No abstract. Evidence, Information, Knowlegde) principles for patient safety. The new book appears to successfully complete the daunting task of extrapolating the ¿dry¿ theoretical aspects of interest to librarians and patient safety professionals, to relevant clinical processes and applications of interest to practicing physicians (including surgeons).The published literature on patient safety principles is largely anecdotal and the evidence-based knowledge in the field remains scarce. Lorri Zipperer, the editor of this new and groundbreaking book (Box), has to be commended for her effort in providing a fresh perspective on the impact of ¿EI&K¿ , allows for the reader to easily comprehend the complex content of this book, particularly from a clinician¿s perspective.The textbook is structured into five main sections. These include an introductory part on the basic context for innovation and improvement, followed by three specific sections devoted to the ¿EI&K¿ paradigm and its practical applicability in patient safety, and finalized by a section dedicated to future perspectives. Each chapter is written by distinguished experts in the field. Multiple tables, ¿infoboxes¿, and algorithms enhance the readibility of the individual chapters. In addition, the appendices at the end of the book serve as a valued resource to the reader. For example, appendix 1 provides a concise and highly appealing historic timeline on the evolution of patient safety, stratified from a ¿sporadic period¿ and a ¿cult period¿ to the current ¿breakout period¿ of the 21st century following the publication of the Institute of Medicine¿s seminal report, The key objective of this textbook is to inform healthcare professionals about the relevance of EI&K to core principles of patient safety, and their applicability in the clinical setting. The book furthermore raises awareness of the potential for failure of EI&K processes in the extrapolation to the clinical practice, and outlines the underlying root causes of failure.Beyond a doubt, this meritorious work was desperately needed, and will hopefully allow to foster the ¿buy-in¿ and support by healthcare providers in sustaining and growing the current global momentum of the patient safety initiative.


Human memory can store large amount of information. Nevertheless, recalling is often a challenging task. In a classical free recall paradigm, where participants are asked to repeat a briefly presented list of words, people make mistakes for lists as short as 5 words. We present a model for memory retrieval based on a Hopfield neural network where transition between items are determined by similarities in their long-term memory representations. Meanfield analysis of the model reveals stable states of the network corresponding (1) to single memory representations and (2) intersection between memory representations. We show that oscillating feedback inhibition in the presence of noise induces transitions between these states triggering the retrieval of different memories. The network dynamics qualitatively predicts the distribution of time intervals required to recall new memory items observed in experiments. It shows that items having larger number of neurons in their representation are statistically easier to recall and reveals possible bottlenecks in our ability of retrieving memories. Overall, we propose a neural network model of information retrieval broadly compatible with experimental observations and is consistent with our recent graphical model (Romani et al.,  Human long-term memory capacity for names, facts, episodes and other aspects of our lives is practically unlimited. Yet recalling this information is often challenging, especially when no precise cues are available. A striking example of this deficiency is provided by classical studies of free recall, where participants are asked to recall lists of unrelated words after a quick exposure Murdock, . Even foSeveral influential models of recall were developed. Some of them were driven by the description of behavioral aspects  model, items presented for recall acquire a set of mutual associations when stored temporarily in working memory buffers Jij=i such that rthresh. This threshold is chosen so that two memories are never recalled simultaneously. If in a given time interval, e.g., from time 0 to T, the state of the network was in memories μ1, μ2, μ3.. at different times, we say that the network has “retrieved” these memories in a time T.Memory μ is recalled if the average firing rate of neurons corresponding to memory μ   and temporal contiguity (J+ = J− = 0). To quantify the degree of memory activations we introduce the “overlaps” defined as in Amit and Tsodyks {mμ(m0(t) measures the average firing rate in the network at time t, each mμ(t) measures the difference between the average firing rate of neurons encoding memory μ and all other neurons:While r for each neuron i given the set of m′s. Pluggin Equation (10) into Equation (7) we obtain a a system of P + 1 equations for the overlaps m′s. The solutions to such a system are the possible fixed points of the network. Consider a vector i. There are 2P possible realizations of vector ηi that are denoted by a random vector v ∈ {0, 1}P where each component is indipendent from any other being 1 with probability f and zero otherwise. Each realization of v identifies a population of neurons. We say that neuron i belongs to a population v if ηi = v that is v belongs to a memory μ if vμ = 1  the synaptic currents can be expressed via the values of the overlaps:The cardinality of a vector is defined asv is:v is:The probability for each vector N → ∞ in terms of these population vectors. Plugging Equation (10) into Equation (7) and summing up we obtain in the limit N → ∞:Sv as:The fixed point solutions can then be characterized in the limit ansatz of the solution it is possible to determine the region, in the parameter space, for its existence and stability. The type of solutions that we analyze are those that represent either a single memory or the intersection between memories. The correct ansatz for these solutions are easily expressed in terms of the synaptic currents. A single memory solution is then defined by the following conditions:This system determines the fixed points of the network in the meanfield limit. It cannot be solved in general but for a given v that belongs to the active memory μ are uniformly above threshold cv + θ > 0 if vμ = 1;the currents to each population cv + θ < 0 if vμ = 0;the currents to each population that doesn't belong to the active memory μ are below threshold m different from zero is the one of the active memory mμ. Similarly we define the ansatz for the intersection between two or more memories. In this state only two overlaps m are different from zero. For each of these ansatz one can find its region of existence and stability in parameter space. In such a region the solution is steady state of the system. A detailed theoretical analysis of these regions goes beyond the scope of this paper and will be presented in a future publications.This two conditions define our ansatz for a single memory state. From this definition it follows that in the state of single memory the the only overlap N = 105 neurons. To achieve this goal we simplify the system in Equation (2). This is a dimensionality reduction of the network that reduces the number of simulated units. All the neurons that have the same vector ηi  can be described by a single unit. For these neurons the afferent connections given by the matrix J are identical. Each neuron receives the same input and projects equally on other neurons. It is not possible to differentiate their activity except for the effect of the noise term ξ. But in Equation (2) we can average terms which share the same connections averaging also their noise. For a given realization of the network we can write the fraction of neurons in a given population v as:N → ∞. Defining cv(t), the averaging synaptic current c(t) for a neuron in population v at time t, it is then possible to write an equation for the dynamics of cv(t). By summing Equation (2) over all neurons which belong to the same population v we obtain:To study the influence of finite size effects and noise on the dynamics of the network we simulate the dynamic of a network of v and w are binary vectors of length P identifying different populations. The system of Equation (17) is a reduction of the original system of Equation (2), it has 2P equations instead of the N. In this reduction the only piece of information which is not accessible is the precise value of the firing rate of each single neuron. Only the average firing rate of the population it belongs to is now accessible. The actual number of equations to simulate depends on the particular realization of the network given by the choice of ηP}μ∈{1... Although in principle the system has 2P equations, in practice, due to the finite size of the network and its sparse connectivity, there are much less