A lumped parameter model of mechanically mediated acute and long-term adaptations of contractility and geometry in lymphatics for characterization of lymphedema

A primary purpose of the lymphatic system is to transport fluid from peripheral tissues to the central venous system in order to maintain tissue–fluid balance. Failure to perform this task results in lymphedema marked by swelling of the affected limb as well as geometric remodeling and reduced contractility of the affected lymphatic vessels. The mechanical environment has been implicated in the regulation of lymphatic contractility, but it is unknown how changes in the mechanical environment are related to loss of contractile function and remodeling of the tissue. The purpose of this paper was to introduce a new theoretical framework for acute and long-term adaptations of lymphatic vessels to changes in mechanical loading. This theoretical framework combines a simplified version of a published lumped parameter model for lymphangion function and lymph transport, a published microstructurally motivated constitutive model for the active and passive mechanical behavior of isolated rat thoracic ducts, and novel models for acute mechanically mediated vasoreactive adaptations and long-term volumetric growth to simulate changes in muscle contractility and geometry of a single isolated rat thoracic duct in response to a sustained elevation in afterload. The illustrative examples highlight the potential role of the mechanical environment in the acute maintenance of contractility and long-term geometric remodeling, presumably aimed at meeting fluid flow demands while also maintaining mechanical homeostasis. Results demonstrate that contractility may adapt in response to shear stress to meet fluid flow demands and show that pressure-induced long-term geometric remodeling may attenuate these adaptations and reduce fluid flow. The modeling framework and illustrative simulations help suggest relevant experiments that are necessary to accurately quantify and predict the acute and long-term adaptations of lymphangions to altered mechanical loading.     

Evolution of acoustically vaporized microdroplets in gas embolotherapy

Acoustic vaporization dynamics of a superheated dodecafluoropentane (DDFP) microdroplet inside a microtube and the resulting bubble evolution is investigated in the present work. This work is motivated by a developmental gas embolotherapy technique that is intended to treat cancers by infarcting tumors using gas bubbles. A combined theoretical and computational approach is utilized and compared with the experiments to understand the evolution process and to estimate the resulting stress distribution associated with vaporization event. The transient bubble growth is first studied by ultra-high speed imaging and then theoretical and computational modeling is used to predict the entire bubble evolution process. The evolution process consists of three regimes: an initial linear rapid spherical growth followed by a linear compressed oval shaped growth and finally a slow asymptotic nonlinear spherical bubble growth. Although the droplets are small compared to the tube diameter, the bubble evolution is influenced by the tube wall. The final bubble radius is found to scale linearly with the initial droplet radius and is approximately five times the initial droplet radius. A short pressure pulse with amplitude almost twice as that of ambient conditions is observed. The width of this pressure pulse increases with increasing droplet size whereas the amplitude is weakly dependent. Although the rise in shear stress along the tube wall is found to be under peak physiological limits, the shear stress amplitude is found to be more prominently influenced by the initial droplet size. The role of viscous dissipation along the tube wall and ambient bulk fluid pressure is found to be significant in bubble evolution dynamics.     

A homogenized constrained mixture (and mechanical analog) model for growth and remodeling of soft tissue

Most mathematical models of the growth and remodeling of load-bearing soft tissues are based on one of two major approaches: a kinematic theory that specifies an evolution equation for the stress-free configuration of the tissue as a whole or a constrained mixture theory that specifies rates of mass production and removal of individual constituents within stressed configurations. The former is popular because of its conceptual simplicity, but relies largely on heuristic definitions of growth; the latter is based on biologically motivated micromechanical models, but suffers from higher computational costs due to the need to track all past configurations. In this paper, we present a temporally homogenized constrained mixture model that combines advantages of both classical approaches, namely a biologically motivated micromechanical foundation, a simple computational implementation, and low computational cost. As illustrative examples, we show that this approach describes well both cell-mediated remodeling of tissue equivalents in vitro and the growth and remodeling of aneurysms in vivo. We also show that this homogenized constrained mixture model suggests an intimate relationship between models of growth and remodeling and viscoelasticity. That is, important aspects of tissue adaptation can be understood in terms of a simple mechanical analog model, a Maxwell fluid (i.e., spring and dashpot in series) in parallel with a “motor element” that represents cell-mediated mechanoregulation of extracellular matrix. This analogy allows a simple implementation of homogenized constrained mixture models within commercially available simulation codes by exploiting available models of viscoelasticity.     

