable and diverse cell expression, the study of such multi-scale problems requires a proper mapping between cell function and cell location with the architecture of vascular territoriesA solution to circumvent the lack of information about the vascular architecture of peripheral beds was found through the development of methodologies aimed at generating vascular networks in an automatic manner, driven by physiological criteria and in compliance with a set of morphometric constraints and empirical laws. The so-generated networks of vessels can be statistically consistent with the anatomical descriptions in the sense that they can reproduce the main topological features and functional response observed in vascular networks.35. The second class of algorithms allows one to generate a network of vessels inside a vascular territory defined in (2D or 3D) space47. A particular class of such space-filling algorithms is termed Constrained Constructive Optimisation (CCO) because the sequential generation of the vessel network is driven by the constrained minimisation of a cost function. Recently, methods for sprouting angiogenesis have also been proposed to study the angiogenic process involved in the formation of new blood vessels48.There are two classes of algorithms for the automatic generation of vascular beds: i) Fractal algorithms; and ii) Space-filling algorithms. The first class of algorithms can easily follow statistical models of the main morphometric measures , regardless of the shape of the vascular territory53, bifurcation asymmetries55, fractal properties56, staged-growth57, shear stress distribution59, among others62. Variants have also been proposed either to recreate more complex vascular networks in hollow organs64, or to speed-up the construction of such networks65. More recently, cases of territories supplied by multiple inlet vessels were the focus of attempts to tackle more realistic scenarios. In Blanco et al.45, Ii et al.46 and Di Gregorio et al.47, partitioning of a territory into subdomains was proposed so that the CCO algorithm could independently be applied to vascularise non-overlapping subdomains. Meanwhile, Jaquet et al.66 proposed to solve concurrency by assigning a relative flow quota for each input, while those who temporally exceed their quota are put on hold. Additionally, the latest works focused on describing whole-organ microvasculature67 defining multiple steps to generate a physiologically accurate tree. Each strategy defines different ad-hoc steps depending on the specific organ. In this work, we propose a staged growth strategy generalising the definition of such steps for the vascularisation of different tissues.In particular, the family of CCO algorithms addresses different types of study involving the influence of anatomical variability69. Similarly, the use of automatically generated networks in practice has mainly been restricted to academic cases or specific organs with a simplified description of the perfusion, because of intrinsic limitations in the generation procedure. For example, the use of fractal networks to assess closure boundary conditions in hemodynamic simulations71, or the use of CCO networks to predict the arteriolar pressure in the brain72. More detailed generated networks have been proposed for heart66 and brain67 following a methodology specific for the organ of interest.Some contributions have reported results of blood flow simulations performed with vascular networks reconstructed from images of animal models74, it is also possible to foresee in silico models of human physiology with an unprecedented level of vascular detail, by including arterioles and capillaries specifically tailored for each vascular territory across the whole model, making possible the coupling with organ-specific physiology.In this work, we extend the capabilities of the traditional CCO algorithm, aiming to develop a general-purpose versatile approach for the generation of vascular networks in complex geometrical domains and, also, enhance the modelling capabilities to encode architectural features and constraints in the derived anatomical description. One example is the possibility of automatically generating vessels of networks either from scratch or from already existing networks of vessels. In fact, generation of networks from existing data  is extremely important in providing a viable solution for the (still open) problem of setting patient-specific boundary conditions in hemodynamics. If the domain to be vascularised is known, and the larger vessels that supply such a territory are known, then it is possible to provide an anatomically consistent patient-specific completion of the vascular network. Moreover, if we consider studies employing the framework provided by the Anatomically Detailed Arterial Network (ADAN) modelSpecifically, we propose an aDaptive CCO (DCCO) algorithm that can be used to vascularise empty regions of space as well as to fill pre-existing vascularised domains with additional vessels. The method is termed as adaptive because it provides new features to change the behaviour of the CCO –through different optimality