A Contemporary Look at Biomechanical Models of Myocardium.

Understanding and predicting the mechanical behavior of myocardium under healthy and pathophysiological conditions are vital to developing novel cardiac therapies and promoting personalized interventions. Within the past 30 years, various constitutive models have been proposed for the passive mechanical behavior of myocardium. These models cover a broad range of mathematical forms, microstructural observations, and specific test conditions to which they are fitted. We present a critical review of these models, covering both phenomenological and structural approaches, and their relations to the underlying structure and function of myocardium. We further explore the experimental and numerical techniques used to identify the model parameters. Next, we provide a brief overview of continuum-level electromechanical models of myocardium, with a focus on the methods used to integrate the active and passive components of myocardial behavior. We conclude by pointing to future directions in the areas of optimal form as well as new approaches for constitutive modeling of myocardium.

Assessing Patient-Specific Mechanical Properties of Aortic Wall and Peri-Aortic Structures From In Vivo DENSE Magnetic Resonance Imaging Using an Inverse Finite Element Method and Elastic Foundation Boundary Conditions.

The establishment of in vivo, noninvasive patient-specific, and regionally resolved techniques to quantify aortic properties is key to improving clinical risk assessment and scientific understanding of vascular growth and remodeling. A promising and novel technique to reach this goal is an inverse finite element method (FEM) approach that utilizes magnetic resonance imaging (MRI)-derived displacement fields from displacement encoding with stimulated echoes (DENSE). Previous studies using DENSE MRI suggested that the infrarenal abdominal aorta (IAA) deforms heterogeneously during the cardiac cycle. We hypothesize that this heterogeneity is driven in healthy aortas by regional adventitial tethering and interaction with perivascular tissues, which can be modeled with elastic foundation boundary conditions (EFBCs) using a collection of radially oriented springs with varying stiffness with circumferential distribution. Nine healthy IAAs were modeled using previously acquired patient-specific imaging and displacement fields from steady-state free procession (SSFP) and DENSE MRI, followed by assessment of aortic wall properties and heterogeneous EFBC parameters using inverse FEM. In contrast to traction-free boundary condition, prescription of EFBC reduced the nodal displacement error by 60% and reproduced the DENSE-derived heterogeneous strain distribution. Estimated aortic wall properties were in reasonable agreement with previously reported experimental biaxial testing data. The distribution of normalized EFBC stiffness was consistent among all patients and spatially correlated to standard peri-aortic anatomical features, suggesting that EFBC could be generalized for human adults with normal anatomy. This approach is computationally inexpensive, making it ideal for clinical research and future incorporation into cardiovascular fluid-structure analyses.

Thromboresistance comparison of the HeartMate II ventricular assist device with the device thrombogenicity emulation- optimized HeartAssist 5 VAD.

Approximately 7.5 × 106 patients in the US currently suffer from end-stage heart failure. The FDA has recently approved the designations of the Thoratec HeartMate II ventricular assist device (VAD) for both bridge-to-transplant and destination therapy (DT) due to its mechanical durability and improved hemodynamics. However, incidence of pump thrombosis and thromboembolic events remains high, and the life-long complex pharmacological regimens are mandatory in its VAD recipients. We have previously successfully applied our device thrombogenicity emulation (DTE) methodology for optimizing device thromboresistance to the Micromed Debakey VAD, and demonstrated that optimizing device features implicated in exposing blood to elevated shear stresses and exposure times significantly reduces shear-induced platelet activation and significantly improves the device thromboresistance. In the present study, we compared the thrombogenicity of the FDA-approved HeartMate II VAD with the DTE-optimized Debakey VAD (now labeled HeartAssist 5). With quantitative probability density functions of the stress accumulation along large number of platelet trajectories within each device which were extracted from numerical flow simulations in each device, and through measurements of platelet activation rates in recirculation flow loops, we specifically show that: (a) Platelets flowing through the HeartAssist 5 are exposed to significantly lower stress accumulation that lead to platelet activation than the HeartMate II, especially at the impeller-shroud gap regions (b) Thrombus formation patterns observed in the HeartMate II are absent in the HeartAssist 5 (c) Platelet activation rates (PAR) measured in vitro with the VADs mounted in recirculation flow-loops show a 2.5-fold significantly higher PAR value for the HeartMate II. This head to head thrombogenic performance comparative study of the two VADs, one optimized with the DTE methodology and one FDA-approved, demonstrates the efficacy of the DTE methodology for drastically reducing the device thrombogenic potential, validating the need for a robust in silico/in vitro optimization methodology for improving cardiovascular devices thromboresistance.

