Arterial wall morphology depends strongly on the hemodynamic environment experienced in vivo. The mammalian heart pumps blood through rhythmic contractions forcing blood vessels to undergo cyclic, mechanical stimulation in the form of pulsatile blood pressure and flow. While it has been shown that stepwise, chronic increases in blood pressure and flow modify arterial wall thickness and diameter respectively, few studies on arterial remodeling have examined the influences that pulsatility (i.e., the range of cyclic stimuli) may have on biaxial wall morphology. We experimentally studied the biaxial behavior of carotid arteries from 8 control (CCA), 15 transgenic, and 21 mechanically altered mice using a custom designed mechanical testing device and correlated those results with hemodynamic measurements using pulsed Doppler. In this dissertation, we establish that increased pulsatile stimulation in the right carotid artery after banding (RCCA-B) has a strong affect on wall morphological parameters that peak at 2 weeks and include thickness (CCA=24.8±0.878, RCCA-B=99.0±8.43 μ m), inner diameter (CCA=530±7.36, RCCA-B=680±32.0μ m), and in vivo axial stretch (CCA=1.7±0.029, RCCAB= 1.19±0.067). These modifications entail stress and the change in stress across the cardiac cycle from an arterial wall macro-structural point of view (i.e., cellular and extracellular matrix) citing increases in collagen mass fraction (CCA=0.223±0.056, RCCA-B=0.314±0.011), collagen to elastin ratio (CCA=0.708±0.152, RCCA-B=1.487±0.26), and cross-sectional cellular nuclei counts (CCA=298±58.9, RCCA-B=578±28.3 cells) at 0, 7, 10, 14, and 42 post-banding surgery. Furthermore, we study the biomechanical properties of carotid arteries from a transgenic mouse of Marfan Syndrome. This arterial disease experiences increased pulse transmission and our findings indicate that alterations occur primarily in the axial direction. The above results are all applied to a predictive biaxial model of Cauchy stress vs. strain.

Characterization of multiaxial mechanical properties of cardiovascular soft tissue is essential in order to better understand their growth and remodeling in homeostatic conditions and in response to injury or pathological conditions. Though numerous phenomenological models have been proposed to characterize such multiaxial mechanical behavior, the approach has certain drawbacks regarding experimental determination of the model coefficients. We propose a method that aims to overcome these drawbacks. The approach makes use of orthogonal polynomials to fit the biaxial test data and suggests a way to derive the strain energy function from these analytical fits by way of minimizing the deviation of the behavior from hyperelastic ideal. Using the proposed method, a strain energy function for a lymphatic vessel is derived and the method is compared with traditional ones that used non-orthogonal polynomials as independent variables in the functional form for strain energy. The unique coefficient values obtained using the proposed method, for the first time gives us an opportunity to attribute a physical characteristic of the material to the coefficient values. The method also provides a way to assess two different material behaviors by way of comparing their deviation from the hyperelastic behavior when a similar test protocol is used to collect the data, over a similar deformation range and the order of polynomial function is chosen so as to give a similar error of fit. The behavior of mesenteric lymph vessels from normal cows, cows subjected to sham surgery and those subjected to 3 days of edematous conditions by venous occlusion are compared using this method. To be able to better understand the changes in mechanical behavior, morphological analysis of the vessels was carried out and the geometric and structural changes in these vessels were studied. We found that the behavior of bovine mesenteric lymph vessels subjected to a high flow condition shows a small difference in their mechanical behavior as compared to the vessels from normal a cow and a cow subjected to sham surgery. The geometry and structure of these vessels also showed marked differences from the other two. The thickness to radius ratio increased and a rise in percentage of area occupied by smooth muscle cells and medial collagen was observed. Though not all the differences were statistically significant, we conclude that the behavior and the morphology are suggestive of the remodeling of the vessel in response to altered hemodynamic conditions and require further investigation.

