Abdominal aortic aneurysm (AAA) is a permanent, localized enlargement of the abdominal aorta that accompanies disturbed blood flow, which is thought to perpetuate aneurysm progression. AAA rupture is a leading cause of death in the elderly and an exact intervention decision for this disease has always been associated with uncertainty. There is currently no medicinal treatment of AAA, however lower extremity exercise has been a proposed therapy. Specifically, elevated flow rates in the abdominal aorta, reduced retrograde flow, higher mean wall shear stress, and lower oscillatory shear index resulting from exercise have been hypothesized as beneficial in preventing or slowing AAA. Computational fluid dynamics (CFD) has recently been used to model flow conditions inside AAA with an aim to better understand the biomechanical underpinnings of this disease. Recent studies have used patient-specific computational models, however few studies have looked in detail to AAA transport topology or correlated their results with aneurysm progression data. This study aims to (1) compare the flow topology between rest and exercise conditions in patients with small AAA to understand specifically how blood transport changes from rest to exercise, and (2) compare flow parameters obtained by CFD to the aneurysm progression.

Because the left ventricle (LV) is not completely emptied during systole, oxygenated blood from the left atrium interacts with residual blood from preceding cycles. It is hypothesized that LV flow is optimal for transporting blood under normal conditions; yet proving this remains a challenge. Furthermore, clinical evaluation of LV hemodynamics has tremendous diagnostic importance for patients with cardiomyopathy. We have performed Doppler-echocardiography on 6 patients with dilated cardiomyopathy and 6 healthy volunteers. Using novel processing of the color-Doppler data, bi-directional velocity field maps in the apical long axis plane were derived. Resulting flow data was used to perform Lagrangian coherent structure (LCS) computation, which enabled novel characterization of the transport topology in the LV during filling and ejection. This framework was used to quantify stasis in the LV, which can be used as a surrogate for diagnosing pumping deficiencies and thrombosis risk. This framework also enables characterization of LV vortices, which have previously received much attention using Eulerian characterizations. The framework presented here uncovers the well-defined boundaries to both E-wave and A-wave filling vortices, which has not been previously reported.

Fibrous proteins, such as collagen and elastin, form the underlying structure of many soft tissues. These proteins form micrometer-scale networks of varying topology that play a role in governing the mechanics of tissues at larger length scales [1]. The relationship between a network’s topology and its mechanics, however, are poorly understood. This disconnect presents an important challenge in constructing realistic multiscale models of tissues informed by collagen network micrographs and subsequently reconstructed networks [2]. Accurate multiscale simulations may require thousands to millions of such unique networks. It is imperative that a method be developed to generate random networks that are functionally similar to ones derived experimentally. In the current study, we present a probabilistic method for generating de novo networks that mimic the mechanical properties of previously characterized networks. We chose Delaunay and Voronoi networks as model targets because they have been used successfully to model the mechanics of collagenous tissues [3] and since their topologies are well characterized. Understanding the role of topology in network mechanics is fundamental to building improved models of the mechanics of fibrous soft tissues — models that can aid in the rational design of engineered tissues or that can help assess the mechanical impact of damage or disease on native tissues.

Forces generated by the muscles actuating the fingers are transmitted through a complex network of tendons. Current models of the hand either ignore or simplify the structure of these networks [1]. It has been shown that the deformable nature of these tendinous networks results in a nonlinear transformation of muscle forces [2]. Our long-term objective is to understand how the topology of this network affects the control of finger force and motion. To achieve this, we will use a machine learning approach to evolve models of this network that can best replicate experimental results [3]. Here we present an anatomically realistic solver developed to model mechanical force transmission by a network of tendons in the human fingers. While most existing solvers neglect mechanics of tendon networks, there has been recent work on dynamic simulators accounting for tendon-bone interactions [4]. The solver we present here advances work in this field by being able to simulate mechanics of complex networks wrapped on arbitrarily shaped objects (like bones), and can be effectively used to model isometric force production in complex biomechanical systems. Its speed makes it an ideal simulation engine for the evolutionary algorithms we use to infer complex anatomical structures from sparse experimentation [3].

Abdominal aortic aneurysms (AAA) are characterized by disturbed flow patterns, low and oscillatory wall shear stress with high gradients, increased particle residence time, and mild turbulence. Diameter is the most common metric for rupture prediction, although this metric can be unreliable. We hypothesize that understanding the flow topology and mixing inside AAA could provide useful insight into mechanisms of aneurysm growth. AAA morphology has high variability, as with AAA hemodynamics, and therefore we consider patient-specific analyses over several small to medium sized AAAs. Vortical patterns dominate AAA hemodynamics and traditional analyses based on the Eulerian fields (e.g. velocity) fail to convey the complex flow structures. The computation of finite-time Lyapunov exponent (FTLE) fields and underlying Lagrangian coherent structures (LCS) help reveal a Lagrangian template for quantifying the flow [1].