Quantification of the heterogeneous effect of static and dynamic perivascular structures on patient-specific local aortic wall mechanics using inverse finite element modeling and DENSE MRI.

Recent studies have highlighted the relevance of perivascular interactions on aortic wall mechanics. Most of the approaches assume static perivascular structures; however, the beating heart dynamically displaces the neighboring aorta. We develop a model to account for the effect of periaortic interactions due to static and dynamic structures by prescribing a moving elastic foundation boundary condition (EFBC) embedded into an inverse finite element algorithm using in vivo displacements from 2D displacement encoding with stimulated echoes (DENSE) MRI as target data. We applied this method at three different locations of interest, the distal aortic arch (DAA), descending thoracic aorta (DTA), and infrarenal abdominal aorta (IAA) for a total of 27 cases in healthy humans. The model reproduces the target diastole-to-systole deformation and bulk displacement of the aortic wall with median displacement errors below 0.5mm. The EFBC showed good agreement with the location of anatomical features and was consistent among individuals of similar characteristics. Results show that an energy source acting on the adventitia is required to reproduce the displacements measured at the vicinity of the heart, but not at the abdomen. The average adventitial load as a percentage of the luminal pulse-pressure was found to increase with age and to decrease along the descending aorta, from 61% at the DAA to 37% at the DTA, and 30% at the IAA. This approach offers a patient-specific method to estimate in vivo adventitial loads and aortic wall stiffness, which can bring a better understanding of normal and pathological in vivo aortic function.

Patient-Specific Inverse Modeling of In Vivo Cardiovascular Mechanics with Medical Image-Derived Kinematics as Input Data: Concepts, Methods, and Applications.

Inverse modeling approaches in cardiovascular medicine are a collection of methodologies that can provide non-invasive patient-specific estimations of tissue properties, mechanical loads, and other mechanics-based risk factors using medical imaging as inputs. Its incorporation into clinical practice has the potential to improve diagnosis and treatment planning with low associated risks and costs. These methods have become available for medical applications mainly due to the continuing development of image-based kinematic techniques, the maturity of the associated theories describing cardiovascular function, and recent progress in computer science, modeling, and simulation engineering. Inverse method applications are multidisciplinary, requiring tailored solutions to the available clinical data, pathology of interest, and available computational resources. Herein, we review biomechanical modeling and simulation principles, methods of solving inverse problems, and techniques for image-based kinematic analysis. In the final section, the major advances in inverse modeling of human cardiovascular mechanics since its early development in the early 2000s are reviewed with emphasis on method-specific descriptions, results, and conclusions. We draw selected studies on healthy and diseased hearts, aortas, and pulmonary arteries achieved through the incorporation of tissue mechanics, hemodynamics, and fluid-structure interaction methods paired with patient-specific data acquired with medical imaging in inverse modeling approaches.

Evaluation of perfusion-driven cell seeding of small diameter engineered tissue vascular grafts with a custom-designed seed-and-culture bioreactor.

Tissue engineering commonly entails combining autologous cell sources with biocompatible scaffolds for the replacement of damaged tissues in the body. Scaffolds provide functional support while also providing an ideal environment for the growth of new tissues until host integration is complete. To expedite tissue development, cells need to be distributed evenly within the scaffold. For scaffolds with a small diameter tubular geometry, like those used for vascular tissue engineering, seeding cells evenly along the luminal surface can be especially challenging. Perfusion-based cell seeding methods have been shown to promote increased uniformity in initial cell distribution onto porous scaffolds for a variety of tissue engineering applications. We investigate the seeding efficiency of a custom-designed perfusion-based seed-and-culture bioreactor through comparisons to a static injection counterpart method and a more traditional drip seeding method. Murine vascular smooth muscle cells were seeded onto porous tubular electrospun polycaprolactone scaffolds, 2 mm in diameter and 30 mm in length, using the three methods, and allowed to rest for 24 hours. Once harvested, scaffolds were evaluated longitudinally and circumferentially to assess the presence of viable cells using alamarBlue and live/dead cell assays and their distribution with immunohistochemistry and scanning electron microscopy. On average, bioreactor-mediated perfusion seeding achieved 35% more luminal surface coverage when compared to static methods. Viability assessment demonstrated that the total number of viable cells achieved across methods was comparable with slight advantage to the bioreactor-mediated perfusion-seeding method. The method described is a simple, low-cost method to consistently obtain even distribution of seeded cells onto the luminal surfaces of small diameter tubular scaffolds.

