A Computer Modeling Study to Evaluate the Potential Effect of Air Cell-based Cushions on the Tissues of Bariatric and Diabetic Patients

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Ostomy Wound Management 2016;62(1):22–30
Ayelet Levy, MSc; Kara Kopplin, BSc; and Amit Gefen, PhD

Abstract

Sitting-acquired pressure ulcers (PUs) are a potentially life-endangering complication for wheelchair users who are obese and have diabetes mellitus. The increased body weight and diabetes-related alterations in weight-bearing tissue properties have been identified in the literature to increase the risk for PUs and deep tissue injuries (DTIs).

A computer modeling study was conducted to evaluate the biomechanical effect of an air cell-based (ACB) cushion on tissues with increased fat mass and diabetes, which causes altered stiffness properties in connective tissues with respect to healthy tissues. Specifically, 10 finite element (FE) computer simulations were developed with the strain and stress distributions and localized magnitudes considered as measures of the theoretical risk for PUs and DTIs to assess the effects of fat mass and pathological tissue properties on the effective strains and stresses in the soft tissues of buttocks during sitting on an ACB cushion. The FE modeling captured the anatomy of a seated buttocks acquired in an open magnetic resonance imaging examination of an individual with a spinal cord injury. The ACB cushion facilitated a moderate increase in muscle strains (up to 15%) and stresses (up to 30%), and likewise a moderate increase in size of the affected tissue areas with the increase in fat mass, for both diabetic and nondiabetic conditions. These simulation results suggest wheelchair users who are obese and have diabetes may benefit from using an ACB to minimize the increased mechanical strains and stresses in the weight-bearing soft tissues in the buttocks that result from these conditions. Clinical studies to increase understanding about the risk factors of both obesity and diabetes mellitus for the development of PUs and DTIs, as well as robust preclinical comparative studies, may provide much-needed evidence to help clinicians make informed PU prevention and wheelchair cushion decisions for this patient population and other wheelchair-bound individuals. 

 

In the medical literature and clinical guidelines,1 pressure ulcers (PUs) are defined as localized injury to the skin and/or underlying tissues that develop as a result of excessive and sustained pressure and/or shear, usually under a weight-bearing bony prominence. After more than a decade of rigorous research work, it is now well established that severe PUs are caused primarily due to exposure to sustained large tissue deformations over critical time periods that compromise the integrity and homeostasis of cells and the viability of tissues.1-6

PUs are categorized with respect to either their depth or the types of tissues involved. Superficial (skin) PUs are commonly associated with frictional forces, shear loads, and microclimate factors, whereas deep tissue injuries (DTIs) are caused by sustained deformations and localized forces in muscle and fat.1,7,8 PUs are generally associated with a number of contributing or confounding factors, primarily impaired mobility and sensory capacities, as well as compromised perfusion, abnormal body mass index (BMI), and type 2 diabetes, to name a few.9,10 Populations at general risk are the elderly and frail; patients who sustained a spinal cord injury (SCI); individuals with neurological diseases, brain trauma or stroke, and neuromuscular diseases that restrict mobility; and surgical patients.9 All of these individuals are more likely to spend prolonged time periods in a static position in a bed or a wheelchair.

Bariatric patients, who are less mobile as well, are known to be at risk for DTIs, particularly when undergoing a surgery that results in prolonged immobility.11,12 According to obesity.org, obesity is highly correlated with type 2 diabetes; nearly 90% of people living with type 2 diabetes are overweight or obese. This increases the risk of neuropathy/sensory impairment; it is common to see not only bariatric tissue changes, but also diabetes-related tissue changes in these patients, a syndrome often termed diabesity

Sitting-acquired PUs and DTIs are a common and life-endangering complication for individuals who chronically sit or depend on a wheelchair for mobility. As described in the prospective, inception cohort study by Allman et al13 and the phenomenological pilot study of Hopkins et al,14 the onset of sitting-acquired DTIs can lead to septicemia, osteomyelitis, renal failure, organ system failure, and serious infection, hindering functional recovery, causing pain, and reducing the quality of life for both patients and caregivers. Reddy et al’s15 systematic review demonstrated the burden on health care systems: the management of a single full-thickness PU can cost up to $70,000, and annual PU treatment costs are estimated at $11 billion in the United States alone. Therefore, prevention should be the primary strategy for minimizing the impact of sitting-acquired DTIs.