In order to create informed predictive models that capture artery dependent responses during atherosclerosis progression and the long term response to hypertension, one needs to know the structural, biochemical and mechanical properties as a function of time in these diseased states. In the case of hypertension more is known about the mechanical changes; while, less is known about the structural changes over time. For atherosclerotic plaques, more is known about the structure and less about the mechanical properties. We established a congruent multi-scale model to predict the adapted salient arterial geometry, structure and biochemical response to an increase in pressure. Geometrical and structural responses to hypertension were then quantified in a hypertensive animal model. Eventually this type of model may be used to predict mechanical changes in complex disease such as atherosclerosis. Thus for future verification and implementation we experimentally tested atherosclerotic plaques and quantified composition, structure and mechanical properties. Using the theoretical models we can now predict arterial changes in biochemical concentrations as well as salient features such as geometry, mass of elastin, smooth muscle, and collagen, and circumferential stress, in response to hemodynamic loads. Using an aortic coarctation model of hypertension, we found structural arterial responses differ in the aorta, coronary and cerebral arteries. Effects of elevated pressure manifest first in the central arteries and later in distal muscular arteries. In the aorta, there is a loss and then increase of cytoskeleton actin fibers, production of fibrillar collagen and elastin, hyperplasia or hypertrophy with nuclear polypoid, and recruitment of hemopoeitic progenitor cells and monocytes. In the muscular coronary, we see similar changes albeit it appears actin fibers are recruited and collagen production is only increased slightly in order to maintain constant the overall ratio of ~55 percent. In the muscular cerebral artery, despite a temporary loss in actin fibers there is little structural change. Contrary to hypertensive arteries, characterizing regional stiffness in atherosclerotic plaques has not been done before. Therefore, experimental testing on atherosclerotic plaques of Apolipoprotein E Knockout mice was performed and revealed nearly homogenously lipidic plaques with a median axial compressive stiffness value of 1.5 kPa.

Hypertension is a risk factor for many cardiovascular and cerebrovascular diseases such as atherosclerosis and stroke. It is therefore important to understand the effect of hypertension on temporal growth and remodeling of arteries. In this study, experimental hypertension was induced in the mini-pig by aortic coarctation. Basilar arteries and aortas were collected for analysis over an eight week period of hypertension with specimens from normotensive animals serving as controls. Changes in mechanical properties of the basilar artery were evaluated by in vitro pressure-diameter tests on intact cylindrical segments at their in situ length. The basilar arteries from hypertensive animals became less distensible, reflecting increases in both structural and material stiffness, compared to their normotensive counterparts. The circumferential stress rapidly returned toward its homeostatic value by increasing the wall thickness within two weeks. Immunohistochemistry, which is capable of illustrating the localization and distribution of protein expression, was performed to examine changes in wall constituents in the aorta. The increased medial thickness observed in hypertensive pigs compared to normotensive pigs was due to hyperplasia of smooth muscle cells (SMCs) and accumulation of extracellular matrix proteins, which were accompanied by the phenotypic modulation of SMCs. The increased interlamellar thickness, collagen fibers, and the thickness of elastic lamina found in the inner media of hypertensive animal may be associated with the gradient of stress decreasing into the outer media. SMC proliferation, if any, was found evenly distributed across the media, however. In cases showing increased proliferation and matrix protein synthesis, the SMC contractile markers were down-regulated whereas the SMC synthetic markers were up-regulated. While the aortic intima appeared normal in the normotensive animals, neointima formation, which may predispose the vessel to atheroma formation, was found in the hypertensive animals. Immunohistochemistry of Hsp47 and procollagen revealed that the endothelial cells (ECs) may produce collagen, specifically type I collagen in response to hypertension and contribute to the thickened intima. In addition, lectin staining for ECs markers and immunostaining for eNOS suggested that endothelial cells may transdifferentiate into intimal SMCs. These findings suggested an alternative role that ECs may play in hypertension-induced atherogenesis.