The impact of myocardial compressibility on organ-level simulations of the normal and infarcted heart.

Myocardial infarction (MI) rapidly impairs cardiac contractile function and instigates maladaptive remodeling leading to heart failure. Patient-specific models are a maturing technology for developing and determining therapeutic modalities for MI that require accurate descriptions of myocardial mechanics. While substantial tissue volume reductions of 15-20% during systole have been reported, myocardium is commonly modeled as incompressible. We developed a myocardial model to simulate experimentally-observed systolic volume reductions in an ovine model of MI. Sheep-specific simulations of the cardiac cycle were performed using both incompressible and compressible tissue material models, and with synchronous or measurement-guided contraction. The compressible tissue model with measurement-guided contraction gave best agreement with experimentally measured reductions in tissue volume at peak systole, ventricular kinematics, and wall thickness changes. The incompressible model predicted myofiber peak contractile stresses approximately double the compressible model (182.8 kPa, 107.4 kPa respectively). Compensatory changes in remaining normal myocardium with MI present required less increase of contractile stress in the compressible model than the incompressible model (32.1%, 53.5%, respectively). The compressible model therefore provided more accurate representation of ventricular kinematics and potentially more realistic computed active contraction levels in the simulated infarcted heart. Our findings suggest that myocardial compressibility should be incorporated into future cardiac models for improved accuracy.

On the in vivo systolic compressibility of left ventricular free wall myocardium in the normal and infarcted heart.

Although studied for many years, there remain continued gaps in our fundamental understanding of cardiac kinematics, such as the nature and extent of heart wall volumetric changes that occur over the cardiac cycle. Such knowledge is especially important for accurate in silico simulations of cardiac pathologies and in the development of novel therapies for their treatment. A prime example is myocardial infarction (MI), which induces profound, regionally variant maladaptive remodeling of the left ventricle (LV) wall. To address this problem, we conducted an in vivo fiduciary marker-based study in an established ovine model of MI to generate detailed, time-evolving transmural in vivo volumetric measurements of LV free wall deformations in the normal state, as well as up to 12 h post-MI. This was accomplished using a transmural array of sonomicrometry crystals that acquired fiducial positions at ∼250 Hz with a positional accuracy of ∼0.1 mm, covering the entire infarct, border, and remote zones. A convex-hull method was used to directly calculate the Jacobian J(t)=Δv(t)/ΔVED from sonocrystal positions over the entire cardiac cycle, where ΔV is the volume of each convex polyhedral at end diastole (ED) (typically ∼1 cc). We demonstrated significant in vivo compressibility in normal functioning LV free wall myocardium, with JES=0.85±0.07 at end systole (ES). We also observed substantial regional variations, with the largest reduction in local myocardial tissue volume during systole in the base region accompanied by substantial transmural gradients. These patterns changed profoundly following loss of perfusion post-MI, with the apical region showing the greatest loss of volume reduction at ES. To verify that the sonocrystals did not affect local volumetric measurements, JES measures were also verified by non-invasive magnetic resonance imaging, exhibiting very similar changes in regional volume. We note that while our estimates of regional compressibility were in close agreement with the values previously reported for large animals, ranging from 5% to 20%, the direct, comprehensive measurements of wall compressibility presented herein improved on the limitations of previous reports. These limitations included dependency on the small local volumes used for analysis and often indirect measurement of compressibility. Our novel findings suggest that proper accounting for the myocardial effective compressibility at the ∼1 cc volume scale can improve the accuracy of existing kinematic indices, such as wall thickening and axial shortening, and simulations of LV remodeling following MI.