Mechanics, mechanobiology, and modeling of human abdominal aorta and aneurysms

Biomechanical factors play fundamental roles in the natural history of abdominal aortic aneurysms (AAAs) and their responses to treatment. Advances during the past two decades have increased our understanding of the mechanics and biology of the human abdominal aorta and AAAs, yet there remains a pressing need for considerable new data and resulting patient-specific computational models that can better describe the current status of a lesion and better predict the evolution of lesion geometry, composition, and material properties and thereby improve interventional planning. In this paper, we briefly review data on the structure and function of the human abdominal aorta and aneurysmal wall, past models of the mechanics, and recent growth and remodeling models. We conclude by identifying open problems that we hope will motivate studies to improve our computational modeling and thus general understanding of AAAs.     

Stability analysis of a continuum-based constrained mixture model for vascular growth and remodeling

A stabilizing criterion is derived for equations governing vascular growth and remodeling. We start from the integral state equations of the continuum-based constrained mixture theory of vascular growth and remodeling and obtain a system of time-delayed differential equations describing vascular growth. By employing an exponential form of the constituent survival function, the delayed differential equations can be reduced to a nonlinear ODE system. We demonstrate the degeneracy of the linearized system about the homeostatic state, which is a fundamental cause of the neutral stability observations reported in prior studies. Due to this degeneracy, stability conclusions for the original nonlinear system cannot be directly inferred. To resolve this problem, a sub-system is constructed by recognizing a linear relation between two states. Subsequently, Lyapunov’s indirect method is used to connect stability properties between the linearized system and the original nonlinear system, to rigorously establish the neutral stability properties of the original system. In particular, this analysis leads to a stability criterion for vascular expansion in terms of growth and remodeling kinetic parameters, geometric quantities and material properties. Numerical simulations were conducted to evaluate the theoretical stability criterion under broader conditions, as well as study the influence of key parameters and physical factors on growth properties. The theoretical results are also compared with prior numerical and experimental findings in the literature.     

Effects of myocardial constraint on the passive mechanical behaviors of the coronary vessel wall

The large epicardial coronary arteries and veins span the surface of the heart and gradually penetrate into the myocardium. It has recently been shown that remodeling of the epicardial veins in response to pressure overload strongly depends on the degree of myocardial support. The nontethered regions of the vessel wall show significant intimal hyperplasia compared with the tethered regions. Our hypothesis is that such circumferentially nonuniform structural adaptation in the vessel wall is due to nonuniform wall stress and strain. Transmural stress and strain are significantly influenced by the support of the surrounding myocardial tissue, which significantly limits distension of the vessel. In this finite-element study, we modeled the nonuniform support by embedding the left anterior descending artery into the myocardium to different depths and analyzed deformation and strain in the vessel wall. Circumferential wall strain was much higher in the untethered than tethered region at physiological pressure. On the basis of the hypothesis that elevated wall strain is the stimulus for remodeling, the simulation results suggest that large epicardial coronary vessels have a greater tendency to become thicker in the absence of myocardial constraint. This study provides a mechanical basis for understanding the local growth and remodeling of vessels subjected to various degrees of surrounding tissue.     

Steady flow and wall compression in stenotic arteries: a three-dimensional thick-wall model with fluid-wall interactions.