The evolution of biomechanical behavior of arteries plays a key role in the onset and progression of cardiovascular disease. Biomechanical behavior is governed by the content and organization of the key structural constituents (e.g., collagen, elastin, and smooth muscle) and vessel geometry. The evolution of biomechanical behavior of arteries is governed by biologically-mediated synthesis, degradation, and reorganization of these key structural constituents. A hallmark goal in biomechanics is quantifying the relationship between the microstructure of tissues and their mechanical response throughout tissue growth and remodeling; this will provide a crucial link in understanding the tissue level effects of biological processes involved in disease and normal growth Fibulin-5 (fbln5) is an ECM protein that binds tropoelastin and interacts with integrins. Arteries from fbln5 knockout mice lack functional elastic fibers and provide a system for investigating the link between an artery's microstructure and its mechanical response. The overall goal of this project was to develop multi-scaled theoretical and experimental frameworks to quantify the relationship between microstructural content and organization and tissue level material properties of arteries from fbln5 null mice and littermate controls and to quantify the effects of fbln5 on the in vivo maturation of mouse carotid arteries. We found significant differences in the mechanical properties of carotid arteries of fbln5 null mice, and these differences were correlated with altered extracellular matrix organization. We also developed a microstructurally-motivated 3-dimensional constrained mixture model for vascular growth and remodeling. Using physiological rates of constituent growth and turnover, the model captured the salient findings found in the literature. Incorporating experimentally measured fiber angle data into constitutive relations yielded greater predictive accuracy. This dissertation incorporates experimental data quantified at the micro (microstructural-level fiber distributions) and macro (tissue-level mechanical response) scale and incorporates these data into microstructurally motivated constitutive relations. The use of structurally motivated constitutive relations and experimentally measured microstructural data provides a foundation for future work in further understanding the relationship between processes governing microstructure and the tissue level effects of disease and normal growth.

<p>Breast cancer affects 12.5\% of women over their life time and tissue expansion (TE) is the most common technique for breast reconstruction after mastectomy. However, the rate of complications with TE can be as high as 15\%. Even though the first documented case of TE happened in 1957, there has yet to be a standardized procedure established due to the variations among patients and the TE protocols are currently designed based on surgeon's experience. There are several studies of computational and theoretical framework modeling skin growth in TE but these tools are not used in the clinical setting. This dissertation focuses on bridging the gap between the already existing skin growth modeling efforts and it's potential application in the clinical setting.</p> <p><br></p> <p>We started with calibrating a skin growth model based on porcine skin expansions data. We built a predictive finite element model of tissue expansion. Two types of model were tested, isotropic and anisotropic models. Calibration was done in a probabilistic framework, allowing us to capture the inherent biological uncertainty of living tissue. We hypothesized that the skin growth rate was proportional to stretch. Indeed, the Bayesian calibration process confirmed that this conceptual model best explained the data. </p> <p><br></p> <p>Although the initial model described the macroscale response, it did not consider any activity on the cellular level. To account for the underlying cellular mechanisms at the microscopic scale, we have established a new system of differential equations that describe the dynamics of key mechanosensing pathways that we observed to be activated in the porcine model. We calibrated the parameters of the new model based on porcine skin data. The refined model is still able to reproduce the observed macroscale changes in tissue growth, but now based on mechanistic knowledge of the cell mechanobiology.  </p> <p><br></p> <p>Lastly, we demonstrated how our skin growth model can be used in a clinical setting. We created TE simulations matching the protocol used in human patients and compared the results with clinical data with good agreement. Then we established a personalized model built from 3D scans of a patient unique geometry. We verified our model by comparing the skin growth area with the area of the skin harvested in the procedure, again with good agreement.</p> <p><br></p> <p>Our work shows that skin growth modeling can be a powerful tool to aid surgeons design TE procedures before they are actually performed. The simulations can help with optimizing the protocol to guarantee the correct amount of skin is growth in the shortest time possible without subjecting the skin to deformations that can compromise the procedure.</p>