A Computational Cardiac Model for the Adaptation to Pulmonary Arterial Hypertension in the Rat.

Pulmonary arterial hypertension (PAH) imposes pressure overload on the right ventricle (RV), leading to RV enlargement via the growth of cardiac myocytes and remodeling of the collagen fiber architecture. The effects of these alterations on the functional behavior of the right ventricular free wall (RVFW) and organ-level cardiac function remain largely unexplored. Computational heart models in the rat (RHMs) of the normal and hypertensive states can be quite valuable in simulating the effects of PAH on cardiac function to gain insights into the pathophysiology of underlying myocardium remodeling. We thus developed high-fidelity biventricular finite element RHMs for the normal and post-PAH hypertensive states using extensive experimental data collected from rat hearts. We then applied the RHM to investigate the transmural nature of RVFW remodeling and its connection to wall stress elevation under PAH. We found a strong correlation between the longitudinally-dominated fiber-level adaptation of the RVFW and the transmural alterations of relevant wall stress components. We further conducted several numerical experiments to gain new insights on how the RV responds both normally and in the post-PAH state. We found that the effect of pressure overload alone on the increased contractility of the RV is comparable to the effects of changes in the RV geometry and stiffness. Furthermore, our RHMs provided fresh perspectives on long-standing questions of the functional role of the interventricular septum in RV function. Specifically, we demonstrated that an inaccurate identification of the mechanical adaptation of the septum can lead to a significant underestimation of RVFW contractility in the post-PAH state. These findings show how integrated experimental-computational models can facilitate a more comprehensive understanding of the cardiac remodeling events during PAH.

An integrated inverse model-experimental approach to determine soft tissue three-dimensional constitutive parameters: application to post-infarcted myocardium.

Knowledge of the complete three-dimensional (3D) mechanical behavior of soft tissues is essential in understanding their pathophysiology and in developing novel therapies. Despite significant progress made in experimentation and modeling, a complete approach for the full characterization of soft tissue 3D behavior remains elusive. A major challenge is the complex architecture of soft tissues, such as myocardium, which endows them with strongly anisotropic and heterogeneous mechanical properties. Available experimental approaches for quantifying the 3D mechanical behavior of myocardium are limited to preselected planar biaxial and 3D cuboidal shear tests. These approaches fall short in pursuing a model-driven approach that operates over the full kinematic space. To address these limitations, we took the following approach. First, based on a kinematical analysis and using a given strain energy density function (SEDF), we obtained an optimal set of displacement paths based on the full 3D deformation gradient tensor. We then applied this optimal set to obtain novel experimental data from a 1-cm cube of post-infarcted left ventricular myocardium. Next, we developed an inverse finite element (FE) simulation of the experimental configuration embedded in a parameter optimization scheme for estimation of the SEDF parameters. Notable features of this approach include: (i) enhanced determinability and predictive capability of the estimated parameters following an optimal design of experiments, (ii) accurate simulation of the experimental setup and transmural variation of local fiber directions in the FE environment, and (iii) application of all displacement paths to a single specimen to minimize testing time so that tissue viability could be maintained. Our results indicated that, in contrast to the common approach of conducting preselected tests and choosing an SEDF a posteriori, the optimal design of experiments, integrated with a chosen SEDF and full 3D kinematics, leads to a more robust characterization of the mechanical behavior of myocardium and higher predictive capabilities of the SEDF. The methodology proposed and demonstrated herein will ultimately provide a means to reliably predict tissue-level behaviors, thus facilitating organ-level simulations for efficient diagnosis and evaluation of potential treatments. While applied to myocardium, such developments are also applicable to characterization of other types of soft tissues.

A mathematical model for the determination of forming tissue moduli in needled-nonwoven scaffolds.