Tremendous effort is being invested to thoroughly understand DTI etiology, with the aim of facilitating more efficient risk assessment and revision of prevention strategies targeting population-specific risk factors. In particular, the purpose is to minimize internal tissue deformations and localized forces, now recognized in the scientific literature16-18 as well as in the current (2014) International Guidelines for Pressure Ulcer Prevention and Treatment1 as the most important factors causing the injury.

Many studies, both clinical and computational,16,18-21 recently have shown persons with obesity (defined by the World Health Organization22 [WHO] to be a BMI >30) and/or diabetes are at an increased risk for PUs. For individuals who are obese and especially morbidly obese according to the WHO classification (BMI >40), greater body-weight loads are transferred to the soft tissues of the buttocks through the ischial tuberosities (ITs) during sitting. Previous computer simulation studies16,18 have shown increased body-weight loads cause increased internal tissue loads, which are quantified by means of the mechanical strains (dimensionless deformations, measured by means of magnetic resonance imaging [MRI] and/or through biomechanical modeling) and stresses (forces per unit area of tissue evaluated, again, using biomechanical modeling) in the muscle and fat tissues of the buttocks. Per the clinical study of Cox et al,23 for example, individuals with a SCI are expected to gain 1.3–1.8 kg per week during their rehabilitation phase due to a lower level of physical activity. Additionally, as mentioned previously, obesity is commonly associated with diabetes, which increases the risk for PU development due to impaired perfusion, which can be amplified by vascular disease, ischemic heart disease, or congestive heart failure.24 Moreover, diabetes inflicts abnormal biomechanical changes to tissue stiffness. As shown in both animal studies and human cadaveric measurements,25-27 type 2 diabetes is associated with stiffening of collagen-rich connective tissues such as skin and subcutaneous fat. These changes to the biomechanical properties of tissues, where the affected tissues cannot adequately deform to dissipate body-weight loads, may add to the overall risk of injury. Furthermore, as suggested by Gefen,28 in the case of type 2 diabetes, peripheral sensory neuropathy may prevent patients from detecting the onset and progression of tissue damage.

Given the knowledge that sustained excessive and localized strains and stresses in soft tissues may jeopardize cell and tissue viability, the most important principle in preventing sitting-acquired PUs and DTIs is to minimize exposure to these strains and stresses in tissues. For this purpose, clinicians are normally guided to prescribe a soft, thick cushion on the wheelchair to better redistribute the buttocks-support contact pressures as well as the internal tissue loads.1 However, despite the known increased risk of PUs for persons with obesity and diabetes, no specific recommendations of a preferred support surface type (a cushion in particular) are available for these populations.

Finite element (FE) computational modeling is a powerful tool in PU research. It facilitates determination of internal mechanical loads (eg, deformations, strains, and stresses measured in Pascals) in tissues of weight-bearing body parts such as the heels and buttocks. Based on these data, FE modeling further facilitates isolation of the influence of specific intrinsic and extrinsic biomechanical risk factors for PUs and DTIs.10, 29-32 In practice, the sophisticated 3-dimensional (3D) geometry of body organs, typically acquired from medical imaging (such as MRI), is used to build an anatomically realistic reconstruction in the computer, which then is divided into numerous small elements (“finite” elements), each with a simple geometry (eg, bricks or pyramids). Then, the equations that describe the biophysical mechanical interactions between the weight-bearing tissues and the support surface are solved for each element with respect to its neighboring elements to ultimately form diagrams of the transfer of mechanical loads within the entire studied organ. This method allows researchers to artificially manipulate the anatomy and biophysical properties of the tissues (through changes in the geometrical features or mechanical properties assigned to the tissues) in order to identify the influence of different biomechanical factors (eg, muscle atrophy, presence of scars, and so on) on the resulting loads and hence their affect on PU and DTI risk.

The authors have been investigating the biomechanical efficacy of flat foam cushions, contoured foam cushions, and air cell-based (ACB) cushions for several years, using state-of-the-art, imaging-based FE modeling.30,31,33,34 The effect of increased BMI or fat mass on internal tissue loads in the buttocks also has been studied.16,18,33 However, work regarding these specific patient populations was limited to interactions of the seated buttocks with uniform flat or contoured foam cushions; more sophisticated cushion designs were not studied, although such data are needed to strengthen the volume of evidence in the field, particularly in light of certain findings. ACB technology was found to be superior to foams,31,34 and ACB cushions were noted to be used extensively on bariatric wheelchairs in clinical practice.