criteria, vessel bifurcation sites, geometric constraints– across the filling procedure. This is accomplished by establishing staged hierarchies and constraints along the network generation process, being driven by possibly adaptive optimisation criteria. This flexibility in the setting of constraints and the cost function enables one to establish a connection between the vascularisation processes and underlying biological mechanisms. In fact, while the vascularisation of a certain organ from scratch can be viewed as a global architectural process, the addition of small vessels to an already highly vascularised region could be driven by models of angiogenic stimuli, for which optimisation criteria differ.74 in anatomically representative territories of the human body. For the various examples discussed here, we report the statistical properties of the circulatory networks obtained from the applied vascularisation processes.We test the DCCO algorithm for the generation of vascular networks in academic scenarios with simple domains and also in realistic scenarios involving multi-stage vascular outgrowth, starting from existing vascular networks taken from detailed human modelsIn this section, we introduce the standard CCO techniques followed by our extended approach as a set of new features and modelling tools. "e.g. Schreiner et al.49), the criterion was engineered to minimise the biological infrastructure and energy expenditure for blood supply to the surrounding tissues. In this case, the optimisation problem for the vascularisation of a territory Q such thati-th vessel of the tree N is the total number of vessels of CCO methods provide an algorithmic approach for the construction of a binary vascular tree through the minimisation of a biologically-inspired cost functional. From early works in the field  with the chosen viscosity model.More complex models for viscosity –v to 56, we fix the radius of the vascular inputs and the domain size, since such an approach offers advantages for the extensions proposed in the following sections. To generate a new vessel, a terminal point is randomly created following a uniform distribution across the entire domain and is then attached to A vascular tree is generated by incrementally adding vessels one by one. After the addition of each vessel, the vascular tree is remodelled to meet the geometric and hemodynamic restrictions. In that manner, the tree optimisation problem  is approx, and the current tree x and D are, respectively, the characteristic length and dimension of It is noteworthy that random (uniform) generation of terminal points may be prone to imbalance for a certain region of the domain, due to a biased early growth of the tree. Assuming a convex domain, balanced trees are more efficient in terms of tree volume and energy expenditure. Because the early steps of the tree generation determine the main topological features of the tree, it is the key to promoting a homogeneous dispersion of such points . Thus, a minimum distance constraint between a new terminal point, say mentclasspt{minimai.e.,In the definition of mentclasspt{minima satisfy .i.e. such that the vessel belongs to i.e., 51 to update the tree radii, based on a fixed-point scheme, as introduced in Algorithm 1. Once a new plausible terminal point has been obtained, we must find the connection point in ptimises  while samentclass2pt{minimmentclass2pt{minimi.e., we search for the vessel Taking into account all the descriptions above, we formulate a procedure to generate the vascular tree atisfies  with an 57, where the CCO domain grows as a function of an elapsing pseudo-time which evolves as terminals are added to the tree. Interestingly, dominant directions of the domain growth imprint an anisotropic pattern in the vascular tree. In our proposal, the concept of stage is rather different. Here the stage is a static problem where a tree grows by adding a given number of new terminals. Also, each of them may involve a different domain , different geometrical or hemodynamic parameters and different growing conditions  sequential vascular growth; (ii) hierarchical perfusion; and (iii) scale-specific vascularisation patterns. Consider in the following descriptions the schemes displayed in Fig. The following sections introduce new strategies that enhance the staged growth capabilities to attain highly customised vascular architectures.This case embraces the simplest scenario in which a given domain is vascularised, then another domain is vascularised –with possibly different parameters–, and so on. For example, a pre-existing tree  and \doentclass1pt{minimaThe proposed formulation allows us to weigh contributions related to growth factor expression and the parent vessel remodelling. Particularly, the degradation term favours smaller parent vessels while the growth-signal diffusion term favours closer parent vessels to the new terminal point. By selecting appropriate values of the weighing parameters, we obtain a balanced vascularisation of the tissue in term of its inputs . These Most organs in the human body present a heterogeneous blood flow distribution. The particular