Seungik Baek

A Theoretical Model of Enlarging Intracranial Fusiform Aneurysms

The mechanisms by which intracranial aneurysms develop, enlarge, and rupture are unknown, and it remains difficult to collect the longitudinal patient-based information needed to improve our understanding. We submit, therefore, that mathematical models hold promise by allowing us to propose and test competing hypotheses on potential mechanisms of aneurysmal enlargement and to compare predicted outcomes with limited clinical information--in this way, we may begin to narrow the possible mechanisms and thereby focus experimental studies. In this paper, we present a constrained mixture model of evolving thin-walled, fusiform aneurysms and compare multiple competing hypotheses with regard to the production, removal, and alignment of the collagen that provides the structural integrity of the wall. The results show that this type of approach has the capability to infer potential means by which lesions enlarge and whether such changes are likely to produce a stable or unstable process. Such information can better direct the requisite histopathological examinations, particularly on the need to quantify collagen orientations as a function of lesion geometry.

Complementary vasoactivity and matrix remodelling in arterial adaptations to altered flow and pressure

Arteries exhibit a remarkable ability to adapt to sustained alterations in biomechanical loading, probably via mechanisms that are similarly involved in many arterial pathologies and responses to treatment. Of particular note, diverse data suggest that cell and matrix turnover within vasoaltered states enables arteries to adapt to sustained changes in blood flow and pressure. The goal herein is to show explicitly how altered smooth muscle contractility and matrix growth and remodelling work together to adapt the geometry, structure, stiffness and function of a representative basilar artery. Towards this end, we employ a continuum theory of constrained mixtures to model evolving changes in the wall, which depend on both wall shear stress-induced changes in vasoactive molecules (which alter smooth muscle proliferation and synthesis of matrix) and intramural stress-induced changes in growth factors (which alter cell and matrix turnover). Simulations show, for example, that such considerations help explain the different rates of experimentally observed adaptations to increased versus decreased flows as well as differences in rates of change in response to increased flows or pressures.

Diffusion of a fluid through an elastic solid undergoing large deformation

Abstract This paper is concerned with the modeling of slow diffusion of a fluid into a swelling solid undergoing large deformation. Both the stress in the solid as well as the diffusion rates are predicted. The approach presented here, based on the balance laws of a single continuum with mass diffusion, overcomes the difficulties inherent in the theory of mixtures in specifying boundary conditions. A “natural” boundary condition based upon the continuity of the chemical potential is derived by the use of a variational approach, based on maximizing the rate of dissipation. It is shown that, in the absence of inertial effects, the differential equations resulting from the use of mixture theory can be recast into a form that is identical to the equations obtained in our approach. The boundary value problem of the steady flow of a solvent through a gum rubber membrane is solved and the results show excellent agreement with the experimental data of Paul and Ebra-Lima (J. Appl. Polym. Sci. 14 (1970) 2201) for a variety of solvents.

Importance of initial aortic properties on the evolving regional anisotropy, stiffness and wall thickness of human abdominal aortic aneurysms

Complementary advances in medical imaging, vascular biology and biomechanics promise to enable computational modelling of abdominal aortic aneurysms to play increasingly important roles in clinical decision processes. Using a finite-element-based growth and remodelling model of evolving aneurysm geometry and material properties, we show that regional variations in material anisotropy, stiffness and wall thickness should be expected to arise naturally and thus should be included in analyses of aneurysmal enlargement or wall stress. In addition, by initiating the model from best-fit material parameters estimated for non-aneurysmal aortas from different subjects, we show that the initial state of the aorta may influence strongly the subsequent rate of enlargement, wall thickness, mechanical behaviour and thus stress in the lesion. We submit, therefore, that clinically reliable modelling of the enlargement and overall rupture-potential of aneurysms may require both a better understanding of the mechanobiological processes that govern the evolution of these lesions and new methods of determining the patient-specific state of the pre-aneurysmal aorta (or correlation to currently unaffected portions thereof) through knowledge of demographics, comorbidities, lifestyle, genetics and future non-invasive or minimally invasive tests.

Biochemomechanics of Cerebral Vasospasm and its Resolution: II. Constitutive Relations and Model Simulations

Cerebral vasospasm is a poorly understood clinical condition that appears to result from complex biochemical and biomechanical processes that manifest as yet another example of vascular growth and remodeling. We submit that mathematical modeling holds great promise to help synthesize diverse types of data and thereby to increase our understanding of vasospasm. Toward this ultimate goal, we present constitutive relations and parametric studies that illustrate the potential utility of a new theoretical framework that combines information on wall mechanics, hemodynamics, and chemical kinetics. In particular, we show that chemical and mechanical mediators of cellular and extracellular matrix turnover can differentially dominate the progression and resolution of vasospasm. Moreover, based on our simulations, endothelial damage can significantly alter the time-course and extent of vasospasm as can impairment of autoregulation. Although the present results are consistent with salient features of clinically reported vasospasm, and thus provide some new insight, we suggest that most importantly they reveal areas of pressing need with regard to the collection of additional experimental data. Without appropriate data, our understanding of cerebral vasospasm will remain incomplete.

Simulation of abdominal aortic aneurysm growth with updating hemodynamic loads using a realistic geometry.