Accordingly, a computer modeling study was conducted using ACB cushions (provided by the manufacturer, ROHO Inc, Belleville, IL) to integrate previous modeling concepts regarding the ACB technology with documented pathoanatomical and biomechanical tissue changes that result from obesity and diabetes. The purpose of this biomechanical modeling study, which had a theoretical (computer simulation) study design, was to determine the trends of changes in internal tissue loads (strains and stresses) in individuals seated on an ACB cushion if obesity and diabetes occurs and evolves to assess the efficacy of the ACB technology in protecting these individuals if these diseases are present. 

Methods

In order to examine the effects of increased fat tissue mass and the presence of diabetes on the resulting biomechanical risk for developing PUs and DTIs, a theoretical/computational study was designed. Taken together, the literature reviewed in the Introduction section of this article indicates the higher the internal tissue load in the seated buttocks, the greater the biomechanical risk for the aforementioned injuries. A set of 10 computational model variants was developed to assess the biomechanical characteristics of sitting using the ACB cushion. Each computational model variant included a geometrical description of the IT bone, the gluteus maximus skeletal muscle, the colon smooth muscle, fat tissues, skin, and an ACB cushion (see Figure 1a). A single coronal MRI slice of the left buttock of a 21-year-old man 1 year post SCI was used for segmenting the anatomical features, as described in detail in previous publications.30,31,33,35 Briefly, the ScanIP® module of the Simpleware® software suite (Simpleware, Exeter, UK) was used to segment the different tissue components from the MRI slice. Then, a uniform 4-mm thickness was defined for the entire computational model.36 In 8 of the model variants, 4 levels of increased fat mass were incorporated by artificially increasing the original fat volume shown in the MRI, consistent with the work of Shoham et al,33 with either diabetic or nondiabetic tissue conditions (see Table 1: 4 fat masses times 2 tissue conditions equals 8 variants). The 2 other variants were the reference anatomy directly extracted from the MRI with nondiabetic or diabetic tissue properties (see Table 1). owm_0116_gefen_figure1

To generate the geometrical model of the ACB cushion, the tops of the pre-inflated air cells were cut. Detailed considerations regarding the geometrical and mechanical modeling of the ACB cushion are available in a previously published study.31 Briefly, the computer aided design (+CAD) module of the Simpleware® software suite was used to convert a CAD slice to a voxel-based array database and then define a uniform 4-mm thickness to the ACB cushion computational model.36 Next, to simulate the interaction between the buttocks anatomy and the ACB cushion, the anatomical model variants were incorporated with the ACB cushion geometric models using the Preview module of the FEBio FE simulation software package.37,38 To achieve a thin slice model, the front and back planes of the anatomical model and the ACB cushion were fixed in the perpendicular direction to eliminate any out-of-plane motions. The bottom surface of the cushion model was fixed in all directions, and frictional sliding was defined between the outer surface of the skin and the cushion, as was done in previously published studies.31,34 Distributed forces were applied over the inner surfaces of the air cells in order to stabilize the numerical calculations and to achieve a realistic collapse pattern of the air cells, as was done previously.31 owm_0116_gefen_table1

The mechanical behaviors and properties of all tissues were adopted from the literature and were the same as in the previously published studies with regard to sitting on ACB cushions31,34; a list of the relevant tissue types and stiffness properties is provided in Table 2. The specific considerations and description of the experimental evaluation of the material and structural behavior of the ACB cushion have been detailed previously.31 Diabetic skin and fat tissues were considered as being 40% stiffer than nondiabetic tissues, as noted by the measurements of Pai and Ledoux25 of cadaveric plantar tissues undergoing shear loading (see Table 2). owm_0116_gefen_table2

Vertical mechanical forces were applied on the buttocks model in the computer simulations to represent weight-bearing of the seated buttocks when immersing into the ACB cushion, as described in previous studies.30,31,34 Assuming the increased fat mass in model variants 3 through 10 (see Table 1) directly reflects changes in body weight, the pressure inside the air cells was iteratively adjusted until the total vertical reaction force acting back from the ACB cushion was linearly proportional to the change in the fat tissue mass in each model variant. As noted in previous studies,31 the collapse pattern of the air cells was verified to be realistic using photographs of the deformed ACB cushion through a transparent physical phantom of the buttocks made of plastic and representing the external anatomical surfaces of the human buttocks.