populations since Sv = 0 for most v  to the ≈1000 of the reduced one of Equation (17).The vectors Ntrials. For each simulation the network is initialized in the state of a single, randomly chosen memory μ. In this state all the populations v which belong to memory μ are initialized to a rate rini while the others are initialized to a zero rate. In the model the transitions between memories are triggered by oscillations of the variable φ. This oscillates sinusoidally between the values φmax and φmin. The oscillations have a period τo which is much larger than τ so that the network is undergoing an adiabatic process. Integrations of Equation (17) are performed with the Euler method with a time step of dt and the simulated interval is [0..T]. The total number of cycles of oscillations is T∕τo.Simulations are run according to Equation 17) employing the parameters in Table 7 employiThe data analyzed in this manuscript were collected in the lab of M. Kahana as part the Penn Electrophysiology of Encoding and Retrieval Study. Here we analyzed the results from the 141 participants (age 17–30) who completed the first phase of the experiment, consisting of 7 experimental sessions. Participants were consented according the University of Pennsylvanias IRB protocol and were compensated for their participation. Each session consisted of 16 lists of 16 words presented one at a time on a computer screen and lasted approximately 1.5 h. Each study list was followed by an immediate free recall test. Words were drawn from a pool of 1638 words. For each list, there was a 1500 ms delay before the first word appeared on the screen. Each item was on the screen for 3000 ms, followed by jittered 800–1200 ms inter-stimulus interval (uniform distribution). After the last item in the list, there was a 1200–1400 ms jittered delay, after which the participant was given 75 s to attempt to recall any of the just-presented items. Only trials without errors  were used in the analysis.Figures 5B,D. Of all the trials we exclude those where items not belonging to the presented list were reported (intrusions) and those where at least one word was retrieved twice (repetitions). For each list we then associate to each pair of words their LSA score as obtained from online datasets. We then consider the pairs formed by orderly associating two consecutively reported items. For each of these pairs we obtain the transition rank by ranking the LSA score the pair among all the scores of the first item with any other word in the list. As there are 16 words the maximum rank is 15 and the minimum is 1. This is the quantity shown on the x-axis of Figure 5B.We analyze this dataset to validate our model. We investigated several aspects of the dataset as described in Katkov et al. , 2015. HFigure 5B vs. the LSA score of the same pair.For each pair of consecutive reported items we compute the IRT by the difference of their times of retrieval. This is the quantity shown on the y-axis of Q memories. These solutions are characterized by Q positive overlaps: m1 = … = mQ = mactive. The overlaps have all the same values as all the active neurons in the intersection of Q memories fire at the same firing rate. The precise solution depends on the choice of the gain function in Equation (3). For concreteness, we chose a saturating gain function with threshold, with the exponent of γ = 1∕2 that allows analytical solution. The solution to Equation (15) ismactive and minactive are respectively the value of the overlap for an active and inactive memory and m0 denotes the average activity of the network. f denotes the sparseness of memory representations, k scales the strength of the recurrent associative synapses and φ defines the relative strength of inhibition, Figure The main principle of recall that was suggested in Romani et al.  is that Based on this analysis, we simulate the network while modulating the inhibition to cause the transitions between these two states (see Section 2 for details of simulations). We also add noise in order to trigger the transitions to the intersections between two attractors when inhibition rises. To mimic the experimental protocol (see Section 2), we simulate multiple recall trials where random samples of 16 items are selected for each trial. One sample epoch of simulations is shown in Figures rthresh we regard the corresponding memory as retrieved. We note that the precise sequence of retrieved items is not predictable for a given list of presented words, as it strongly depends on the first item being recalled (here assumed to be chosen randomly) and is sensitive to noise.Each of the colored line in Figure The effect of the oscillations is to modulate the overall activity in such a way that at each cycle the state of the network can potentially move from one attractor to another. The details of the underlying dynamics are shown in the plot of Figure Although a switch between different states of the network is induced at every oscillation cycle, not always the state of the network shifts toward a new memory Figures . Rather Since the recall of subsequent memories is a stochastic process triggered by noise in the input, we perform multiple simulations to characterize the average accumulation of recalled memories with time Figure . We obseHere we study the dependence of the recall process on the statistics of memory representations as defined by the memory patterns introduced in Section 2 (see Equation 4). In particular we consider the effects of representation size (number of neurons encoding a given item) and the size of intersections between the representations of two memories (number of neurons encoding both of the items). The representation size higly influences the probability of recall for a given memory. Our simulations show that simulating the network many times with items having a randomly drawn size, the probability to recall an item is monotonically increasing with the size of the corresponding representation Figure , Katkov Latent Semantic Analysis, or LSA), which represent the number of times two words appear together in a representative corpora of natural text . More realistic implementation of the model with high loading levels should be considered in future.Our network model is based on the basic assumption that when a word is recalled, a corresponding neuronal ensemble that represents this word in long-term memory is temporarily activated. The issue that we dont explicitly address is how the words that are presented for recall are selected, or primed and why other word representations are not reactivated . In the spirit of Kahanas TCM model (Howard and Kahana, Another simplifying unrealistic assumption of the model concerns the statistics of long-term representations that are taken as random uncorrelated binary vectors of fixed average sparsity. Real statistics of word representations is not clear but can be safely assumed to be much more complicated, possibly reflecting the rich semantic associations between words and the frequency of their usage. With our assumptions, overlaps between different representations exhibit Gaussian distribution with variance to mean ratio decaying in the limit of infinitely large networks. Considering the effects of overlap distribution in this limit requires an extended mean-field analysis that will be presented elsewhere.Very often the same attractor is repeatedly activated before noise causes the transition to a new one, and it can still be activated again at a later time. Since participants are instructed to only recall each word once, we assume that they suppress the report of a word after it is already recalled. In some experiments, subjects are explicitly instructed to report a word as many times as it comes to mind during a recall. Comparing the model to the results of such experiments could be of interest for a future work.We considered modulated inhibition as a driving force for transitions between network attractors. Other mechanisms could potentially play this role, e.g., neuronal adaptation or synaptic depression. We believe that oscillatory mechanism is more plausible as it allows the system to regulate the transitions by controlling the amplitude and frequency of oscillations. The oscillations of network activity could correspond to increased amplitude of theta rhythm observed in human subjects during recall Kahana,  and otheAt the current level of realism, we propose to view our model as a platform for further development of realistic neural network models of information retrieval and other related types of cognitive tasks. Future modifications should include effects of positional order on recall, or positional chunking, i.e., the tendency to divide the presented lists on groups of contiguous words Miller, , as wellMT and SR designed the study; SR developed and simulated the model; MT, MK, and SR performed a mathematical analysis, SR and MK performed data analysis; all the authors wrote the paper.The 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.


