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Even when entirely unloaded, biological structures are not stress-free, as shown by Y.C. Fung׳s seminal opening angle experiment on arteries and the left ventricle. As a result of this prestrain, subject-specific geometries extracted from medical imaging do not represent an unloaded reference configuration necessary for mechanical analysis, even if the structure is externally unloaded. Here we propose a new computational method to create physiological residual stress fields in subject-specific left ventricular geometries using the continuum theory of fictitious configurations combined with a fixed-point iteration. We also reproduced the opening angle experiment on four swine models, to characterize the range of normal opening angle values. The proposed method generates residual stress fields which can reliably reproduce the range of opening angles between 8.7±1.8 and 16.6±13.7 as measured experimentally. We demonstrate that including the effects of prestrain reduces the left ventricular stiffness by up to 40%, thus facilitating the ventricular filling, which has a significant impact on cardiac function. This method can improve the fidelity of subject-specific models to improve our understanding of cardiac diseases and to optimize treatment options.

Currently, there is no full three-dimensional (3D) microstructural mechanical model of coronary artery based on measured microstructure including elastin, collagen and smooth muscle cells. Many structural models employ mean values of vessel microstructure, rather than continuous distributions of microstructure, to predict the mechanical properties of blood vessels. Although some models show good agreements on macroscopic vessel responses, they result in a lower elastin stiffness and earlier collagen recruitment. Hence, a full microstructural constitutive model is required for better understanding vascular biomechanics in health and disease. Here, a 3D microstructural model that accounts for all constituent microstructure is proposed to predict macroscopic and microscopic responses of coronary arteries. Coronary artery microstructural parameters were determined based on previous statistical measurements while mechanical testing of arteries (n = 5) were performed in this study to validate the computational predictions. The proposed model not only provides predictions of active and passive stress distributions of vessel wall, but also enables reliable estimations of material parameters of individual fibers and cells and thus predicts microstructural stresses. The validated microstructural model of coronary artery sheds light on vascular biomechanics and can be extend to diseased vessels for better understanding of initiation, progression and clinical treatment of vascular disease.

Heart failure is a progressive chronic condition in which the heart undergoes detrimental changes in structure and function across multiple scales in time and space. Multiscale models of cardiac growth can provide a patient-specific window into the progression of heart failure and guide personalized treatment planning. Yet, the predictive potential of cardiac growth models remains poorly understood. Here, we quantify predictive power of a stretch-driven growth model using a chronic porcine heart failure model, subject-specific multiscale simulation, and machine learning techniques. We combine hierarchical modeling, Bayesian inference, and Gaussian process regression to quantify the uncertainty of our experimental measurements during an 8-week long study of volume overload in six pigs. We then propagate the experimental uncertainties from the organ scale through our computational growth model and quantify the agreement between experimentally measured and computationally predicted alterations on the cellular scale. Our study suggests that stretch is the major stimulus for myocyte lengthening and demonstrates that a stretch-driven growth model alone can explain \\[52.7\\%\\] of the observed changes in myocyte morphology. We anticipate that our approach will allow us to design, calibrate, and validate a new generation of multiscale cardiac growth models to explore the interplay of various subcellular-, cellular-, and organ-level contributors to heart failure. Using machine learning in heart failure research has the potential to combine information from different sources, subjects, and scales to provide a more holistic picture of the failing heart and point toward new treatment strategies.