The simulations were constructed using the PreView module of the FEBio FE software suite (Version 1.14), analyzed using the Pardiso linear solver of FEBio (http://mrl.sci.utah.edu/software/febio) (Version 2.0.1), and post-processed using PostView of FEBio (Ver. 1.6).37 The runtime of each model variant was between 7 hours and 32 hours using a 64-bit Windows 8-based workstation with 2× Intel Xeon E5-2620 2.00 GHz CPU and 32 GB of RAM.

The average effective strains and stresses for muscle, fat, and skin tissues (calculated in Pascals) were compared among all the model variants. For fat tissue, strain and stress data were collected only from fat elements below the imaginary horizontal line passing through the point of intersection between the fat, muscle, and bone regions. For skin and muscle tissues, strain and stress data were collected and stored automatically by means of the FE modeling software from all the elements belonging to the skin and gluteus maximus muscle. The average effective strains and stresses were normalized with respect to the reference model variant 1 (see Table 1) in order to facilitate comparisons between simulation cases using Excel software (Microsoft Corp, Seattle, WA).

Results

Comparisons of the effective stress distributions, reported in Pascals, in the gluteus maximus muscle when seated on an ACB cushion between the reference anatomy (variant 1) and 4 cases of a gradual increase in fat mass (model variants 3,5,7,9) are shown in Figure 2. Stresses in muscle tissue for the simulated sitting on the ACB cushion and different fat mass conditions (as indicated in Figure 2) were in the range of 0–0.12 Pa. Consistent with previous studies,30,31,34 stress concentrations appeared in muscle tissue near the tip of the IT (see Figure 2), and peak strains appeared in fat tissue between the gluteus muscle and the skin. In all simulation cases (nondiabetic and diabetic), average effective strains and stresses in muscle tissue increased in value and in size of the affected tissue areas with the increase in fat mass (see Figures 2, 3a, 4a). Specifically, in the most extreme case of 40% increased fat mass with healthy tissue conditions, average effective strains and stresses in muscle tissue increased by 15% and 30%, respectively; the distribution of stress is shown in Figure 2. owm_0116_gefen_figure2

A comparison of the effective stress distributions in skin tissues when seated on an ACB cushion across all the model variants is shown in Figure 5 (quantitative trends of effects of increased fat mass and diabetic tissue conditions on skin tissue strains and stresses were reported in the C panels of Figures 3 and 4, respectively). In all of the simulated anatomies and in both nondiabetic and diabetic cases, the skin tissue was affected similarly to muscle, with a substantial increase in effective stresses with the increase in fat mass (see Figures 4c, 5). Interestingly, the average effective strains and stresses in fat tissues were only mildly affected by the increased fat mass (ie, within a ±20% range). However, differences between nondiabetic and diabetic tissue properties had a more pronounced effect on fat tissue strains (ie, exceeding a ±20% change) than on muscles and skin (see Figure 3). 

owm_0116_gefen_figure3owm_0116_gefen_figure4

In the simulation cases that incorporated diabetic (stiffer) tissue conditions, the average effective stresses in skin ranged between 0 and 0.5 Pa, which was the same range that had been calculated for the nondiabetic skin (see Figure 5). However, as diabetic fat and skin tissues become stiffer due to the disease, the effective strains in fat and skin tissues decreased with respect to the nondiabetic cases (see Figure 3b,c). Although the stiffness of skeletal muscle tissues has not been reported to be directly affected by diabetes, muscle tissue in the simulations was shown to be subjected to lower effective stresses in the diabetic cases, as shown in Figure 4a. owm_0116_gefen_figure5

Discussion

The authors’ previous work16,33 demonstrated strains and stresses in the weight-bearing soft tissues of the buttocks increase considerably with the increase in BMI or fat mass in the buttocks. Sopher and Gefen16 used a set of FE model variants to investigate how variations in BMI influence strain and stress distributions in the buttocks when a person is seated on flat stiff versus soft supports. Recently, Shoham et al33 used the same method to explore how variations in fat mass, coupled with intramuscular fat infiltration and muscular atrophy, affect the loads in the soft tissues of the buttocks on a contoured foam cushion fitted for the patient close to the time of the injury. Both studies reported a considerable increase in peak strains and stresses in gluteal muscle tissues, as well as increased volumetric exposures to critical levels of strains and stresses in the gluteus with an increased BMI or fat mass.