The prognosis of acute limb ischemia is severe, with amputation rates of up to 25% and in-hospital mortality of 9-15%. Delay in treatment increases the risk of major amputation and may be present at different stages, including patient delay, doctors´ delay and waiting time in the emergency department. It is important to identify existing problems in order to reduce time delay.The aim of this study was to collect data for patients with acute limb ischemia and to evaluate the time delay between the different events from onset of symptoms to specialist evaluation and further treatment with focus on pre-hospital and in-hospital time delays.We conducted a prospective cross-sectional cohort study including all patients suspected with acute limb ischemia who were admitted to the emergency department of a community hospital in a six months period. Temporal delay in the different phases between the time of occurrence of symptoms and completion of treatment was recorded prospectively. All patients who underwent intervention had a 30 days follow-up with regard to major amputation of the leg and survival.A total of 42 patients (21 men and 21 women) age 73 (20–95) years (median (range)) was identified.From onset of symptoms to first contact with a doctor the time for all patients were 24 (0–1200) hours. Thirty patients needed immediate intervention. In the group of fourteen patients who had immediate operation, the median time from vascular evaluation to revascularization was 324.5 (122–873) minutes and in the group of eight patients that went through an imaging procedure before an operation the median delay was 822 (494–1185) minutes from specialist assessment to revascularization. The median time for revascularization among four patients, who were treated with arterial thrombolysis was 5621 (1686–8376) minutes.At 30 days follow up, six patients had had the ischemic limb amputated above the ankle and four patients had died.We found that the largest time delay was between onset of symptoms and first contact to a medical doctor. A greater public awareness is needed, so as to facilitate urgent revascularisation and improve outcomes. Acute limb ischemia (ALI) is a sudden decrease in limb perfusion causing a potential threat to the limb viability . The eveThe delay may be present at different stages, including patient delay, delay caused by the referring medical doctor, waiting time in the emergency department, waiting time for diagnostic imaging, or time for preparation at the operating theatre, including anaesthesia. Before creating strategies for reducing treatment delay, existing problems need to be identified.It has been shown that implementation of ED fast track systems reduces ED waiting time and overcrowding –10. In DThe aim of this study was to collect data for patients with ALI and evaluate the time delay between the different events from onset of symptoms to specialist evaluation and further treatment with focus on pre-hospital and in-hospital time delays.We conducted a prospective cross-sectional cohort study. The study was approved by the Danish Data Protection Agency. Data collection took place from 01.10.12 to 31.03.13, at Kolding Hospital, a community hospital with a department for vascular surgery with a catchments area covering both suburban and rural districts.The patients´ first contact with the medical care system is with a non-vascular specialist outside the hospital. When ALI is suspected, the non-vascular specialist consults a specialist in vascular surgery and the patients are admitted to the hospital. The ED fast track unit is notified by the vascular surgeon. All patients suspected with ALI are admitted to the fast track area in the ED.The fast track unit is separated from the rest of the ED. It is open 24 hours a day and has its own nurses and staff station. There are two senior doctors, one specialist in internal medicine and one specialist in surgery, in the department from 08.00 am to 12.00 pm and at night they are on call. Also there are a number of junior doctors associated with unit.The vascular specialist is summoned to the ED when the patient suspected with ALI arrives and will be the first doctor to see the patient within the ED fast track area.For each patient admitted, the specialist vascular surgeon on call started the data collection of the particular patient. A registration form was filled in with information about gender, age and earlier vascular procedures. Furthermore, onset of symptoms, first contact with a medical doctor , time for referral to the vascular department, time for arrival and time for vascular evaluation were registered. All patients were scored according to the classification suggested by Rutherford, where the severity of ALI is divided into four categories . In clasIf the patient was not judged to have ALI the registration was stopped after the vascular examination. If they had ALI and needed further intervention, time was registered for the beginning and end of the procedure. Further interventions were computed tomography (CT) or magnetic resonance (MR)-imaging, operation, endovascular procedure or amputation.When the patient arrived to the ED, examination of the leg was used to define the severity of the ischemia. ALI was classified into one of four categories based on clinical findings and Doppler measurements.All patients who underwent intervention had a 30 days follow-up with regard to major amputation of the limb and death.For each patient the time between the registrations, in a chronological order, was measured. Descriptive statistics were performed using Microsoft Excel Version 7.0. To compare patient related time delay in patient with and without prior vascular surgery we performed Wilcoxon rank sum test using Stata, .A total of 42 patients (21 men and 21 women) ages 73 (20–95) years (median (range) were admitted on suspicion of ALI. Twenty-one patients (50%) had a prior history of vascular surgery for periphery arterial disease (PAD) in one or both legs. Twelve patients did either not have ALI or had ALI class 1, which did not need immediate intervention, and registration stopped after vascular examination. Of these patients three had deep venous thrombosis (DVT), one had neuropathic pain, seven had ALI class 1 and one had class 2A ischemia, but it was found that no immediate treatment was required. The distribution of patients according to levels of severity of acute limb ischemia is shown in Figure For all patients the time from onset of symptoms to specialist assessment the median time was 27.25 (1.65 – 1202.5) hours. This time period was divided into smaller time periods as showed in Figure Median time from onset of symptoms to first contact with a medical doctor was 24 (0–1200) hours. For patients with a prior history of vascular surgery the median time was 22 (0–240) hours and for patients with no earlier history of vascular surgery the time was 26.35 (0.17- 1200) hours. The time difference between the two groups was not significant (p = 0.4).The time from first contact to a doctor until the ED was notified was 1.25 (0–67.5) hours and transportation time to the ED was 1.7 (0–19.9) hours. Median time from arrival to the ED to evaluation by a vascular specialist was 0.33 (0–1.5) hours. A total of 26 patients (62%) were assessed by the vascular surgeon on call within 30 minutes after arrival, 9 (21%) within an hour, and 7 (17%) waited for more than one hour.Thirty patients were classified with ALI and needed immediate intervention as seen in Figure Among the 14 patients operated immediately, it was possible to restore blood flow to the limb in 12. Eight of the 11 patients who underwent imaging had an operation afterwards; each having successful revascularization, yet two patients had re-operation due to new occlusions. Three patients underwent thrombolysis and one had an endovascular procedure, all of them resulting in restored blood flow.In the group of patients who had immediate operation, 10 had an embolectomy, two had a thrombendarterectomy and two had peripheral bypass operation. The median time from vascular evaluation to revascularization (defined as time to end of successful surgery) was 324.5 (122–873) minutes, whereas in the group of patients that went through an imaging procedure before operation the median delay was 822 (494–1185) minutes from vascular evaluation to revascularization. The median time for revascularization in the thrombolytic group was 5621 (1686–8376) minutes Figure At 30 days follow up, six patients had had the ischemic limb amputated above the ankle; four of these amputations were above the knee. Three of the patients were amputated without prior attempt of revascularization. In the amputation group (n = 6) the median time from onset of symptoms to arrival at the ER was 68.8 (24–1202) hours. The patient who did not arrive until 1202 hours (50 days) after onset of symptoms was an 83 years old man suffering from a neurodegenerative disease. He was referred acutely, without being able to tell for how long he had had symptoms. The hospital files showed that he had been seen in the emergency department 50 days earlier with complaints about pain in the leg. At that time, it was suspected to be muscle or join discomfort and he was released without seeing a vascular specialist. Fifty days later his family doctor was called to see him and he referred the patient to the hospital suspecting ALI.Five out of the six patients who were amputated were assessed by a vascular specialist within 30 minutes after arrival; one waited 90 minutes. Three of these patients had an attempt of surgical revascularization. From vascular specialist assessment to revascularization it took 122, 365 and 620 minutes respectively. Two of the patients had an amputation above knee within 24 hours after attempt of revascularization and the last one had an amputation below knee after 9 days.Four patients died within 30 days after referral to the vascular department, two had had a revascularization procedure that failed to restore blood flow, one had an amputation below the knee and the last one died of myocardial infarct shortly after arrival to the emergency department.Patients with acute limb ischemia have a poor prognosis with regard to major limb amputations and death. The rate of major amputations is reported to be up to 25%, including both non-salvageable limbs and limbs thought to be salvageable . For patEliason and colleagues reported 9.3% in-hospital mortality for patients admitted with ALI , while KThere is a relationship between the delay from onset of symptoms to revascularisation and subsequent mortality or