The three-dimensional (3D) representation of the bifurcation anatomy and disease burden is essential for better understanding of the anatomical complexity of bifurcation disease and planning of stenting strategies. We propose a novel methodology for 3D reconstruction of coronary artery bifurcations based on the integration of angiography, which provides the backbone of the bifurcation, with optical coherence tomography (OCT), which provides the vessel shape. Our methodology introduces several technical novelties to tackle the OCT frame misalignment, correct positioning of the OCT frames at the carina, lumen surface reconstruction, and merging of bifurcation lumens. The accuracy and reproducibility of the methodology were tested in n = 5 patient-specific silicone bifurcations compared to contrast-enhanced micro-computed tomography (µCT), which was used as reference. The feasibility and time-efficiency of the method were explored in n = 7 diseased patient bifurcations of varying anatomical complexity. The OCT-based reconstructed bifurcation models were found to have remarkably high agreement compared to the µCT reference models, yielding r 2 values between 0.91 and 0.98 for the normalized lumen areas, and mean differences of 0.005 for lumen shape and 0.004 degrees for bifurcation angles. Likewise, the reproducibility of our methodology was remarkably high. Our methodology successfully reconstructed all the patient bifurcations yielding favorable processing times (average lumen reconstruction time < 60 min). Overall, our method is an easily applicable, time-efficient, and user-friendly tool that allows accurate and reproducible 3D reconstruction of coronary bifurcations. Our technique can be used in the clinical setting to provide information about the bifurcation anatomy and plaque burden, thereby enabling planning, education, and decision making on bifurcation stenting.

A rigorous analysis of blood flow must be based on the branching pattern and vascular geometry of the full vascular circuit of interest. It is experimentally difficult to reconstruct the entire vascular circuit of any organ because of the enormity of the vessels. The objective of the present study was to develop a novel method for the reconstruction of the full coronary vascular tree from partial measurements. Our method includes the use of data on those parts of the tree that are measured to extrapolate the data on those parts that are missing. Specifically, a two-step approach was employed in the reconstruction of the entire coronary arterial tree down to the capillary level. Vessels > 40 microm were reconstructed from cast data while vessels < 40 microm were reconstructed from histological data. The cast data were reconstructed one-bifurcation at a time while histological data were reconstructed one-sub-tree at a time by \"cutting\" and \"pasting\" of data from measured to missing vessels. The reconstruction algorithm yielded a full arterial tree down to the first capillary bifurcation with 1.9, 2.04 and 1.15 million vessel segments for the right coronary artery (RCA), left anterior descending (LAD) and left circumflex (LCx) trees, respectively. The node-to-node connectivity along with the diameter and length of every vessel segment was determined. Once the full tree was reconstructed, we automated the assignment of order numbers, according to the diameter-defined Strahler system, to every vessel segment in the tree. Consequently, the diameters, lengths, number of vessels, segments-per-element ratio, connectivity and longitudinal matrices were determined for every order number. The present model establishes a morphological foundation for future analysis of blood flow in the coronary circulation.

The stresses and strains that remain in an organ when the external load is removed (the no-load state) are called residual stresses and strains. They can be relieved by cutting up the organ to obtain the zero-stress configuration. This phenomenon was demonstrated more than 15 years ago in cardiovascular research but until recently it was not realized by the gastrointestinal research community. The function of the gastrointestinal tract is to propel food by peristaltic motion, which is a result of the interaction of the tissue forces in the wall and the hydrodynamic forces in the food bolus. To understand the tissue forces, it is necessary to know the stress-strain relationships of the tissues that must be measured in reference to the zero-stress state. It has become clear that the zero-stress configuration of the gastrointestinal tract is very different from that of the no-load condition and that the zero-stress state is sensitive to structural and mechanical remodeling. The purpose of this review is to describe the basic theory and experiments of residual stress and to explore its physiological and pathophysiological implications in the gastrointestinal system.

This is a review of the current state of data, methodologies and models available for the construction of an anatomically accurate, three-dimensional coronary vasculature in a dynamic model of the beating heart that integrates vascular morphology, blood-vessel elasticity and tissue mechanics. The model is discussed in relation to the Cardiome, an anatomically based integrated model of cardiac function.