distribution pattern depends not only upon constitutive and functional characteristics of the underlying tissue such as cell metabolism, density and phenotype, but also upon the chronological record of developmental events. Thus, the generation of physiologically compatible vascular trees must be endowed with a mechanism to prescribe distribution criteria in the vascularised domain which can mirror prior knowledge about that specific territory.Q across a certain domain M terminal vessels. In that setting, all terminals are assumed to have the same outflow As previously stated in "Q. In Fig. Another important physiological aspect is that not the entire blood inflow is to be distributed in the domain. Some vessels may divert part of the flow to adjacent vascular territories. To model this behaviour, the vascular tree is bestowed with a certain number of distal arteries with prescribed outflows, denoted as N-ary tree  description of the vasculature can be available for different organs or tissues. Once the geometrical description is modelled as a ree see "" sectionree see " that areHere, we summarise two other minor contributions of the proposed DCCO approach.Two different constraints are proposed: (i) the bifurcation angle mentclass2pt{minimN-ary tree where an arbitrary number of vessels can branch at each junction. This feature enhances the capabilities to represent pre-existing vascular descriptions from anatomic atlases or medical images , where we defined the position of the central retinal artery based on anatomical definitions of the ADAN model74 . As initial condition In this second case, we vascularise the grey matter tissue in the left frontal gyrus of a prototypical human brain. Its geometrical definition was based on a human brain reconstruction from BodyParts3D database  mentclass2pt{minim83. All main branches perfusing the gyrus are well developed providing significant blood flow to the tissue. In Fig. distal vessel branching behaviour . The three functionally different layers, namely serosa, muscularis and mucosa layers, were modelled using a thickness ratio of 1:4:3. As initial condition non-branching vessels with exception of the perforator terminals located at the gastric, gastro-omental and splenic arteries which were modelled as distal perforator vessels.As a final case, we built a vascularisation for the stomach following the anatomical description presented in Geboes et al. and Gorczyca et al.The vascularisation process was modelled through five stages. The first stage is responsible for growing the main vessels of the subserosal plexus, which is achieved by optimising a sprouting cost functional. The strategy ensures a homogeneous proliferation of all perforator vessels from the posterior side, lesser, and greater curvatures alike. Then, a second stage completes the plexus using a volumetric cost functional, providing a more volumetric efficient arborisation. The third stage generates muscularis perforators from the subserosal plexus to the mucosa layer. These are straight vessels that run orthogonally to the layer, and which are generated by imposing angle constraints. The fourth stage relaxes the angle constraints and develops the submucosa plexus from the muscularis perforators using the conventional volumetric cost functional. Finally, the fifth stage vascularises the muscularis layer from both the muscularis perforators and the submucosa plexus.84 where the subserosal plexus delivers a homogeneous perfusion to the serosal layer, while perforators arising from this subserosal network feed the submucosa plexus. Lastly, the blood to the muscularis layer is provided simultaneously by such serosal perforators and by the submucosa plexus. The complex architecture of this organ rendered a more complex distribution of vessel radii at all stages due to the presence of vessels transporting blood to the neighbour at all regions . Figure The resulting vascular tree see Fig.  is in quVessels with such a transport role present larger diameters proportional to their effective distal resistance, producing a larger radius mode in the distributions than terminal vessels in the same region . The particular cases presented in Fig. in vivo imaging techniques are only capable of rendering vascular structures with a pixel resolution of 86, hindering in vivo examination of microvasculature in healthy and pathological scenarios. In turn, ex vivo examination88 yields a detailed description of the microvascular architecture. As shown in the previous section, the proposed approach allowed the construction of different vascular architectures whose features resemble those reported ex vivo. We accomplished this by using a reduced number of growth stages with a proper rationale to select parameters and model each vascular stage. Moreover, the initialisation of the DCCO processes was performed with arterial geometries and blood flow measurements in the same manner as could be performed in an in vivo setup, initiating the process from medical images. As a result, the proposed methodology enables the generation of in silico models encoding refined architectural knowledge of the vascular tree