limb loss. As an example, Morris-Stiff and colleagues recently compared the results after peripheral arterial embolectomy from two different historical time periods in the same community hospital . In bothIn our study the largest pre-hospital time delay occurred between the onset of symptoms and the first contact to a doctor, this was the case for all patients, including the ones with irreversible ischemia. The median time was 24 hours, which is similar to findings in earlier studies , 16. BurPatients with a prior history of vascular surgery for PAD tended to respond faster to symptoms than patients without prior history, suggesting that the first group is more aware of the importance of symptoms. This difference was, however, not statistically significant. Time delay between the first contact to a doctor and the arrival at the emergency department was reasonable taking into consideration that most patients were seen and examined by the non-vascular specialist outside the hospital before referral. To our knowledge, this is the first study evaluating the different time steps from onset of symptoms to revascularisation.When looking at the in-hospital delay one of the main goals in the fast track program is to have the patients evaluated by a specialist within 30 minutes after arrival. In our study 62% of the patients were evaluated within 30 minutes, which leaves place for improvement. On the other hand, only 17% waited for more than one hour due to the fact that the surgeon was occupied with other acute tasks. Whether the fast track programme has shortened the in-hospital time delay is not certain, because our data collection started after the implementation.A bit surprisingly we found that patients who went for imaging before further intervention had an almost 8.5 hours longer in-hospital delay than patients who needed immediately operation. This was mainly due to waiting time for the CT- or MR-imaging. Though imaging is considered a part of the fast track programme and should be done within the first four hours after arrival. Local changes have now been done in order to meet this goal of the fast track programme. We recognize limitations of the study, including especially a small sample size and also the fact that we only studied practice in one hospital. The relative importance of each of the different phases of in hospital delay cannot be expected to be the same in other locations, although the method used may be thought of as an inspiration for local analyses in other hospitals. However, the primary finding; that patient delay is the main reason for treatment delay in ALI, seems to be consistent with findings from other geographical areas and other time periods , 16 and In summary, we found that the main component of treatment delay is the time between onset of symptoms and the first contact to a doctor. Although we have not specifically asked the patients about the reasons for this delay, it seems safe to suggest that greater public awareness is needed, so as to facilitate urgent revascularisation and improve outcomes. Public campaigns, stressing the need for urgent treatment of ALI, might be a tool to improve results. In order to avoid misdiagnosing patients with ALI it may be helpful if all patients with acute pain in a leg, not caused by fractures or other obvious causes, are seen by a vascular specialist when referred to an emergency department according to the fast track organisation . We recoAccording to Danish legislation and The National Committee on Health Research Ethics written consent from the patients is not required.


A novel, goal function-based formulation for the growth dynamics of arteries is introduced and used for investigating the development of growth instability in blood vessels. Such instabilities would lead to abnormal growth of the vessel, reminiscent of an aneurysm. The blood vessel is modeled as a thin-walled cylindrical tube, and the constituents that form the vessel wall are assumed to deform together as a constrained mixture. The growth dynamics of the composite material of the vessel wall are described by an evolution equation, where the effective area of each constituent changes in the direction of steepest descent of a goal function. This goal function is formulated in such way that the constituents grow toward a target potential energy and a target composition. The convergence of the simulated response of the evolution equation toward a target homeostatic state is investigated for a range of isotropic and orthotropic material models. These simulations suggest that elastin-deficient vessels are more prone to growth instability. Increased stiffness of the vessel wall, on the other hand, gives a more stable growth process. Another important finding is that an increased rate of degradation of materials impairs growth stability. The vascular system of the human body adapts to changing conditions, such as body mass changes, injury or disease. This is facilitated by the growth and remodeling of individual blood vessels in response to variations in blood pressure , whose primary functions are to contract and dilate the blood vessel wall and thus to regulate the blood flow and pressure. There are limits to how much a blood vessel can expand or contract , as obtained from in vivo and in vitro measurements found in the literature. We are interested in the stability of this dynamical system subject to changes in the flow conditions. Particularly, we consider under which conditions instabilities arise that cause the dimensions of the artery to drift in a manner similar to the development of an aneurysm.We consider the blood vessel to be a thin-walled, cylindrical tube. For this model vessel, neither the geometry of the cross-section nor the composition of the vessel wall varies in the axial or the circumferential direction. We use CMT to model its mechanics and thus assume that the load-bearing constituents deform together, but have individual material behavior. The growth dynamics of the composite vessel wall material is described by the evolution of the effective cross-sectional areas of each constituent. The growth control is modeled using the dynamical systems approach to optimization. That is, the change in effective areas follows the direction of steepest descent of a goal function. We formulate this goal function in such way that the constituents grow toward a target potential energy and a target composition. The properties of the evolution equation are investigated numerically, using the parameters of the radial artery  and (ii) are denoted by When the imposed flow conditions (i), Eq.  reduces ,and Eq.  becomes2ii), Eq.  yields \into Eq. , becoming to Eq. .Introducing Eq.  or Eq.  into theAs described in Sect. As indicated in the introduction, we approach the formulation of equations for growth in a novel way, assuming the existence of a goal function and an evolution in a steepest descent direction of this function. As a measure of the mechanical state, we then use the total potential energy of the system, which readsrium Eq.  for timefrom Eq. , \documef Murray , the worf Murray . In the rium Eq. , which wrium Eq. : The potrium Eq.  is impliThe partial derivatives of the goal function are calculated as follows:It is now assumed that the gradient of the goal function governs the evolution toward a steady state. The simplest assumption that achieves this is given by. In Eq. ]. This earteria radialis). Averaging in vivo measurements yields a radius The properties of the evolution equation are investigated numerically, using the parameters of the radial artery \documentt et al. , as showt et al.  used an d et al.  measuredd et al.  but withmentclass2pt{minimIt is assumed that the vessel wall can be divided into two components: One component, Again, it is required that To identify the parameters of the dynamical system, its evolution equation is nondimensionalized by introducing a referential length An index ‘tion Eq.  for consTwo nondimensional parameters governing the system’s behavior are thus identified: We are interested in the stability of the proposed dynamical system subject to changes in the flow conditions, which in turn affect the target state ^ of Eq. . The parase, Eq. , this alEquation  is integFor each investigated parameter pair, The development of In Fig. Finally, we study the response for 0-2 Fig. . After tThese three different behaviors, convergence, monotonic divergence and oscillatory divergence, are observed for the one-constituent, orthotropic material model and for the two-constituent model as well.By systematically exploring the nondimensional parameter two-space of the evolution equation, the regions corresponding to convergent and divergent model responses are uncovered. The three observed behaviors, Conv., MD and OD, form three simply connected domains in the A straight line with slope one in the log–log diagram separates the MD regime from the other two regimes. This shows that MD is observed when the ratio Consider the extreme case of a goal function that is only controlled by the target composition. In our stability analysis, this corresponds to the case Now, consider the extreme case of a goal function that only includes the potential energy term. This corresponds to When there are multiple components that remodel, inspection of the goal function, Eq. , impliesWhen both terms of the goal function are included, convergence depends on the ratio The active control of the vessel diameter by VSM to maintain a homeostatic wall shear stress is not included in the model, and previous investigations indicate that this active control has a stabilizing effect on growth Taber . The regAs people age, the elastin concentration of some blood vessels, such as the ascending thoracic aorta, is reduced  that produce and degrade the constituent  and one anisotropic material that degrades and grows. Simulations show that the conditions for stability are qualitatively similar for these three models. Stability can be achieved if the goal function is based only on potential energy, or on both potential energy and composition.We identified and analyzed two nondimensional parameters, We also investigated how the material properties and composition affect the stability of the blood vessel, with the intent to relate the model to disease states. This was done by modifying the two-constituent material model. An elastin-deficient vessel was investigated, exhibiting an increased risk for growth instability. In addition, a vessel composed of stiffer materials was investigated, showing that a stiffer material yields a more stable growth process.