Severe stenosis may cause critical flow and wall mechanical conditions related to artery fatigue, artery compression, and plaque rupture, which leads directly to heart attack and stroke. The exact mechanism involved is not well understood. In this paper a nonlinear three-dimensional thick-wall model with fluid-wall interactions is introduced to simulate blood flow in carotid arteries with stenosis and to quantify physiological conditions under which wall compression or even collapse may occur. The mechanical properties of the tube wall were selected to match a thick-wall stenosis model made of PVA hydrogel. The experimentally measured nonlinear stress-strain relationship is implemented in the computational model using an incremental linear elasticity approach. The Navier-Stokes equations are used for the fluid model. An incremental boundary iteration method is used to handle the fluid-wall interactions. Our results indicate that severe stenosis causes considerable compressive stress in the tube wall and critical flow conditions such as negative pressure, high shear stress, and flow separation which may be related to artery compression, plaque cap rupture, platelet activation, and thrombus formation. The stress distribution has a very localized pattern and both maximum tensile stress (five times higher than normal average stress) and maximum compressive stress occur inside the stenotic section. Wall deformation, flow rates, and true severities of the stenosis under different pressure conditions are calculated and compared with experimental measurements and reasonable agreement is found.     

Effects of a sustained extension on arterial growth and remodeling: a theoretical study

Three recent studies reveal that the unloaded length of a carotid artery increases significantly and rapidly in response to sustained increases in axial extension. Moreover, such lengthening involves an "unprecedented" increase in the rate of turnover of cells and matrix. Although current data are not sufficient for detailed biomechanical analyses, we present general numerical simulations that are consistent with the reported observations and support the hypothesis that rates of turnover correlate with the extent that stresses are perturbed from normal. In particular, a 3-D analysis of wall stress suggests that moderate (15%) increases in axial extension can increase the axial stress to a much greater extent than marked (50%) increases in blood pressure increase the circumferential stress. Furthermore, such increases in axial stress can occur without inducing significant gradients in stress within the wall. Consequently, we use a new, 2-D constrained mixture model to study evolving changes in the geometry, structure, and properties of carotid arteries in response to a sustained increase in axial extension. These simulations are qualitatively similar to the reports in the literature and support the notion that the stress-free lengths of individual constituents evolve during growth and remodeling.     

Combined computational modeling and experimental analysis integrating chemical and mechanical signals suggests possible mechanism of shoot meristem maintenance

Stem cell maintenance in multilayered shoot apical meristems (SAMs) of plants requires strict regulation of cell growth and division. Exactly how the complex milieu of chemical and mechanical signals interact in the central region of the SAM to regulate cell division plane orientation is not well understood. In this paper, simulations using a newly developed multiscale computational model are combined with experimental studies to suggest and test three hypothesized mechanisms for the regulation of cell division plane orientation and the direction of anisotropic cell expansion in the corpus. Simulations predict that in the Apical corpus, WUSCHEL and cytokinin regulate the direction of anisotropic cell expansion, and cells divide according to tensile stress on the cell wall. In the Basal corpus, model simulations suggest dual roles for WUSCHEL and cytokinin in regulating both the direction of anisotropic cell expansion and cell division plane orientation. Simulation results are followed by a detailed analysis of changes in cell characteristics upon manipulation of WUSCHEL and cytokinin in experiments that support model predictions. Moreover, simulations predict that this layer-specific mechanism maintains both the experimentally observed shape and structure of the SAM as well as the distribution of WUSCHEL in the tissue. This provides an additional link between the roles of WUSCHEL, cytokinin, and mechanical stress in regulating SAM growth and proper stem cell maintenance in the SAM.     