delivering microvasculature models which are anatomically compatible with the available data. Moreover, if additional clinical data is available, further specialisation of the model can be achieved by using the blood flow distribution techniques presented in "The techniques introduced in this work constitute a set of modelling tools to generate vascular networks compliant with anatomical knowledge, broadening the range of applicability and capabilities from models reported in previous works. Most traditional As demonstrated from the examples reported in the previous sections, different tissues and organs feature specific vascular architectures associated with corresponding embryonic, developmental, and remodelling driving-forces. As a consequence, this imprints intrinsic characteristics onto the hemodynamic response and perfusion. Thus, it is expected that physiologically compatible models for representing the peripheral beds should reproduce the specific architectural patterns that account for the proper and specific functional response of the tissue. Hence we developed our approach to offer expressive modelling capabilities which enable the instantiation of a myriad of vascular layouts in the loci of interest, enhancing the customisation characteristics of previous CCO approaches, and aiming to improve the description of anatomical structures.N-ary tree; (ii) prescribing the bifurcation behaviour at the given (and generated) vessels ; and (iii) prescribing outflows (i.e. known data) to adjacent vascular territories.In such regard, the use of staged growth allowed us to model particular features at each step, simplifying the modelling of a complex architecture in a divide and conquer manner. At each stage, the goal was to focus on a particular anatomical feature such as balanced vascularisation from the inputs , homogeneous vascularisation , generation of perforator vessels across subdomains (perforator vessels), communication between domains (transport vessels), or constraining the geometrical characteristics at a given region or spatial scale . Also, the definition and interaction with initial conditions, such as patient-specific vascular networks reconstructed from MRI or CT imaging modalities, have been enhanced by: (i) generalising the tree representation as an a priori. Moreover, the change in the network statistics experienced by each branch subtree through the growth stages is not a simple scaling, but is the result of the interplay between cost function, the topology of the domain to be perfused, and the set of parameters. This emphasises the fact that the proposed algorithm is endowed with the versatility and flexibility to embody networks of vessels with different probabilistic features concerning vascular geometry and connectivity.The analysis of the vessel radius distributions for the cases of the cortex and the stomach see Fig.  show thaNonetheless, there are still difficulties that must be addressed to reproduce certain anatomical scenarios. Vascularisation over curved shell-like domains such as organ surfaces or interfaces present a challenging task when using linear segments because they may fail to be constrained to the geometry of the vascular territory. The projection of these vessels over the domain would offer a solution although more expensive computations are required. In this work, we tackled this problem in the brain cortex case by extruding its surface inwards, generating a thin shell volume. Such a workaround yielded a proper cortical network to the detriment of a more computationally intensive optimisation procedure due to the large number of trials required to generate vessels inside the thin domain. Another challenge yet to be addressed is the generation of a vascular network with a graph-like topology. Anastomoses between arborisations are widespread throughout the different vascular scales in the cardiovascular system. The problem of introducing such capabilities to the DCCO  is that the heuristic optimisation strategy employed is not appropriate for graph structures. Furthermore, the way to proceed with the recruitment of anastomotic connections is not entirely clear.e.g. up to e.g. order of 42 to obtain a larger speedup. Note that the latter small-scale vessels are expected to be more homogeneous without different architectural traits, and the vascularisation could be executed in an “embarrassingly parallel” manner.It is important to mention that the methodology presented in this work aims at the generation of vascular networks from arteries/veins to pre-capillary levels, where the main features of the vascular network are reasonably described by a tree-like structure. The methodology has no theoretical impediments for the generation of large networks  were fixed for all cases, to demonstrate that no fine-tuning of the parameters is required to model the construction of the vascular architecture. At this point, it is important to highlight that the main focus of this work was to present a new set of modelling tools with potential to generate complex models.Finally, the generation of vascular networks in an automatic manner, either from scratch