XTe content (from 0.01 to 0.06) was measured. From the obtained results, Wagner’s interaction parameter The activity coefficient of oxygen  The by-product of the electrolytic refining of copper, i.e., “anode slime” , is a vaTellurium in silver slimes is a harmful impurity element, because of limited volatilization during converter blow (contrary to selenium and bismuth), and it tends to accumulate in the metal phase. As a result of the low stability of oxides it cannot be oxidized easily during the Kaldo process in a rotary furnace.Such conventional processing by smelting of slimes in converters with the addition of fluxes and oxidizing agents and with the injection of oxygen into the molten bath reduces the amount of Cu, Se, and Te. The refining step of the liquid alloy by oxidation is very efficient for selenium, whereas oxidation of tellurium does not take place until the Se/Te mass ratio decreases to 0.55 , 4. ThusIt is worth noting that as far as we know from the literature study, no measurements have been carried out to determine the interaction parameter of oxygen in liquid silver–tellurium alloys.The modified coulometric titration method is suitable for the determination of oxygen concentration and activity in liquid metals, e.g., Ag  or Te 66, 7. As The activity coefficient of oxygen in liquid silver has been determined several times , 11–25. The objective of this study was to determine experimentally the influence of Te impurity on the activity coefficient of oxygen in liquid Ag–Te alloys and to describe it by means of the Wagner  interactBecause of nonexistence of silver oxides at elevated temperatures it is impossible to quench the oxygen saturated solutions of Ag in order to analyze them. Therefore, the electrochemical coulometric titration method seems to be appropriate to study the thermodynamics of oxygen interaction in liquid silver and its alloys in a wide range of oxygen partial pressures.In the present study the experimental method of high temperature coulometric titration with a galvanic cell was employed for the investigation of the activity coefficient of oxygen in silver-based liquid solutions. The applied oxygen concentration cell with YSZ (yttria stabilized zirconia) solid electrolyte can be described schematically asE1 (in volts) of the concentration cell is connected with the oxygen partial pressure, R and T are the gas constant and experimental temperature (in kelvin), respectively, and F is Faraday’s constant.The initial electromotive force (emf) of galvanic cell E2, is related to the activity coefficient and final oxygen concentration by Eq. (CO(2) is the final oxygen concentration (in at.%) in the liquid metal or alloy and fO is an oxygen activity coefficient in pure liquid silver rescaled for concentration in at. %. At infinite dilution the value of the oxygen activity coefficient The final open circuit emf, n by Eq. :3\documeM and W are the reduced molar mass and reduced sample mass of the liquid metal or alloy, respectively. CO(1) is an initial oxygen concentration (in at.%) in the liquid metal or alloy. The charge transferred, Qion, caused by ionic current, Iion, was obtained by integrating the obtained curve of Iion versus time. The ionic current passing through the cell should be corrected by subtracting the final residual current from the total cell current. It can be assumed that such constant residual current is a part of the cell current due to electron transfer in the electrolyte.The oxygen concentration change in the sample during the titration experiment can be calculated from Eq. :5\documeFrom the Nernst equation, Eq. , which rEquation  and 6),,6\documeThe standard Gibbs free energy of oxygen dissolution in liquid metallic melt according to the reactionE1. The averaged values of The solubility of oxygen in Ag was measured at the beginning to test the assembly and to obtain the reference state to study the influence of tellurium on the activity coefficient of oxygen in pure liquid silver. The titration experiments were carried out twice in the temperature range 1,285–1,485 K using solid oxide galvanic cells represented schematically by Eq.  were measured in the temperature range 1,285–1,485 K using the following concentration galvanic cells with the solid YSZ zirconia electrolyte:Next, the oxygen activity coefficients in dilute Ag–(Te)–O alloys for variable fO values are shown in Table As an example, the experimental results for 2 at.% of Te and temperature 1,385 K including the calculated ln To study the influence of admixture of tellurium on the activity coefficient of oxygen in dilute liquid silver alloys the dependence of oxygen on tellurium mole fraction was established in the form of Eq. :12\documXTe  were supplied by Friatec AG (Germany). The purity of silver rod  used in the present investigation was 99.95 %. The iridium wire tip (diameter 0.5 mm) electrically welded to Kanthal™ wire  was used as the lead wire for liquid silver and silver–tellurium alloys. The tellurium was added in the form of silver telluride supplied by Sigma-Aldrich (USA) but its purity was not mentioned. The metal sample was prepared from the appropriate amounts of pure silver and/or silver telluride by melting together in the electrolyte tube. The outer platinum electrode was separated into two connections (sensing and reference electrodes) in order to keep the emf measurements at the reference electrode out from polarization during a coulometric titration run. The platinum wires of outer electrodes were obtained from the Polish Mint (Poland). Before each experiment the electrolyte tube was flushed by purified argon via an H-shape tube for 10–12 h and then the furnace was slowly heated to the desired temperature.The scheme of an oxygen concentration cell with zirconia solid electrolyte YSZ represented by Eq.  can be fE1, the steady liquid metal or alloy was deoxidized by applying a chosen voltage ΔE and the final emf E2 was detected. During such titration experiments the electric current and the quantity of electrical charge were controlled by an electrochemical analyzer CHI 600C Series  and multimeter Keithley 2001  connected to a PC computer with acquisition software.The initial oxygen concentration in the liquid metal and alloys was set at a preselected value by passing the appropriate current through the cell. After stabilization of the open circuit voltage, Iion was calculated by integrating the remaining current over time. Titration experiments were carried out several times at constant temperature and then the temperature was changed by a defined step and the whole procedure was repeated.The quantity of electrical charge contributed by corrected The separately measured temperature dependence of emf,


We describe two experiments demonstrating that a cylindrical cloak formerly introduced for linear surface liquid waves works equally well for sound and electromagnetic waves. This structured cloak behaves like an acoustic cloak with an effective anisotropic density and an electromagnetic cloak with an effective anisotropic permittivity, respectively. Measured forward scattering for pressure and magnetic fields are in good agreement and provide first evidence of broadband cloaking. Microwave experiments and 3D electromagnetic wave simulations further confirm reduced forward and backscattering when a rectangular metallic obstacle is surrounded by the structured cloak for cloaking frequencies between 2.6 and 7.0 GHz. This suggests, as supported by 2D finite element simulations, sound waves are cloaked between 3 and 8 KHz and linear surface liquid waves between 5 and 16 Hz. Moreover, microwave experiments show the field is reduced by 10 to 30 dB inside the invisibility region, which suggests the multi-wave cloak could be used as a protection against water, sonic or microwaves. Eight years ago, two seminal papers by Pendry, Schurig and Smith6In the tracks of electromagnetic cloaks, control of acoustic and water wave trajectories has been