It is critically important to state that in the aforementioned previous studies16,21 about PU and DTI risks that obese individuals who sit on foam cushions, either flat foams or contoured foams, were consistently found to develop tissue stresses in the order of fPa. In this study using an ACB cushion, even the most extreme obese and diabetic conditions resulted in substantially lower tissue stresses with respect to the extents of increase in tissue stresses reported in the literature for obese individuals sitting on foam cushions or even for nonobese individuals sitting on foams, as mentioned previously. Hence, the potential biomechanical protective effect of ACB cushions still applies for obese and diabetic body and tissue conditions (see Figure 2).    

The current study also found an ACB cushion is able to keep the effective average strain and stress values from exceeding a +20% increase (see Figures 3a, 4a) for up to +20% increase in fat mass, which is equivalent in this model to reaching a BMI of 30 (the obesity threshold).16 The +20% increase in tissue strains and stresses on the ACB cushion when reaching obesity is a relatively moderate increase with respect to the previous findings,16 where the same extent of increase in fat mass had substantially more profound effects when sitting on flat foam supports (which required quantification using a logarithmic scale). Again, even after a 20% rise, tissue stresses on the ACB cushion are still substantially lower than those developing while sitting on flat foams and ill-fitting contoured foam cushions.30,34

To be cautious, and given the known limitations of computer simulations in biomechanical research, morbidly obese patients always should be considered as being at a high risk for DTI on any cushion because their body weight deforms their internal soft tissues to such a great extent.16 However, based on the above discussion, in less severe cases (eg, patients who are overweight and obese class I according to the definitions of the WHO used by the US National Institutes of Health,22 including those who exhibit diabetic tissue conditions), the present data suggest these patients may experience enhanced tissue protection from an ACB cushion with respect to flat or contoured foam cushions. 

Although many clinicians may consider diabetes a risk factor for PUs due to impaired blood perfusion and sensation, based on their clinical experience, they have found the altered mechanical properties of collagen-rich connective tissues (eg, skin and subcutaneous fat) also seem to play an important role in the etiology of PUs and DTIs in patients with diabetes.28 The locally increased soft tissue stiffness in skin and fat imposes the risk of elevated tissue stresses while also subjecting nearby tissue segments to an increased risk of deformation-inflicted injury (adjacent tissue regions need to deform more in order to compensate for the lack of deformability of the tissue sites more affected by the disease). Locally increased tissue deformations may be particularly dangerous in diabetes because these local deformations may distort, obstruct, or occlude capillaries and other microvessels that could compromise the performance of the vasculature and lymphatics in the affected sites in a situation where perfusion and tissue repair capacities often already are poor. Although average tissue strains decreased when (stiffer) diabetic tissue properties were considered in the current study (see Figure 3), localized tissue deformations and strains actually may rise at certain times because diabetes may not have a uniform homogeneous effect on tissues. Specifically, the slight decrease in strains and stresses found in the muscle tissue is likely due to an effective stiffening of the entire buttocks structure, which shields the muscle (but increases the stresses in fat and skin) when diabetes is present.

Unlike flat foam cushions, which offer low immersion and envelopment and zero adaptability as shown in previous biomechanical modeling work,29 and contoured foam cushions, which are custom-fitted to the patient at a specific time-point but then become less effective and may even endanger tissue viability as the body changes after the fitting as indicated by computer simulations,33 ACB cushions offer adjustability as well as adaptability. The ACB technology provides these adjustability and adaptability characteristics by conforming to the contours of the body and keeping this conformation ongoing even if the body contours change or if tissue stiffness properties are pathologically altered. Hence, an ACB cushion is able to conform to a wide variety of anatomical and physiological structures and changes in the bodies of patients. In previous biomechanical modeling studies,31,34 ACB cushions were shown to have the ability to accommodate disuse-related anatomical changes in the hard and soft tissues of the buttocks and also protect tissues when deep or superficial scars already exist. The present study expands the authors’ previous investigations; specifically, it illustrates the potential of the ACB cushion technology to protect tissues of individuals who are obese and diabetic.