Formation of engineering tissues (ET) remains an important scientific area of investigation for both clinical translational and mechanobiological studies. Needled-nonwoven (NNW) scaffolds represent one of the most ubiquitous biomaterials based on their well-documented capacity to sustain tissue formation and the unique property of substantial construct stiffness amplification, the latter allowing for very sensitive determination of forming tissue modulus. Yet, their use in more fundamental studies is hampered by the lack of: (1) substantial understanding of the mechanics of the NNW scaffold itself under finite deformations and means to model the complex mechanical interactions between scaffold fibers, cells, and de novo tissue; and (2) rational models with reliable predictive capabilities describing their evolving mechanical properties and their response to mechanical stimulation. Our objective is to quantify the mechanical properties of the forming ET phase in constructs that utilize NNW scaffolds. We present herein a novel mathematical model to quantify their stiffness based on explicit considerations of the modulation of NNW scaffold fiber-fiber interactions and effective fiber stiffness by surrounding de novo ECM. Specifically, fibers in NNW scaffolds are effectively stiffer than if acting alone due to extensive fiber-fiber cross-over points that impart changes in fiber geometry, particularly crimp wavelength and amplitude. Fiber-fiber interactions in NNW scaffolds also play significant role in the bulk anisotropy of the material, mainly due to fiber buckling and large translational out-of-plane displacements occurring to fibers undergoing contraction. To calibrate the model parameters, we mechanically tested impregnated NNW scaffolds with polyacrylamide (PAM) gels with a wide range of moduli with values chosen to mimic the effects of surrounding tissues on the scaffold fiber network. Results indicated a high degree of model fidelity over a wide range of planar strains. Lastly, we illustrated the impact of our modeling approach quantifying the stiffness of engineered ECM after in vitro incubation and early stages of in vivo implantation obtained in a concurrent study of engineered tissue pulmonary valves in an ovine model. STATEMENT OF SIGNIFICANCE: Regenerative medicine has the potential to fully restore diseased tissues or entire organs with engineered tissues. Needled-nonwoven scaffolds can be employed to serve as the support for their growth. However, there is a lack of understanding of the mechanics of these materials and their interactions with the forming tissues. We developed a mathematical model for these scaffold-tissue composites to quantify the mechanical properties of the forming tissues. Firstly, these measurements are pivotal to achieve functional requirements for tissue engineering implants; however, the theoretical development yielded critical insight into particular mechanisms and behaviors of these scaffolds that were not possible to conjecture without the insight given by modeling, let alone describe or foresee a priori.

Modeling of Myocardium Compressibility and its Impact in Computational Simulations of the Healthy and Infarcted Heart.

Simulation of heart function requires many components, including accurate descriptions of regional mechanical behavior of the normal and infarcted myocardium. Myocardial compressibility has been known for at least two decades, however its experimental measurement and incorporation into compu-tational simulations has not yet been widely utilized in contemporary cardiac models. In the present work, based on novel in-vivo ovine experimental data, we developed a specialized compressible model that reproduces the peculiar unim-odal compressible behavior of myocardium. Such simulations will be extremely valuable to understand etiology and pathophysiology of myocardium remodeling and its impact on tissue-level properties and organ-level cardiac function.

Biomechanical Challenges to Polymeric Biodegradable Stents.

Biodegradable implants have demonstrated clinical success in simple applications (e.g., absorbable sutures) and have shown great potential in many other areas of interventional medicine, such as localized drug delivery, engineered tissue scaffolding, and structural implants. For endovascular stenting and musculoskeletal applications, they can serve as temporary mechanical support that provides a smooth stress-transfer from the degradable implant to the healing tissue. However, for more complex device geometries, in vivo environments, and evolving load-bearing functions, such as required for vascular stents, there are considerable challenges associated with the use of biodegradable materials. A biodegradable stent must restore blood flow and provide support for a predictable appropriate period to facilitate artery healing, and subsequently, fail safely and be absorbed in a controllable manner. Biodegradable polymers are typically weaker than metals currently employed to construct stents, so it is difficult to ensure sufficient strength to keep the artery open and alleviate symptoms acutely while keeping other design parameters within clinically acceptable ranges. These design challenges are serious, given the general lack of understanding of biodegradable polymer behavior and evolution in intimal operating conditions. The modus operandi is mainly empirical and relies heavily on trial-and-error methodologies burdened by difficult, resource-expensive, and time-consuming experiments. We are striving for theoretical advancements systematizing the empirical knowledge into rational frameworks that could be cast into in silico tools for simulation and product development optimization. These challenges are evident when one considers that there are no biodegradable stents on the US market despite more than 30 years of development efforts (and currently only a couple with CE mark). This review summarizes previous efforts at implementing biodegradable stents, discusses the specific challenges involved, and presents recently developed material-modeling frameworks that can benefit this exciting field.