proposed91011121415In contrast to Maxwell’s equations, the form of Navier equations is not preserved under geometric transforms such as space folding, whereby the image plane of a flat lens with a negative refractive index is expected to map onto its source planeet al.242526272829Notwithstanding the fact that cloaking displays some universal features such as enhanced control of wave wavefronts (one might say a wave is a wave), some word of caution should be made regarding invisibility versus protection in various physical contexts. Indeed, cloaking for diffusion of heat2021We proceed with the mathematical approach of homogenization29It can be shown, that sound waves with a wavelength much larger (in practice three times larger) than the largest structural elements of the cloak are governed by the following homogenized wave equation (written in polar coordinates)where the effective tensor of density is given byHere, δS of the inclusion S in a unit cell Y.where n is the outer unit normal to the boundary The inverse of the effective bulk modulus is such thatHere r’ and θ’ are radial and azimuthal microscopic variables, and it should be noted that In a similar way, transverse electric waves are solution of the following homogenized Maxwell’ equation in the cloak see also :μeff is the effective permeability which is such that H = .where μeff above that μeff < μ0 i.e. that the effective permeability has slightly lower, yet strictly positive, values than permeability of vacuum and its spatial radial variation is small. Hence, one can safely divide by μeff throughout in (5). In the same way, from the expression in (4) one can multiply throughout by κeff in (1). This leads to reduced effective parameters.It transpires from the integral expression of It can be shown that the reduced effective parameters in (1)-(4) are good approximations for well-known transformed density and permittivity in their reduced forms i.e.In which case the transformed bulk modulus and permeability can be normalized to 1.1 = 4.1 cm and outer radius R2 = 10 cm which has been first divided into 14 layers whose thickness varies with respect to r as Ψij solution of this annex problem in the context of linear surface liquid waves. This leads to the reduced effective parameters in (6) and (7). In order to quantitatively assess the cloaking efficiency of the metamaterial, following the procedure proposed in362 as the cloak. Moreover, in all these configurations, we consider the ground plane (5 mm thick) which is part of the cloak: this ground plane cannot be omitted in the three dimensional electromagnetic experimental setup. The RCS of the cloak (dark blue dashed curve) and of the small obstacle surrounded by the cloak are nearly superimposed in the frequency interval  GHz and much lower than the small obstacle on its own (dotted red curve). We have numerically checked that the shape and size of the small obstacle matters very little .Modeling of the invisibility cloak has been carried out using the commercial finite elements package COMSOL MULTIPHYSICS. In practice, the cloak consists of a ring of inner radius RWe further show in For the same 2D setup as in Acoustic experiments were performed in MIT  for sound waves and in Fresnel Institute  for microwaves. We considered the two-dimensional Helmholtz model for the comparison between theory and acoustic experiments, therefore it came as a good surprise that our intuition was right: experiments in et al.et al.4The experimental electromagnetic setup at Institut Fresnel is actually more in the spirit of that of Kanté Regarding the electromagnetic cloaking experiment, we were able to monitor both the phase and intensity of the longitudinal component of the magnetic field, in backward and forward scattering, as well as within the cloak. This experimental result clearly shows that the electromagnetic signal is much reduced inside the core of the cloak, where a metal plate is placed. Similar tests (not reported) have been performed for a cloud of metal nails and here again we observed very little electromagnetic field inside the core of the cloak (a reduction of magnetic field intensity by 13.5 to 38 dB at the cloaking frequency 3.550 GHz). This suggests some form of electromagnetic protection for the square metal plate  can be achieved at cloaking frequencies thanks to the cloak. We also observe that transmission is good for the electromagnetic wave propagating though the structured metal cloak. Hence, we not only achieve a good reconstruction of the wave wavefront (the phase), but also preserve its intensity.One of the main features of the cloak is that it works through field averaging and only one phase (vacuum) need be considered in the homogenization and computational results to achieve a good prediction of experimental results. The underlying mechanism  is so simple that it makes the cloak multiphysics: Two-dimensional numerical simulations with COMSOL MULTIPHYSICS show by a simple normalization of the wave frequency in (1) or 5) that cloaking should be at work between 5 and 16 Hz for surface liquid waves in the condition of that cloWe stress that we not only show the phase, but also the intensity of the magnetic field in the experiments. One can see that the phase of the signal is reconstructed behind the cloak in The ability of the cloak to control more than one type of waves could have interesting applications in phoxonics. One could also envisage to increase the number of structural elements to improve cloaking even further. Homogenization tells us that the more structural elements, and the smaller their size compared to the wave wavelength, the better approximate cloaking, see Fig. S3&S4 in rs is the position of the source  and ω is the angular wave frequency.COMSOL Multiphysics with “PDE” module has been used to compute the scattered field in The multiple scale technique2 surface thanks to a 3D axis positioning systemThe microwaves experimental setup was positioned in an anechoic chamber . A ridged horn antenna [1 GHz–18 GHz] was positioned at 24 cm from the structure cloak . A rectaThe antenna and the probe were connected to a vector network analyzerThe vector network analyzer measured the transmission coefficient between the emitter antenna and the magnetic probe. In our case, the transmission coefficient is equivalent to the magnetic field component perpendicular to the loop. The frequency range was from 1 to 6 GHz (our vector network works between 50 KHz and 6 GHz).The complex transmission coefficient between the antenna and the probe is displayed in terms of magnitude in dB to visualize the intensity of the field. The real part of the magnetic field is also displayed since this is related to the phase of the field.2.The acoustic wave experimental setup was positioned on an optical table with open space surrounded. A commercial loudspeaker [20 Hz–18 kHz] was placed at 20 cm from the structure cloak. The loud speaker was driven by a programmable functional generator (Tektronix AFG 3022B) and a power amplifier (Krohn-Hite Model 7500). A high sensitive microphone mounted on an x-y translation stage (Newmark NSL4) was used to record the two-dimensional acoustic pressure field distribution. The loudspeaker, acoustic cloak, and microphone were placed at the same level for characterizing how the pressure field was affected by the cloak. In the experiment, a five-period sinusoidal wave was launched by the loudspeaker. The time-dependent pre-amplified signal collected by the microphone was recorded by an oscilloscope (Agilent DSO 6104A) and downloaded to a computer for further analysis. The signal generation and acquisition were synchronized by the computer program. Therefore, we can map the 2D pressure field distribution with both amplitude and phase information. The scanning area is 25 × 25 cmHow to cite this article: Xu, J. et al. Molding acoustic, electromagnetic and water waves with a single cloak. Sci. Rep. 5, 10678; doi: 10.1038/srep10678 (2015).