A multiscale computational model of arterial growth and remodeling including Notch signaling

Blood vessels grow and remodel in response to mechanical stimuli. Many computational models capture this process phenomenologically, by assuming stress homeostasis, but this approach cannot unravel the underlying cellular mechanisms. Mechano-sensitive Notch signaling is well-known to be key in vascular development and homeostasis. Here, we present a multiscale framework coupling a constrained mixture model, capturing the mechanics and turnover of arterial constituents, to a cell–cell signaling model, describing Notch signaling dynamics among vascular smooth muscle cells (SMCs) as influenced by mechanical stimuli. Tissue turnover was regulated by both Notch activity, informed by in vitro data, and a phenomenological contribution, accounting for mechanisms other than Notch. This novel framework predicted changes in wall thickness and arterial composition in response to hypertension similar to previous in vivo data. The simulations suggested that Notch contributes to arterial growth in hypertension mainly by promoting SMC proliferation, while other mechanisms are needed to fully capture remodeling. The results also indicated that interventions to Notch, such as external Jagged ligands, can alter both the geometry and composition of hypertensive vessels, especially in the short term. Overall, our model enables a deeper analysis of the role of Notch and Notch interventions in arterial growth and remodeling and could be adopted to investigate therapeutic strategies and optimize vascular regeneration protocols.

     

A longitudinal study of remodeling in a revised peripheral artery bypass graft using 3D ultrasound imaging and computational hemodynamics

We report a study of the role of hemodynamic shear stress in the remodeling and failure of a peripheral artery bypass graft. Three separate scans of a femoral to popliteal above-knee bypass graft were taken over the course of a 16 month period following a revision of the graft. The morphology of the lumen is reconstructed from data obtained by a custom 3D ultrasound system. Numerical simulations are performed with the patient-specific geometries and physiologically realistic flow rates. The ultrasound reconstructions reveal two significant areas of remodeling: a stenosis with over 85% reduction in area, which ultimately caused graft failure, and a poststenotic dilatation or widening of the lumen. Likewise, the simulations reveal a complicated hemodynamic environment within the graft. Preliminary comparisons with in vivo velocimetry also showed qualitative agreement with the flow dynamics observed in the simulations. Two distinct flow features are discerned and are hypothesized to directly initiate the observed in vivo remodeling. First, a flow separation occurs at the stenosis. A low shear recirculation region subsequently develops distal to the stenosis. The low shear region is thought to be conducive to smooth muscle cell proliferation and intimal growth. A poststenotic jet issues from the stenosis and subsequently impinges onto the lumen wall. The lumen dilation is thought to be a direct result of the high shear stress and high frequency pressure fluctuations associated with the jet impingement.     

Pulsatile extracorporeal circulation during on-pump cardiac surgery enhances aortic wall shear stress

Controversy on superiority of pulsatile versus non-pulsatile extracorporeal circulation in cardiac surgery still continues. Stroke as one of the major adverse events during cardiopulmonary bypass is, in the majority of cases, caused by mobilization of aortic arteriosclerotic plaques that is inducible by pathologically elevated wall shear stress values. The present study employs computational fluid dynamics to evaluate the aortic blood flow and wall shear stress profiles under the influence of antegrade or retrograde perfusion with pulsatile versus non-pulsatile extracorporeal circulation. While, compared to physiological flow, a non-pulsatile perfusion resulted in generally decreased blood velocities and only moderately increased shear forces (48 Pa versus 20 Pa antegradely and 127 Pa versus 30 Pa retrogradely), a pulsatile perfusion extensively enhanced the occurrence of turbulences, maximum blood flow speed and maximum wall shear stress (1020 Pa versus 20 Pa antegradely and 1178 Pa versus 30 Pa retrogradely). Under these circumstances arteriosclerotic embolism has to be considered. Further simulations and experimental work are necessary to elucidate the impact of our findings on the scientific discourse of pulsatile versus non-pulsatile extracorporeal circulation.     