The recommendation to use a soft, thick cushion on the wheelchair for PU and DTI prevention is a consensus in the medical and biomechanical literature.39 However, this recommendation is typically given in general (and sometimes even in vague) terms without specific indications for subgroups with known or suspected risk factors. In the current authors’ work, it has been observed a clinician who needs to decide which cushion to prescribe makes that decision based on experience and “clinical judgment” or experience combined with pressure mapping (but pressure mapping is limited to quantifying skin pressures per se). Although clinical experience should never be underestimated, the field of PU prevention needs more quantitative decision-making tools, in addition to pressure mapping, now that the current understanding is PUs form as a result of sustained deep tissue deformations and loads. Many clinicians want to make evidence-based decisions regarding prescriptions of cushions to individuals. In this context, while clinicians commonly (and rightfully) assume patients who are obese and have diabetes are at an increased risk for PUs and DTIs, no specific recommendations are available regarding the types of cushion technologies that can better protect these patients.

Limitations

Computational FE modeling is currently the only feasible method for correlating cushion design features (eg, technology, shape, and material types and composition) with internal strains and stresses in the weight-bearing soft tissues of the seated buttocks and the corresponding risk for sitting-related PUs and DTIs.19,40 Nevertheless, computer modeling and simulations always involve limitations stemming from inherent assumptions and simplifications or omissions. First, the mechanical properties of the tissues were selected, as in most computational models, based on animal studies. Given the focus in this study is not on transient biomechanical phenomena in sitting, such as macro- and micro-movements, tissues are assumed to be hyperelastic rather than viscoelastic — that is, their mechanical stiffness is assumed to be time-independent — but this assumption is adequate because sitting is described as lasting tens of minutes to hours, which is longer than the transient stiffness changes associated with viscoelasticity.16 Additionally, the reference anatomical variant is of a person with a SCI rather than a healthy individual. As soon as 1 year following the injury, the reference MRI slice shows some degree of disuse-induced muscular atrophy associated with the SCI. Furthermore, reducing the 3D physical conditions to a slice model imposes additional limitations because the actual 3D mechanical interaction between the buttocks and the cushion are not considered, particularly out-of-plane forces. Finally, the changes in fat mass were introduced artificially under the assumption the volume of fat tissue in the buttocks increases proportionally to the increase in body weight, which is not necessarily the case. However, the authors were encouraged to see despite the limitations of FE modeling, the wound prevention community is now adopting FE as a tool for evaluating the efficacy of prevention technologies.41 Essentially, the international wound prevention industry is catching up with more mature medical device industries such as orthopedic implants or cardiovascular devices, where use of FE modeling for evaluating designs and efficacies is well-established.

Conclusion

The present study shows the tested ACB cushion was able to keep the effective average strain and stress values from increasing substantially as the amount of body fat increased or as diabetic tissue conditions developed. Thus, in theory, wheelchair users who are obese and diabetic may benefit from using an ACB cushion, because the results of this study suggest this may minimize the already increased mechanical strains and stresses in the weight-bearing soft tissues in the buttocks. Prospective clinical studies are needed to increase understanding about the risk factors of both obesity and diabetes mellitus for the development of PUs and DTIs. In addition, robust preclinical comparative studies may facilitate the development of complete, evidence-based guidelines for prescribing different cushion technologies depending on the individual risks for PUs and DTI. n

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Potential Conflicts of Interest: This research project is supported by a grant from ROHO, Inc, Belleville, IL aimed at developing computational models for evaluating the effects of cushioning materials and designs on buttocks tissues during weight bearing. Dr. Gefen is the Chair of ROHO’s Scientific Advisory Board. Ms. Kopplin is employed by ROHO, Inc.

 

Ms. Levy is a doctoral student, Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel. Ms. Kopplin is the Senior Director of Efficacy and Research, ROHO, Inc, Belleville, IL. Dr. Gefen is a Professor in Biomedical Engineering, Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University. Please address correspondence to: Prof. Amit Gefen, Department of Biomedical Engineering, Faculty of Engineering, Tel Aviv University, Tel Aviv 69978, Israel; email: gefen@eng.tau.ac.il.

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