A triphasic constrained mixture model of engineered tissue formation under in vitro dynamic mechanical conditioning.

While it has become axiomatic that mechanical signals promote in vitro engineered tissue formation, the underlying mechanisms remain largely unknown. Moreover, efforts to date to determine parameters for optimal extracellular matrix (ECM) development have been largely empirical. In the present work, we propose a two-pronged approach involving novel theoretical developments coupled with key experimental data to develop better mechanistic understanding of growth and development of dense connective tissue under mechanical stimuli. To describe cellular proliferation and ECM synthesis that occur at rates of days to weeks, we employ mixture theory to model the construct constituents as a nutrient-cell-ECM triphasic system, their transport, and their biochemical reactions. Dynamic conditioning protocols with frequencies around 1 Hz are described with multi-scale methods to couple the dissimilar time scales. Enhancement of nutrient transport due to pore fluid advection is upscaled into the growth model, and the spatially dependent ECM distribution describes the evolving poroelastic characteristics of the scaffold-engineered tissue construct. Simulation results compared favorably to the existing experimental data, and most importantly, distinguish between static and dynamic conditioning regimes. The theoretical framework for mechanically conditioned tissue engineering (TE) permits not only the formulation of novel and better-informed mechanistic hypothesis describing the phenomena underlying TE growth and development, but also the exploration/optimization of conditioning protocols in a rational manner.

Biomechanical Behavior of Bioprosthetic Heart Valve Heterograft Tissues: Characterization, Simulation, and Performance.

The use of replacement heart valves continues to grow due to the increased prevalence of valvular heart disease resulting from an ageing population. Since bioprosthetic heart valves (BHVs) continue to be the preferred replacement valve, there continues to be a strong need to develop better and more reliable BHVs through and improved the general understanding of BHV failure mechanisms. The major technological hurdle for the lifespan of the BHV implant continues to be the durability of the constituent leaflet biomaterials, which if improved can lead to substantial clinical impact. In order to develop improved solutions for BHV biomaterials, it is critical to have a better understanding of the inherent biomechanical behaviors of the leaflet biomaterials, including chemical treatment technologies, the impact of repetitive mechanical loading, and the inherent failure modes. This review seeks to provide a comprehensive overview of these issues, with a focus on developing insight on the mechanisms of BHV function and failure. Additionally, this review provides a detailed summary of the computational biomechanical simulations that have been used to inform and develop a higher level of understanding of BHV tissues and their failure modes. Collectively, this information should serve as a tool not only to infer reliable and dependable prosthesis function, but also to instigate and facilitate the design of future bioprosthetic valves and clinically impact cardiology.

Large strain stimulation promotes extracellular matrix production and stiffness in an elastomeric scaffold model.

Mechanical conditioning of engineered tissue constructs is widely recognized as one of the most relevant methods to enhance tissue accretion and microstructure, leading to improved mechanical behaviors. The understanding of the underlying mechanisms remains rather limited, restricting the development of in silico models of these phenomena, and the translation of engineered tissues into clinical application. In the present study, we examined the role of large strip-biaxial strains (up to 50%) on ECM synthesis by vascular smooth muscle cells (VSMCs) micro-integrated into electrospun polyester urethane urea (PEUU) constructs over the course of 3 weeks. Experimental results indicated that VSMC biosynthetic behavior was quite sensitive to tissue strain maximum level, and that collagen was the primary ECM component synthesized. Moreover, we found that while a 30% peak strain level achieved maximum ECM synthesis rate, further increases in strain level lead to a reduction in ECM biosynthesis. Subsequent mechanical analysis of the formed collagen fiber network was performed by removing the scaffold mechanical responses using a strain-energy based approach, showing that the denovo collagen also demonstrated mechanical behaviors substantially better than previously obtained with small strain training and comparable to mature collagenous tissues. We conclude that the application of large deformations can play a critical role not only in the quantity of ECM synthesis (i.e. the rate of mass production), but also on the modulation of the stiffness of the newly formed ECM constituents. The improved understanding of the process of growth and development of ECM in these mechano-sensitive cell-scaffold systems will lead to more rational design and manufacturing of engineered tissues operating under highly demanding mechanical environments.