Left-ventricular shape determines intramyocardial mechanical heterogeneity

Left-ventricular remodeling is considered to be an important mechanism of disease progression leading to mechanical dysfunction of the heart. However, the interaction between the physiological changes in the remodeling process and the associated mechanical dysfunction is still poorly understood. Clinically, it has been observed that the left ventricle often undergoes large shape changes, but the importance of left-ventricular shape as a contributing factor to alterations in mechanical function has not been clearly determined. Therefore, the interaction between left-ventricular shape and systolic mechanical function was examined in a computational finite-element study. Hereto, finite-element models were constructed with varying shapes, ranging from an elongated ellipsoid to a sphere. A realistic transmural gradient in fiber orientation was considered. The passive myocardium was described by an incompressible hyperelastic material law with transverse isotropic symmetry. Activation was governed by the eikonal-diffusion equation. Contraction was incorporated using a Hill model. For each shape, simulations were performed in which passive filling was followed by isovolumic contraction and ejection. It was found that the intramyocardial distributions of fiber stress, strain, and stroke work density were shape dependent. Ejection performance was reduced with increasing sphericity, which was regionally related to a reduction in the active fiber stress development, fiber shortening, and stroke work in the midwall and subepicardial region at the midheight level in the left-ventricular wall. Based on these results, we conclude that a significant interaction exists between left-ventricular shape and regional myofiber mechanics, but the importance for left-ventricular remodeling requires further investigation.     

A physically motivated constitutive model for cell-mediated compaction and collagen remodeling in soft tissues

Collagen is the main load-bearing component of many soft tissues and has a large influence on the mechanical behavior of tissues when exposed to mechanical loading. Therefore, it is important to increase our understanding of collagen remodeling in soft tissues to understand the mechanisms behind pathologies and to control the development of the collagen network in engineered tissues. In the present study, a constitutive model was developed by coupling a recently developed model describing the orientation and contractile stresses exerted by cells in response to mechanical stimuli to physically motivated collagen remodeling laws. In addition, cell-mediated contraction of the collagen fibers was included as a mechanism for tissue compaction. The model appeared to be successful in predicting a range of experimental observations, which are (1) the change in transition stretch of periosteum after remodeling at different applied stretches, (2) the compaction and alignment of collagen fibers in tissue-engineered strips, (3) the fiber alignment in cruciform gels with different arm widths, and (4) the alignment of collagen fibers in engineered vascular grafts. Moreover, by changing the boundary conditions, the model was able to predict a helical architecture in the vascular graft without assuming the presence of two helical fiber families a priori. Ultimately, this model may help to increase our understanding of collagen remodeling in physiological and pathological conditions, and it may provide a tool for determining the optimal experimental conditions for obtaining native-like collagen architectures in engineered tissues.     

Organic tissues in rotating bioreactors: fluid-mechanical aspects, dynamic growth models, and morphological evolution

This analysis deals with advances in tissue-engineering models and computational methods as well as with novel results on the relative importance of "controlling forces" in the growth of organic constructs. Specifically, attention is focused on the rotary culture system, because this technique has proven to be the most practical solution for providing a suitable culture environment supporting three-dimensional tissue assemblies. From a numerical point of view, the growing biological specimen gives rise to a moving boundary problem. A "volume-of-fraction" method is specifically and carefully developed according to the complex properties and mechanisms of organic tissue growth and, in particular, taking into account the sensitivity of the construct/liquid interface to the effect of the fluid-dynamic shear stress (it induces changes in tissue metabolism and function that elicit a physiological response from the biological cells). The present study uses available data to introduce a set of growth models. The surface conditions are coupled to the transfer of mass and momentum at the specimen/culture-medium interface and lead to the introduction of a group of differential equations for the nutrient concentration around the sample and for the evolution of tissue mass displacement. The models are then used to show how the proposed surface kinetic laws can predict (through sophisticated numerical simulations) many of the known characteristics of biological tissues grown using rotating-wall perfused vessel bioreactors. This procedure provides a validation of the models and associated numerical method and also gives insight into the mechanisms of the phenomena. The interplay between the increasing size of the tissue and the structure of the convective field is investigated. It is shown that this interaction is essential in determining the time evolution of the tissue shape. The size of the growing specimen plays a critical role with regard to the intensity of convection and the related shear stresses. Convective effects, in turn, are found to impact growth rates, tissue size, and morphology, as well as the mechanisms driving growth. The method exhibits novel capabilities to predict and elucidate experimental observations and to identify cause-and-effect relationships.