<div>Excessive deformation and stress of skin following reconstructive surgery plays a crucial role in wound healing, often leading to complications. Yet, despite of this concern, surgeries are still planned and executed based on each surgeon's training and experience rather than quantitative engineering tools. The limitations of current treatment planning and execution stem in part from the difficulty in predicting the mechanical behavior of skin, challenges in directly measuring stress in the operating room, and inability to predict the long term adaptation of skin following reconstructive surgery. Computational modeling of soft tissue mechanics has emerged as an ideal candidate to determine stress contours over sizable skin regions in realistic situations. Virtual surgeries with computational mechanics tools will help surgeons explore different surgeries preoperatively, make prediction of stress contours, and eventually aid the surgeon in planning for optimal wound healing. While there has been significant progress on computational modeling of both reconstructive surgery and skin mechanical and mechanobiological behavior, there remain major gaps preventing computational mechanics to be widely used in the clinical setting. At the preoperative stage, better calibration of skin mechanical properties for individual patients based on minimally invasive mechanical tests is still needed. One of the key challenges in this task is that skin is not stress-free in vivo. In many applications requiring large skin flaps, skin is further grown with the tissue expansion technique. Thus, better understanding of skin growth and the resulting stress-free state is required. The other most significant challenge is dealing with the inherent variability of mechanical properties and biological response of biological systems. Skin properties and adaptation to mechanical cues changes with patient demographic, anatomical location, and from one individual to another. Thus, the precise model parameters can never be known exactly, even if some measurements are available. Therefore, rather than expecting to know the exact model describing a patient, a probabilistic approach is needed. To bridge the gaps, this dissertation aims to advance skin biomechanics and computational mechanics tools in order to make virtual surgery for clinical use a reality in the near future. In this spirit, the dissertation constitutes three parts: skin growth and its incompatibility, acquisition of patient-specific geometry and skin mechanical properties, and uncertainty analysis of virtual surgery scenarios.</div><div>Skin growth induced by tissue expansion has been widely used to gain extra skin before reconstructive surgery. Within continuum mechanics, growth can be described with the split of the deformation gradient akin to plasticity. We propose a probabilistic framework to do uncertainty analysis of growth and remodeling of skin in tissue expansion. Our approach relies on surrogate modeling through multi-fidelity Gaussian process regression. This work is being used calibrate the computational model against animal model data. Details of the animal model and the type of data obtained are also covered in the thesis. One important aspect of the growth and remodeling process is that it leads to residual stress. It is understood that this stress arises due to the nonhomogeneous growth deformation. In this dissertation we characterize the geometry of incompatibility of the growth field borrowing concepts originally developed in the study of crystal plasticity. We show that growth produces unique incompatibility fields that increase our understanding of the development of residual stress and the stress-free configuration of tissues. We pay particular attention to the case of skin growth in tissue expansion.</div><div>Patient-specific geometry and material properties are the focus on the second part of the thesis. Minimally invasive mechanical tests based on suction have been developed which can be used in vivo, but these tests offer only limited characterization of an individual's skin mechanics. Current methods have the following limitations: only isotropic behavior can be measured, the calibration problem is done with inverse finite element methods or simple analytical calculations which are inaccurate, the calibration yields a single deterministic set of parameters, and the process ignores any previous information about the mechanical properties that can be expected for a patient. To overcome these limitations, we recast the calibration problem in a Bayesian framework. To sample from the posterior distribution of the parameters for a patient given a suction test, the method relies on an inexpensive Gaussian process surrogate. For the patient-specific geometry, techniques such as magnetic resonance imaging or computer tomography scans can be used. Such approaches, however, require specialized equipment and set up and are not affordable in many scenarios. We propose to use multi-view stereo (MVS) to capture patient-specific geometry.