A novel mathematical model of activation and sensitization of platelets subjected to dynamic stress histories.

Blood recirculating devices, such as ventricular assist devices and prosthetic heart valves, are burdened by thromboembolic complications requiring complex and lifelong anticoagulant therapy with its inherent hemorrhagic risks. Pathologic flow patterns occurring in such devices chronically activate platelets, and the optimization of their thrombogenic performance requires the development of flow-induced platelet activation models. However, existing models are based on empirical correlations using the well-established power law paradigm of constant levels of shear stress during certain exposure times as factors for mechanical platelet activation. These models are limited by their range of application and do not account for other relevant phenomena, such as loading rate dependence and platelet sensitization to high stress conditions, which characterize the dynamic flow conditions in devices. These limitations were addressed by developing a new class of phenomenological stress-induced platelet activation models that specifies the rate of platelet activation as a function of the entire stress history and results in a differential equation that can be directly integrated to calculate the cumulative levels of activation. The proposed model reverts to the power law under constant shear stress conditions and is able to describe experimental results in response to a diverse range of highly dynamic stress conditions found in blood recirculating devices. The model was tested in vitro under emulated device flow conditions and correlates well with experimental results. This new model provides a reliable and robust mathematical tool that can be incorporated into computational fluid dynamic studies in order to optimize design, with the goal of improving the thrombogenic performance of blood recirculating devices.

Simulation of platelets suspension flowing through a stenosis model using a dissipative particle dynamics approach.

Stresses on blood cellular constituents induced by blood flow can be represented by a continuum approach down to the µm level; however, the molecular mechanisms of thrombosis and platelet activation and aggregation are on the order of nm. The coupling of the disparate length and time scales between molecular and macroscopic transport phenomena represents a major computational challenge. In order to bridge the gap between macroscopic flow scales and the cellular scales with the goal of depicting and predicting flow induced thrombogenicity, multi-scale approaches based on particle methods are better suited. We present a top-scale model to describe bulk flow of platelet suspensions: we employ dissipative particle dynamics to model viscous flow dynamics and present a novel and general no-slip boundary condition that allows the description of three-dimensional viscous flows through complex geometries. Dissipative phenomena associated with boundary layers and recirculation zones are observed and favorably compared to benchmark viscous flow solutions (Poiseuille and Couette flows). Platelets in suspension, modeled as coarse-grained finite-sized ensembles of bound particles constituting an enclosed deformable membrane with flat ellipsoid shape, show self-orbiting motions in shear flows consistent with Jeffery's orbits, and are transported with the flow, flipping and colliding with the walls and interacting with other platelets.

A mixture model for water uptake, degradation, erosion and drug release from polydisperse polymeric networks.

We introduce a general class of mixture models suitable to describe water-dependent degradation and erosion of biodegradable polymers in conjunction with drug release. The ability to predict and quantify degradation and erosion has direct impact in a variety of biomedical applications and is a useful design tool for biodegradable implants and tissue engineering scaffolds. The model is based on a finite number of constituents describing the polydisperse polymeric system, each representing chains of an average size, and two additional constituents, water and drug. Hydrolytic degradation of individual chains occurs at the molecular level and mixture constituents diffuse individually accordingly to Fick's 1st law at the bulk level - such analysis confers a multi-scale aspect to the resulting reaction-diffusion system. A shift between two different types of behavior, each identified to surface or bulk erosion, is observed with the variation of a single non-dimensional parameter measuring the relative importance of the mechanisms of reaction and diffusion. Mass loss follows a sigmoid decrease in bulk eroding polymers, whereas decreases linearly in surface eroding polymers. Polydispersity influences degradation and erosion of bulk eroding polymers and drug release from unstable surface eroding matrices is dramatically enhanced in an erosion-controlled release.