When a single boundary separates three or more different basins of attraction, we say that the set of basins has theWada property and initial conditions near that boundary are even more unpredictable. Many physical systems of interest with this topological property appear in the literature. However, so far the only approach to study Wada basins has been restricted to two-dimensional phase spaces. Here we report a simple algorithm whose purpose is to look for the Wada property in a given dynamical system. Another benefit of this procedure is the possibility to classify and study intermediate situations known as  Sj where each Sj represents a different value or state. For example the sets might be basins of attraction in the phase space of a dynamical system. Numerical and experimental investigations of the property in question can be intricate when the boundaries between the sets are fractal. It may be difficult to predict the state transition of the system as the initial condition is disturbed. This unpredictability increases when the boundaries of Sj are not only fractal but also possess the Wada property; that is, each point on the boundary of any of these regions is in fact on the boundary of all of them. In other words, the sets share the same boundary.Sometimes a physical property can be labeled with different discrete values depending on parameters. Suppose a space has This situation emerges for a variety of systems of high interest in physics such as the basins of the forced damped pendulumSj in the plane have the same boundary? This question was answered in the affirmative by L.E.J. Brouwer inMr. Wada, his Ph.D. supervisor, Takeo Wada. Hocking and Younglakes of Wada, a pun on water, so it was natural to extend the wordplay to dynamical systems by introducing the term basins of Wada11The problem first arose as an investigation of regions in the plane: Can three or more open, disjoint, connected regions q crosses three or more different basins, then the point q is a Wada point, as is every point in the stable manifold of q and in its closure. It can be difficult to show that the closure of that stable manifold is the entire boundary. The procedure for carrying that out is based on a concept called basin cells, which requires detailed knowledge of stable and unstable manifolds. The NY method is an adequate approach for basins in two dimensional phase spaces. However, the method is not suitable in many cases.The Nusse-Yorke (NY) methoddisconnected Wada basins can be illustrated as follows. The Wada property appears in diverse situations such as the parameter space of the Hénon map15partially Wada basins19We propose a simple method, straightforward to implement, to test the Wada property in all kind of systems. Furthermore, our method/terminology allows us to classify intermediate situations where only some basins and some of the boundary present the Wada property, which receives the name of Sj where j = 1, …, NA.There is a bounded region Ω containing G covering Ω. We typically use a 1000 × 1000 grid. Hence Ω is covered by a set K would be 106 for that usual grid.There is a rectangular grid x in Ω, it is possible to determine to which set Sj it belongs to. In other words, there is a function C with C(x) = j if C(x) = 0 if x is in none of the sets Sj. If the sets are basins, the trajectory for each C(x). Notice that we do not impose different labels for each attractor. It is possible to merge several attractors into the same category. For any rectangular box denoted as box we define C(box) = C(x) where x is the point at the center of box. If it does not go to an attractor in our collection of numbered attractors, then C(box) = 0, such events are reported at the end of the run. For convenience we will refer to this numerical value C as the color of the grid box. Of course other points in the same box might lead to different attractors.For each point b(boxj) to be the collection of grid boxes consisting of boxj and all the grid boxes that have at least one point in common with boxj, so in dimension two, b(boxj) is a 3 × 3 collection of boxes with boxj being the central box.We define boxj, we determine the number of different (non-zero) colors in b(boxj) and write M(boxj) for that number.For each boxj with b(boxj) with different colors and trace a line segment between them. We compute the color of the middle point of the segment. In case that the color newly computed completes all colors inside b(boxj), then M(boxj) = NA and the algorithm stops. Otherwise, we compute two new points: one in the middle of the leftmost and central point, and another in the middle of the rightmost and central point. In the second step, four points interspersed with the previous five points would be calculated. In the third step, we would compute eight points interspersed with the previous nine. The procedure keeps on until M(boxj) = NA or the number of calculated points in that segment reaches some maximum value previously set up. A major computational advantage of this method is that the refinement is made in a one dimensional subspace (the segment linking the two points), no matter the dimension of Ω.In each Gm to be the set of all the original grid boxes boxj for which M(boxj) = m.Next we define We first need some assumptions. We will discuss the notation for the case of a two dimensional space though it is easily adapted to other cases.m = 1, all the boxes inside the ball b(boxj) have the same color as they all lead to the same attractor. In fact G1 represents points that are in the interior of a basin. A grid box boxj is in the set G2 (boundary of two) if there are two different colors inside the ball b(boxj), a grid box is in the set G3 (boundary of three) if there are three different colors inside the ball and so forth. To account for the evolution of these sets as the algorithm progresses, we call Gn at step q.For G1 or in the Wada boundary q.Then, we will say that the system is Wada if The basic idea underlying the whole process is that if three basins are Wada, then it is always possible to find a third color between the other two colors (similar reasoning can be done for Wada basins with more than three colors). Notice also that if a boundary separates two basins we will only see those two basins at all resolutions.box1, box2, and box3 on a regular rectangular grid forming a partition P0 of the phase space. The first iteration for box1 shows that it belongs to the interior region box1 in box2, lies in the boundary of two sets because two different colors are found in its ball. The successive iterations of the algorithm classify box2 into G2. A different situation arises for box3. The first iteration classifies box3box3 turns out to be in a boundary of three basins To illustrate the iterative process we represent in m different basins. For that purpose we can define a useful parameterIn order to decide whether a system is Wada, not Wada, or presents an intermediate situation, we can count the number of boxes belonging to the boundary of m basins and it takes a value one if all the boxes in the boundary separate m basins. Thus, if Wm < 1 with Wm is also useful to test the global numerical convergence.where W3 = 1 which means they all share the Wada property.For all the results presented in this work, we use as initial partition a uniform grid of one million boxes, and the verification of the Wada property is subjected to that resolution. In order to illustrate the features of the described method, we will present an analysis of the results for the damped forced pendulum and the Newton method to find complex roots. They could be considered as paradigmatic examples of connected and disconnected Wada sets respectively. Nonetheless, we have also tested our method for the Duffing oscillator21q grows the number of remaining points N decreases exponentially  increases the computational effort of the algorithm (M(boxj) = NA for each box or reach the maximum of allowed steps.A more challenging case arises when we increase the amplitude of the external forcing: lgorithm . The reaWm: the algorithm stops when ε a small positive number previously fixed .


A mathematical model of potentiometric enzyme electrodes for a nonsteady condition has been developed. The model is based on the system of two coupled nonlinear time-dependent reaction diffusion equations for Michaelis-Menten formalism that describes the concentrations of substrate and product within the enzymatic layer. Analytical expressions for the concentration of substrate and product and the corresponding flux response have been derived for all values of parameters using the new homotopy perturbation method. Furthermore, the complex inversion formula is employed in this work to solve the boundary value problem. The analytical solutions obtained allow a full description of the response curves for only two kinetic parameters (unsaturation/saturation parameter and reaction/diffusion parameter). Theoretical descriptions are given for the two limiting cases (zero and first order kinetics) and relatively simple approaches for general cases are presented. All the analytical results are compared with simulation results using Scilab/Matlab program. The numerical results agree with the appropriate theories. Electrochemical biosensors are used as detectors in several commercial analyzers for the accurate and rapid determination of various metabolites such as urea, glucose, lactate, and creatinine –5. TheseA biosensor is an analytical device comprising of a biological element capable to recognize an analyte, coupled with a transducer which generates a signal proportional to the concentration of the analyte and it combines the selectivity and specificity of an immobilized biologically active compound with a signal transducer –8. The aA relatively simple approach was presented by Morf and he obtained an explicit result for the electrode response that applies to the whole range of substrate concentration , 16. TheTo our knowledge, no general analytical expressions of the concentrations of the substrate, product, and current have been reported for all values of parameters . The purd that contains a uniform total concentration of the enzyme E which is contacted on one side with an aqueous solution of the substrate S. The substrate molecules diffuse into the membrane phase where they react in accordance with Michaelis-Menten type enzyme catalyzed reaction em   ≥ KM). Equations u13) are tresults ( and 19)γs and αu in the enzyme membrane of a potentiometric sensor. Figures u versus the dimensionless distance X. The reaction diffusion parameter γs is an indicator of the competition between the reaction and diffusion. When γs is small, the kinetics dominate and the uptake of the substrate are kinetically controlled. From u decreases when the reaction diffusion parameter γs increases for different values of α. γs increases, the concentration of the substrate u decreases even though the value of α is increased. It is obvious from α increases the concentration u decreases and if α is very small, the concentration of the substrate is uniform and the curve becomes a straight line. Recently, Sivasankari and Rajendran em and the product [P]em for the experimental values of the diffusion coefficient D, for the thickness of the membrane d, and for various values of a. From the figures, it is inferred that the concentration of the substrate increases slowly when d ≤ 20 and increases sharply when 20 ≤ d ≤ 30. The values of the concentrations of the substrate do not differ significantly for all values of a whereas the values of the concentration of the product differ significantly for some values of a.The normalized concentration of the product t = 0, the membrane surface at X = 30 is brought in contact with a substrate sample. The substrate molecules then start to diffuse into the enzyme layer whereas X = 0. Also, from the figure, it is confirmed that u + v = 1 or [S]em + [P]em = 1, for all values of time and also for all values of the parameters involved.u increases as the dimensionless time τ increases and v also increases with the increase in the dimensionless time τ. γs and for some α and the figure reveals that the value of the flux increases as γs increases, whereas α decreases.α is small there is a coincidence between both the results, whereas, when α is 1, there is a significant difference between both the results. The same observation for the product concentration is exhibited in Our analytical results  and numeThe theoretical analysis of behaviour of potentiometric biosensor was done. The coupled time-dependent nonsteady state nonlinear diffusion equations have been solved analytically and numerically. Moreover we have obtained analytical expressions for the substrate, product concentrations and steady state flux. A good agreement with numerical simulation data is noticed. These analytical results will be used in determining the kinetic characteristics of the biosensor. The theoretical model presented here can be used for the optimization of the design of the biosensor. Furthermore, based on the outcome of this work, there is a possibility of extending the procedure to find the approximate amounts of substrate and product concentrations and current for the reciprocal competitive inhibition process.