</div><div>The last part of the dissertation focuses on uncertainty analysis of the reconstructive procedure itself. To achieve uncertainty analysis in the clinical setting we propose to create surrogate and reduced order models, especially principal component analysis and Gaussian process regression. We first show the characterization of stress profiles under uncertainty for the three most common flap designs. For these examples we deal with idealized geometries. The probabilistic surrogates enable not only tasks such as fast prediction and uncertainty quantification, but also optimization. Based on a global sensitivity analysis we show that the direction of anisotropy of skin with respect to the flap geometry is the most important parameter controlled by the surgeon, and we show hot to optimize the flap in this idealized setting. We conclude with the application of the probabilistic surrogates to perform uncertainty analysis in patient-specific geometries. In summary, this dissertation focuses on some of the fundamental challenges that needed to be addressed to make virtual surgery models ready for clinical use. We anticipate that our results will continue to shape the way computational models continue to be incorporated in reconstructive surgery plans.</div>

Abdominal aortic aneurysm (AAA) is characterized by a bulge in the abdominal aorta. AAA development is mostly asymptomatic, but such a bulge may suddenly rupture, which is associated with a high mortality rate. Unfortunately, there is no medication that can prevent AAA from expanding or rupturing. Therefore, patients with detected AAA are monitored until treatment indication, such as maximum AAA diameter of 55 mm or expansion rate of 1 cm/year. Models of AAA development may help to understand the disease progression and to inform decision-making on a patient-specific basis. AAA growth and remodeling (G&amp;R) models are rather complex, and before the challenge is undertaken, sound clinical validation is required. In Paper A, an existing thick-walled model of growth and remodeling of one layer of an AAA slice has been extended to a two-layered model, which better reflects the layered structure of the vessel wall. A parameter study was performed to investigate the influence of mechanical properties and G&amp;R parameters of such a model on the aneurysm growth. In Paper B, the model from Paper A was extended to an organ level model of AAA growth. Furthermore, the model was incorporated into a Fluid-Solid-Growth (FSG) framework. A patient-specific geometry of the abdominal aorta is used to illustrate the model capabilities. In Paper C, the evolution of the patient-specific biomechanical characteristics of the AAA was investigated. Four patients with five to eight Computed Tomography-Angiography (CT-A) scans at different time points were analyzed. Several non-trivial statistical correlations were found between the analyzed parameters. In Paper D, the effect of different growth kinematics on AAA growth was investigated. The transverse isotropic in-thickness growth was the most suitable AAA growth assumption, while fully isotropic growth and transverse isotropic in-plane growth produced unrealistic results. In addition, modeling of the tissue volume change improved the wall thickness prediction, but still overestimated thinning of the wall during aneurysm expansion. / Bukaortaaneurysm (AAA) kännetecknas av en utbuktning hos aortaväggen i buken. Tillväxt av en AAA är oftast asymtomatisk, men en sådan utbuktning kan plö̈tsligt brista, vilket har hög dödlighet. Tyvärr finns det inga mediciner som kan förhindra AAA från att expandera eller brista. Patienter med upptä̈ckt AAA hålls därför under uppsikt tills operationskrav är uppnådda, såsom maximal AAA-diameter på 55 mm eller expansionstakt på 1 cm/år. Modeller för AAA-tillväxt kan bidra till att öka förståelsen för sjukdomsförloppet och till att förbättra beslutsunderlaget på en patientspecifik basis. AAA modeller för tillväxt och strukturförändring (G&amp;R) är ganska komplicerade och innan man tar sig an denna utmaning krävs de god klinisk validering. I Artikel A har en befintlig tjockväggig modell för tillväxt av ett skikt av en AAA-skiva utö̈kats till en två-skiktsmodell. Denna modell återspeglar bättre den skiktade strukturen hos kärlväggen. Genom en parameterstudie undersö̈ktes påverkan av mekaniska egenskaper och G&amp;R-parametrar hos en sådan modell för AAA-tillväxt. I Artikel B utvidgades modellen från Artikel A till en organnivå-modell för AAA-tillväxt. Vidare inkorporerades modellen i ett “Fluid–Solid–Growth” (FSG) ramverk. En patientspecifik geometri hos bukaortan användes för att illustrera möjligheterna med modellen. I Artikel C undersöktes utvecklingen av patientspecifika biomekaniska egenskaper hos AAA. Fyra patienter som skannats fem till åtta gånger med “Computed Tomography-Angiography” (CT-A) vid olika tillfällen analyserades. Flera icke triviala statistiska samband konstaterades mellan de analyserade parametrarna. I Artikel D undersöktes effekten av olika tillväxt-kinematik för AAA tillväxt. En modell med transversellt-isotrop-i-tjockleken-tillväxt var den bäst lämpade för AAA tillväxt, medans antagandet om fullt-isotrop-tillväxt och transversellt-isotrop-i-planet-tillväxt producerade orimliga resultat. Dessutom gav modellering av vävnadsvolymsförändring ett förbättrat väggtjockleks resultat men en fortsatt överskattning av väggförtunningen under AAA-expansionen. / <p>QC 20161201</p>