or from initial available data is of the utmost relevance to set the geometrical substrate for physiological models to be applied and explored. The anatomically-consistent disposition of the different generations and layers of arterial/venous vessels is crucial to embody physiological knowledge acquired at the different spatial scales in the human body, and to enable the study of mechanistic interactions among cellular function, microvascular physiology, tissue perfusion, and, eventually, whole-organ function.We introduced the aDaptive CCO (DCCO) as an approach for the generation of vascular networks with a set of functional and architectural traits. This work describes the algorithms that materialise DCCO and, also the rationale for modelling the necessary stages to achieve different and diverse anatomically-realistic representations of the vasculature.Three complex anatomical scenarios were modelled –the retinal layer, a section of the superior frontal cortex, and a three-layered description of the stomach– reproducing experimental observations reported in previous works. To the best of our knowledge, the anatomical detail achieved with the proposed approach is not attainable with other CCO-based techniques.In addition, further extensions were made to integrate the automatic vascularisation process with available data, such as that obtained from medical images or detailed models of the cardiovascular system. These features allow us to use DCCO in patient-specific geometries, enabling new research opportunities to explore the role of small-scale vessels and their physiological characteristics into different clinical scenarios.


Despite the wide use of scaffolds with spherical pores in the clinical context, no studies are reported in the literature that optimize the micro-architecture dimensions of such scaffolds to maximize the amounts of neo-formed bone. In this study, a mechanobiology-based optimization algorithm was implemented to determine the optimal geometry of scaffolds with spherical pores subjected to both compression and shear loading. We found that these scaffolds are particularly suited to bear shear loads; the amounts of bone predicted to form for this load type are, in fact, larger than those predicted in other scaffold geometries. Knowing the anthropometric characteristics of the patient, one can hypothesize the possible value of load acting on the scaffold that will be implanted and, through the proposed algorithm, determine the optimal dimensions of the scaffold that favor the formation of the largest amounts of bone. The proposed algorithm can guide and support the surgeon in the choice of a “personalized” scaffold that better suits the anthropometric characteristics of the patient, thus allowing to achieve a successful follow-up in the shortest possible time. One of the main issues recently investigated in the field of bone tissue engineering and that has received substantial attention is the identification of the optimal geometry of bony tissue scaffolds to support the numerous cellular activities involved in bone formation and regeneration . ScaffolIn general, bone tissue scaffolds can be classified into two principal categories: irregular and regular. Regular scaffolds are fabricated using advanced manufacturing processes such as additive layer manufacturing (ALM) that allow controlling with high precision the specific dimension of the single unit cell the scaffold is made from. The irregular scaffolds are fabricated with conventional physical-chemical processes that allow controlling the average dimensions of the scaffold microarchitecture only on a statistical base . A typicA very interesting scaffold topology is that including spherical pores. It is commonly known that the adhesion and differentiation of stem cells take place more easily on curved surfaces, especially on concave surfaces ,7. ScaffL = 2.548 mm and including 4 × 4 × 4 = 64 unit cells was developed. The same scaffold dimensions were utilized in previous studies : , , , which are close to the typical dimensions of pores commonly adopted in scaffolds for bony tissue [UAF = 0.1 MPa. The displacement u2 , which are the optimal dimensions of the scaffold micro-geometry to achieve a successful follow-up with the formation of the largest amounts of bone in the shortest possible time? In fact, if one knows the anthropometric characteristics of the patient, they can hypothesize the possible value of load acting on the scaffold that will be implanted, and through diagrams such as those shown in In this study, using a mechanobiology-based optimization algorithm, we computed the optimal dimensions of the micro-architecture of scaffolds including spherical pores and cylindrical interconnections. The optimization algorithm perturbs the scaffold geometry until the specific dimensions that favor the formation of the largest amounts of bone are identified. The proposed algorithm can guide and support the surgeon in the choice of a “personalized” scaffold that better suits the anthropometric characteristics of the patient, thus allowing to achieve a successful follow-up in the shortest possible time.