In the last decade electrospinning has shown its potential of being a feasible technique to manufacture scaffolds for tissue engineering [1]. Previous studies observed that, on a micrometer scale, the topology of the scaffold plays a fundamental role in the spreading and the differentiation of the cells [2], and in the growth of neo-extracellular matrix. On a tissue scale (in the order of cm) the stiffness of the construct enables the possibility of applying mechanical cues for the development of a functional engineered tissue [3]. Studies on scaffold mechanics based on volume-averaging theory succeeded in demonstrating that the arrangement of the micro-scale scaffold components influences the macro-scale mechanical behavior [4].

As platelets are transported they are continuously stretched, compressed and sheared by local gradients in the flow. Exposure to elevated gradients can cause platelets to actively react with conformational, chemical and enzymatic responses, i.e. becoming activated. Once switched to the activated state, platelets perform multifaceted roles to orchestrate clotting. Mechanically-induced platelet activation under pathological conditions has been studied since the late 1970s. This work builds on [1], which introduced a trajectory-based level of activation parameter for platelets, and [2] describing coherent structures in cardiovascular flow. We introduce a new direction-independent Lagrangian measure. This measure is introduced as an activation potential in two senses. First, it provides a measure of mechanical strain, which has been shown to have the potential to activate platelets. Second, it is plotted at the initial location of the platelets. This latter condition is subtle, but it enables us to uncover an interesting observation that locations of highest activation potential tend to occur along structures that have important implications to the transport topology.

Passive knee kinematics and kinetics following total knee replacement (TKR) are dependent on the topology of the component joint surfaces as well as the properties of the passive soft tissue structures (ligaments and capsule). Recently, explicit computer models have been used for the prediction of knee joint kinematics based on experimental investigations [1]. However, most of these models replicate experimental knee simulators [2], which simulate soft tissue structures using springs or elastomeric structures. New generations of experimental setups deploy industrial robots for measuring kinematics and kinetics in six degrees of freedom as well as the contribution of soft tissue structures. Based on these experiments, accurate soft tissue properties are available for use in computer models to aid more realistic predictions of kinematics. Final evidence of the quality of the kinematic predictions from these computer models can be provided by direct validation of the models against experimental data. Therefore, the objective of this study was to use in vitro robotic test data to develop, verify, and validate specimen specific virtual models suitable for predicting laxity and kinematics of the reconstructed knee.

Soft tissues are comprised of underlying fiber networks of collagen and other fibrous proteins and biopolymers. Thus, the ability to model the deformation of fiber networks is critical to understanding the mechanics of tissues in vivo and in vitro [1]. Complicating the issue, protein fiber networks are comprised of a range of different topologies that behave differently under load. There is a clear need for a method to derive network parameters that characterize the network and allow for the prediction of their behavior. In this study, we characterized several different random fiber network types based on their intrinsic mechanical and topological properties. Such characterization would improve our ability to select microscale network topologies that match the mechanical properties we observe in healthy and diseased native tissues [2]. It would also improve our ability to discern the outcome of microstructural changes in tissues (such as from remodeling or injury) on their overall mechanics.

The initiation and progression of vessel wall pathologies have been linked to disturbances of blood flow and altered wall shear stress. The development of computational techniques in fluid dynamics, together with the increasing performances of hardware and software allow to routinely solve problems on a virtual environment, helping to understand the role of biomechanics factors in the healthy and diseased cardiovascular system and to reveal the interplay of biology and local fluid dynamics nearly intractable in the past, opening to detailed investigation of parameters affecting disease progression. One of the major difficulties encountered when wishing to model accurately the cardiovascular system is that the flow dynamics of the blood in a specific vascular district is strictly related to the global systemic dynamics. The multiscale modelling approach for the description of blood flow into vessels consists in coupling a detailed model of the district of interest in the framework of a synthetic description of the surrounding areas of the vascular net [1]. In the present work, we aim at evaluating the effect of boundary conditions on wall shear stress (WSS) related vessel wall indexes and on bulk flow topology inside a carotid bifurcation. To do it, we coupled an image-based 3D model of carotid bifurcation ( local computational domain), with a lumped parameters (0D) model ( global domain) which allows for physiological mimicking of the haemodynamics at the boundaries of the 3D carotid bifurcation model here investigated. Two WSS based blood-vessel wall interaction descriptors, the Time Averaged WSS (TAWSS), and the Oscillating Shear Index (OSI) were considered. A specific Lagrangian-based “bulk” blood flow descriptor, the Helical Flow Index (HFI) [2], was calculated in order to get a “measure” of the helical structure in the blood flow. In a first analysis the effects of the coupled 0D models on the 3D model are evaluated. The results obtained from the multiscale simulation are compared with the results of simulations performed using the same 3D model, but imposing a flow rate at internal carotid (ICA) outlet section equal to the maximum (60%) and the minimum (50%) flow division obtained out from ICA in the multiscale model simulation (the presence of the coupled 0D model gives variable internal/external flow division ratio during the cardiac cycle), and a stress free condition on the external carotid (ECA).