Advances in modeling vascular tissue growth and remodeling (G&R) as well as medical imaging usher in a great potential for integrative computational mechanics to revolutionize the clinical treatment of cardiovascular diseases. A computational model of abdominal aortic aneurysm (AAA) enlargement has been previously developed based on realistic geometric models. In this work, we couple the computational simulation of AAA growth with the hemodynamics simulation in a stepwise, iterative manner and study the interrelation between the changes in wall shear stress (WSS) and arterial wall evolution. The G&R simulation computes a long-term vascular adaptation with constant hemodynamic loads, derived from the previous hemodynamics simulation, while the subsequent hemodynamics simulation computes hemodynamic loads on the vessel wall during the cardiac cycle using the evolved geometry. We hypothesize that low WSS promotes degradation of elastin during the progression of an AAA. It is shown that shear stress-induced degradation of elastin elevates wall stress and accelerates AAA enlargement. Regions of higher expansion correlate with regions of low WSS. Our results show that despite the crucial role of stress-mediated collagen turnover in compensating the loss of elastin, AAA enlargement can be accelerated through the effect of WSS. The present study is able to account for computational models of image-based AAA growth as well as important hemodynamic parameters with relatively low computational expense. We suggest that the present computational framework, in spite of its limitations, provides a useful foundation for future studies which may yield new insight into how aneurysms grow and rupture.

Circumferential variations of mechanical behavior of the porcine thoracic aorta during the inflation test

We developed an extension-inflation experimental apparatus with a stereo vision system and a stress-strain analysis method to determine the regional mechanical properties of a blood vessel. Seven proximal descending thoracic aortas were investigated during the inflation test at a fixed longitudinal stretch ratio of 1.35 over a transmural pressure range from 1.33 to 21.33 kPa. Four circumferential regions of each aorta were designated as the anterior (A), left lateral (L), posterior (P), and right lateral (R) regions, and the inflation test was repeated for each region of the aortas. We used continuous functions to approximate the surfaces of the regional aortic wall in the reference configuration and the deformed configuration. Circumferential stretch and stress at the four circumferential regions of the aorta were computed. Circumferential stiffness, defined as the tangent of the stress-stretch curve, and physiological aortic stiffness, named pressure-strain elastic modulus, were also computed for each region. In the low pressure range, the stress increased linearly with increased stretch, but the mechanical response became progressively stiffer in the high-pressure range above a transition point. At a transmural pressure of 12.00 kPa, mean values of stiffness were 416±104 kPa (A), 523±99 kPa (L), 634±91 kPa (P), and 489±82 kPa (R). The stiffness of the posterior region was significantly higher than that of the anterior region, but no significant difference was found in pressure-strain elastic modulus.

Cell Adhesive Behavior on Thin Polyelectrolyte Multilayers: Cells Attempt to Achieve Homeostasis of Its Adhesion Energy

Linearly growing ultrathin polyelectrolyte multilayer (PEM) films of strong polyelectrolytes, poly(diallyldimethylammonium chloride) (PDAC), and sulfonated polystyrene, sodium salt (SPS) exhibit a gradual shift from cytophilic to cytophobic behavior, with increasing thickness for films of less than 100 nm. Previous explanations based on film hydration, swelling, and changes in the elastic modulus cannot account for the cytophobicity observed with these thin films as the number of bilayers increases. We implemented a finite element analysis to help elucidate the observed trends in cell spreading. The simulation results suggest that cells maintain a constant level of energy consumption (energy homeostasis) during active probing and thus respond to changes in the film stiffness as the film thickness increases by adjusting their morphology and the number of focal adhesions recruited and thereby their attachment to a substrate.

On parameter estimation for biaxial mechanical behavior of arteries

This article considers the parameter estimation of multi-fiber family models for biaxial mechanical behavior of passive arteries in the presence of the measurement errors. First, the uncertainty propagation due to the errors in variables has been carefully characterized using the constitutive model. Then, the parameter estimation of the artery model has been formulated into nonlinear least squares optimization with an appropriately chosen weight from the uncertainty model. The proposed technique is evaluated using multiple sets of synthesized data with fictitious measurement noises. The results of the estimation are compared with those of the conventional nonlinear least squares optimization without a proper weight factor. The proposed method significantly improves the quality of parameter estimation as the amplitude of the errors in variables becomes larger. We also investigate model selection criteria to decide the optimal number of fiber families in the multi-fiber family model with respect to the experimental data balancing between variance and bias errors.

Parametric study of effects of collagen turnover on the natural history of abdominal aortic aneurysms

Abdominal aortic aneurysms (AAAs) are characterized by significant changes in the architecture of the aortic wall, notably, loss of functional elastin and smooth muscle. Because collagen is the principal remaining load-bearing constituent of the aneurysmal wall, its turnover must play a fundamental role in the natural history of the lesion. Nevertheless, detailed investigations of the effects of different aspects of collagen turnover on AAA development are lacking. A finite-element membrane model of the growth and remodelling of idealized AAAs was thus used to investigate parametrically four of the primary aspects of collagen turnover: rates of production, half-life, deposition stretch (prestretch) and material stiffness. The predicted rates of aneurysmal expansion and spatio-temporal changes in wall thickness, biaxial stresses and maximum collagen fibre stretch at the apex of the lesion depended strongly on all four factors, as did the predicted clinical endpoints (i.e. arrest, progressive expansion or rupture). Collagen turnover also affected the axial expansion, largely due to mechanical changes within the shoulder region of the lesion. We submit, therefore, that assessment of rupture risk could be improved by future experiments that delineate and quantify different aspects of patient-specific collagen turnover and that such understanding could lead to new targeted therapeutics.