Informed consent during medical practice is an essential component of comprehensive medical care and is a requirement that should be sought all the time the doctor interacts with the patients, though very challenging when it comes to implementation. Since the magnitude and frequency of surgery related risk are higher in a resource limited setting, informed consent for surgery in such settings should be more comprehensive. This study set out to evaluate patients’ experiences and perspectives of informed consent for surgery.This was a survey of post-operative patients at three university teaching hospitals in Uganda. The participants were interviewed using guided, semi-structured questionnaires. Patients from different surgical disciplines participated in the study.A total of 371 patients participated in the study. Eighty percent of the participants reported having been given explanations on the indication for their surgery, 56.1 % had all their questions answered before the operation, 17 % did not know the type of operation they had undergone and another 17 % did not give their consent for the operation. Additionally, more than 81 % of the participants reported giving their own permission for surgery, although only 23.7 % were able to identify the person who obtained consent from them and 22.4 % knew the names of the surgeons who conducted the surgical procedure on them. About 20 % of the participants were not satisfied with the information provided by both the doctor before and after the operation. However, there were varying responses on when doctors should explain to patients with the majority saying it should be done before treatment or surgery, while others thought it should be done on admission, others proposed that it be made immediately after the examination among other responses. On what should be done to improve communication between doctors and patients, a number of suggestions, including the need for a detailed explanation for the patient by the doctor about their disease conditions and treatment options were suggested.Patients’ perceptions of what constitutes informed consent are diverse and many patients undergo surgery without knowledge of the identity of the surgeon or the reason for the surgery. There is a need to improve on patients’ participation in informed decision making, and this can be achieved through continuing medical education for doctors. Informed consent during medical practice is an essential component of comprehensive medical care and is a requirement that should be sought all the time doctor interacts with the patients, although it is very challenging when it comes to implementation –11. EffeThe extent of detail of informed consent varies with the magnitude of the anticipated risk and thus informed consent for surgery is expected to be more detailed as compared to general medical care. Since the magnitude and frequency of surgery related risk is even higher in a resource limited settings, informed consent for surgery in such settings should be more detailed , 12. DesThis was a survey at three university teaching hospitals in Uganda that recruited 371 postoperative patients. Only patients 18 years of age and above participated in the study and were recruited from general surgery, orthopedic surgery, Otorhinolaryngology (Ear-Nose-Throat), ophthalmology, dentistry, obstetrics and gynaecology surgical units. Participants were interviewed within 2 weeks of surgery using an interviewer guided semi-structured questionnaire adopted from a previous study . The stuFor questions that attracted open ended answers, thematic and content analysis was carried out whereby field notes were categorized according to the research themes and interpreted in line with the study objectives and research questions. Relevant comparisons were made between the different groups of informants.Ethical review and approval was sought from the Makerere University School of Biomedical Sciences Research and Ethics Committee, and the Uganda National Council for Science and Technology. Permission to conduct the study was obtained from the respective hospital administrations. Informed consent was obtained before recruitment of any participant into the study. Participant’s identifying information was kept confidential.The study enrolled 371; 50.7 % of the participants were female giving a female to male ratio of almost 1:1. The age range was 18–80 years with a mean age of 31.8 and SD 12.3. More than 47 % of the participants had at least attained secondary school education, while 37.1 % had primary education, giving a literacy level of more than 94 % as shown in Table Although 80 % of the participants admitted having been given explanations on the indication of their surgery only 56.1 % had all their questions answered before the operation, 17 % did not know the type of surgical procedure they had undergone while another 17 % did not give their consent for the operation. Additionally, more that 81 % of the participants reported giving their own permission for surgery, although only 23.7 % would name the person who obtained consent from them and 22.4 % knew the names of the surgeons who operated on them  agreed that treatment should be well explained by the doctors to patients although, what needs to be addressed in our setting is basically to empower the patients with adequate information so that they can actively participate in the surgical decision making process. This is because patients hold their own perceptions of surgery and what constitutes significant risk based on personal values and beliefs .Guidance on how to participate in decision making for surgical care has been tested in other places and can be useful in this setting as well .About 17 % of the participants did not know the type of operation they had undergone which implies that many patients undergo surgery without giving informed consent or even knowing what type of operation they undergo. This is highlighted in a related study where many doctors were found not to obtain informed consent . DoctorsAlthough 23.7 % of the participants knew the identity of the person who obtained consent from them and 22.4 % named the doctor who operated on them Table , yet an Additionally, more that 20 % of the participants reported their lack of satisfaction to doctor’s explanations both before and after operation Table . This 20Despite the fact that more than 98 % of the participants agreed that treatment should be well explained by the doctors to patients, they were varying responses on what should be explained and when doctors should explain to patients with majority saying it should be done before treatment or surgery, while others thought it should be done on admission, others proposed immediately after examination and a number of other answers Fig. . This neThe challenge of inadequate disclosure of information to patients during medical practice has been reported in other parts of the world where health care resources may not be as limited , 16, 17.However, the challenges of informed consent in our setting are still magnificent given that most of the patients are ignorant about what constitutes informed decision making. This is highlighted by the fact that majority of participants could not identify the surgeons who obtained consent or performed the surgical procedure yet they still believed they gave their own permission for surgery.The study was only conducted at university teaching hospitals which may not be reflective of what happens at other hospitals that are not associated with universities.Since the university hospitals are the major referral hospitals in the country and host the most senior surgeons, the findings of this study may not highlight what happens at the lower none referral hospitals.Patients’ perceptions of what constitutes informed consent are diverse and many undergo surgery without knowledge of the identity of the surgeon or the indication for surgery. In this setting, it would be difficult to believe that patients consent was adequately solicited for when the most basic aspect of consent that patients usually appreciate is the doctor’s name even if all the other information is forgotten. There is a need to improve on patients’ participation in informed decision making via continuing medical education for doctors.