In recent years, interest is growing on compact measures for assessing the role of local hemodynamics in the pathogenesis of atherosclerosis and atherogenesis. CFD and its power in evaluating and predicting the effect of some hemodynamic variables in vascular disease is becoming a key factor in clinical research. Recently, Lee and Steinman [1] assessed the importance of blood rheology assumptions to ascertain the effect of constitutive relation for blood on local wall shear stress (WSS) and on the correlated vascular pathology. We present a preliminary in silico investigation on the sensitivity of helical flow measure with respect to the blood constitutive adopted model. Our main objective was to verify if, through the carotid bifurcation model, the rheological properties of blood significantly influence the bulk flow topology, whose evolution and stability are strictly linked to helicity. In fact helicity — an invariant in fluid dynamics — has been demonstrated to describe and reveal the global organization in a fluid flow. For this purpose several blood models (Newtonian and non-Newtonian) were implemented. A specific Lagrangian-based “bulk” flow descriptor, the Helical Flow Index (HFI) [2], was calculated in order to get a “measure” of the helical structure in the blood flow. Therefore, its sensitivity to blood rheology and hematocrit (Ht) was assessed and compared with the sensitivity of WSS based on other fluid dynamics descriptors (Time Averaged WSS, TAWSS, and Oscillating Shear Index, OSI).

Advances in medical imaging technology have allowed the extraction of 3D anatomic information non-invasively in vivo. This information has been used to reconstruct the anatomy of interest and obtain a realistic model of the 3D geometry. Such models provide a parametric shape description which allows for the quantitative comparison of inter or intra individual variability of topologically similar anatomic structures. However, the uncertainty associated with the imaging and reconstruction processes involved in generating these models limits the spatial information that can be accurately resolved utilizing this approach. This, within the context of arterial structures, limits the accuracy of the data obtained from flow simulations using these models. However, the primary effects on the hemodynamics of topology preserving changes in the geometry of arterial structures, such as those occurring due to changes in body posture associated with normal daily activity, could be resolved if the small scale surface features are separated from the strong shape features that characterize the topology. Here we develop geometric tools and methods to achieve this and apply them to assess the influence of head posture on carotid artery hemodynamics [1].

Extracellular matrix (ECM) proteins (e.g. collagen, elastin) play an important role in biological tissues. In addition to conferring mechanical strength to a tissue, the ECM provides a biochemical environment essential for modulation of cellular responses such as growth and migration. Collagens are the dominant protein of the ECM, with collagen type I being most abundant. Our group and others have shown that the mechanical properties of a collagen I matrix change with collagen concentration, and when formed in the presence of a secondary fibril network such as fibrin [1]. We are interested in collagen-fibrin systems because our group uses fibrin as the starting scaffold material for cardiovascular tissue engineering, which produces interpenetrating collagen-fibrin matrices during the remodeling process as the fibrin network is degraded and replaced with cell-deposited collagen [2]. Fibrin and collagen networks are also present together around the thrombus during the wound healing process. Research has shown that ECM mechanical properties are correlated with their overall network structure characteristics such as fibril diameter [3]. Currently we have a modeling framework that generates an ECM microstructural network which can be used to predict the overall properties of a bioengineered tissue [4]. This framework allows exploration of the structure-function relation, but how the structure depends on composition remains poorly understood, especially in multi-component gels. Thus, the objective of this work was to quantify the collagen network architecture in pure collagen gels of different concentrations and in collagen-fibrin co-gels.

Improving fabrication protocols and design strategies, investigating on how fibrous ECM and synthetic architectures affect cell morphology, metabolism and phenotypic expression, predicting mechanical behaviors, have increasingly become crucial goals in the understanding of native tissues and in the development of engineered tissue. In the present study, an image-based analysis approach that provides an automatic tool to fully characterize engineered tissue fiber network topology was developed. The following micro architectural features were detected: fiber angle distribution, fiber connectivity, fiber overlap spatial density, and fiber diameter. In order to demonstrate the potential of this approach Electrospun poly(ester urethane)urea (ES-PEUU) scaffolds were studied. Electrospun scaffolds were chosen for their recognized capability to recapitulate native soft tissue extra cellular matrix (ECM) morphology.

Estimating tendon excursion-joint angle relationships that define moment arm variations is a critical part of biomechanical modeling. The conventional approach has been to assume a specific mathematical form for these relationships and use experimental data to regress the parameters of these assumed mathematical functions. In contrast, here we propose a novel method that uses symbolic regression to simultaneously determine both the appropriate topology, i.e. the form of the mathematical expression, and the parameter values that best fit the experimental data. We demonstrate this method with synthetic data generated using a known model of the human index finger. Cross validation with realistic noise levels shows that this method can extract the correct form and parameter values for nonlinear tendon excursion-joint angle relationships even in the presence of noise.