Blood flow to perfuse the muscle cells of the heart is distributed by the capillary blood vessels via the coronary arterial tree. Because the branching pattern and vascular geometry of the coronary vessels in the ventricles and atria are nonuniform, the flow in all of the coronary capillary blood vessels is not the same. This nonuniformity of perfusion has obvious physiological meaning, and must depend on the anatomy and branching pattern of the arterial tree. In this study, the statistical distribution of blood pressure, blood flow, and blood volume in all branches of the coronary arterial tree is determined based on the anatomical branching pattern of the coronary arterial tree and the statistical data on the lengths and diameters of the blood vessels. Spatial nonuniformity of the flow field is represented by dispersions of various quantities (SD/mean) that are determined as functions of the order numbers of the blood vessels. In the determination, we used a new, complete set of statistical data on the branching pattern and vascular geometry of the coronary arterial trees. We wrote hemodynamic equations for flow in every vessel and every node of a circuit, and solved them numerically. The results of two circuits are compared: one asymmetric model satisfies all anatomical data (including the mean connectivity matrix) and the other, a symmetric model, satisfies all mean anatomical data except the connectivity matrix. It was found that the mean longitudinal pressure drop profile as functions of the vessel order numbers are similar in both models, but the asymmetric model yields interesting dispersion profiles of blood pressure and blood flow. Mathematical modeling of the anatomy and hemodynamics is illustrated with discussions on its accuracy.

The temporal and spatial distribution of coronary blood flow, pressure, and volume are determined by the branching pattern and three-dimensional (3-D) geometry of the coronary vasculature, and by the mechanics of heart wall and vascular tone. Consequently, a realistic simulation of coronary blood flow requires, as a first step, an accurate representation of the coronary vasculature in a 3-D model of the beating heart. In the present study, a large-scale stochastic reconstruction of the asymmetric coronary arterial trees (right coronary artery, RCA; left anterior descending, LAD; and left circumflex, LCx) of the porcine heart has been carried out to set the stage for future hemodynamic analysis. The model spans the entire coronary arterial tree down to the capillary vessels. The 3-D tree structure was reconstructed initially in rectangular slab geometry by means of global geometrical optimization using parallel simulated annealing (SA) algorithm. The SA optimization was subject to constraints prescribed by previously measured morphometric features of the coronary arterial trees. Subsequently, the reconstructed trees were mapped onto a prolate spheroid geometry of the heart. The transformed geometry was determined through least squares minimization of the related changes in both segments lengths and their angular characteristics. Vessel diameters were assigned based on a novel representation of diameter asymmetry along bifurcations. The reconstructed RCA, LAD and LCx arterial trees show qualitative resemblance to native coronary networks, and their morphological statistics are consistent with the measured data. The present model constitutes the first most extensive reconstruction of the entire coronary arterial system which will serve as a geometric foundation for future studies of flow in an anatomically accurate 3-D coronary vascular model.

Biliary tract obstruction results in dilatation of the biliary tract including the gall bladder and induction of symptoms such as abdominal pain. Since the pain receptors are likely mechano-sensitive receptors, it is important to develop tools for studying the distributions of tension and stress in the wall of the gall bladder. Wall tension and stress can be determined using Laplace's equation and the three-dimensional (3-D) geometry of a thin walled organ under equilibrium conditions. The objective of this study was to develop an analytical method to describe the 3-D geometry of the porcine gall bladder. The Fourier series method was used to describe the organ surface geometry obtained from magnetic resonance (MR) images. MR images of nine normal and three obstructed porcine gall bladders were analyzed. The curvature was computed throughout the gall bladder surface and the wall tension was computed using Laplace's equation. The spatial distributions of principal curvatures, tensions, and stresses were nonhomogeneous in the gall bladder because of its complex geometry. The extremum values of curvatures did not differ between normal and 2-day obstructed gall bladders. The pressure, tension, and stress were significantly higher, however, in the obstructed gall bladders (p < 0.05). This study provides an analytical tool for characterizing the complex 3-D geometry of an organ obtained from a clinical imaging modality.