Guidelines for mechanistic modeling and analysis in cardiovascular research.

Computational, or in silico, models are an effective, noninvasive tool for investigating cardiovascular function. These models can be used in the analysis of experimental and clinical data to identify possible mechanisms of (ab)normal cardiovascular physiology. Recent advances in computing power and data management have led to innovative and complex modeling frameworks that simulate cardiovascular function across multiple scales. While commonly used in multiple disciplines, there is a lack of concise guidelines for the implementation of computer models in cardiovascular research. In line with recent calls for more reproducible research, it is imperative that scientists adhere to credible practices when developing and applying computational models to their research. The goal of this manuscript is to provide a consensus document that identifies best practices for in silico computational modeling in cardiovascular research. These guidelines provide the necessary methods for mechanistic model development, model analysis, and formal model calibration using fundamentals from statistics. We outline rigorous practices for computational, mechanistic modeling in cardiovascular research and discuss its synergistic value to experimental and clinical data.

Estimating pulmonary arterial remodeling via an animal-specific computational model of pulmonary artery stenosis.

Pulmonary artery stenosis (PAS) often presents in children with congenital heart disease, altering blood flow and pressure during critical periods of growth and development. Variability in stenosis onset, duration, and severity result in variable growth and remodeling of the pulmonary vasculature. Computational fluid dynamics (CFD) models enable investigation into the hemodynamic impact and altered mechanics associated with PAS. In this study, a one-dimensional (1D) fluid dynamics model was used to simulate hemodynamics throughout the pulmonary arteries of individual animals. The geometry of the large pulmonary arteries was prescribed by animal-specific imaging, whereas the distal vasculature was simulated by a three-element Windkessel model at each terminal vessel outlet. Remodeling of the pulmonary vasculature, which cannot be measured in vivo, was estimated via model-fitted parameters. The large artery stiffness was significantly higher on the left side of the vasculature in the left pulmonary artery (LPA) stenosis group, but neither side differed from the sham group. The sham group exhibited a balanced distribution of total distal vascular resistance, whereas the left side was generally larger in the LPA stenosis group, with no significant differences between groups. In contrast, the peripheral compliance on the right side of the LPA stenosis group was significantly greater than the corresponding side of the sham group. Further analysis indicated the underperfused distal vasculature likely moderately decreased in radius with little change in stiffness given the increase in thickness observed with histology. Ultimately, our model enables greater understanding of pulmonary arterial adaptation due to LPA stenosis and has potential for use as a tool to noninvasively estimate remodeling of the pulmonary vasculature.

Don't go breakin' my heart: cardioprotective alterations to the mechanical and structural properties of reperfused myocardium during post-infarction inflammation.

Myocardial infarctions (MIs) kickstart an intense inflammatory response resulting in extracellular matrix (ECM) degradation, wall thinning, and chamber dilation that leaves the heart susceptible to rupture. Reperfusion therapy is one of the most effective strategies for limiting adverse effects of MIs, but is a challenge to administer in a timely manner. Late reperfusion therapy (LRT; 3 + hours post-MI) does not limit infarct size, but does reduce incidences of post-MI rupture and improves long-term patient outcomes. Foundational studies employing LRT in the mid-twentieth century revealed beneficial reductions in infarct expansion, aneurysm formation, and left ventricle dysfunction. The mechanism by which LRT acts, however, is undefined. Structural analyses, relying largely on one-dimensional estimates of ECM composition, have found few differences in collagen content between LRT and permanently occluded animal models when using homogeneous samples from infarct cores. Uniaxial testing, on the other hand, revealed slight reductions in stiffness early in inflammation, followed soon after by an enhanced resistance to failure for cases of LRT. The use of one-dimensional estimates of ECM organization and gross mechanical function have resulted in a poor understanding of the infarct's spatially variable mechanical and structural anisotropy. To resolve these gaps in literature, future work employing full-field mechanical, structural, and cellular analyses is needed to better define the spatiotemporal post-MI alterations occurring during the inflammatory phase of healing and how they are impacted following reperfusion therapy. In turn, these studies may reveal how LRT affects the likelihood of rupture and inspire novel approaches to guide scar formation.

A Computational Model of Ventricular Dimensions and Hemodynamics in Growing Infants.

Previous computer models have successfully predicted cardiac growth and remodeling in adults with pathologies. However, applying these models to infants is complicated by the fact that they also undergo normal, somatic cardiac growth and remodeling. Therefore, we designed a computational model to predict ventricular dimensions and hemodynamics in healthy, growing infants by modifying an adult canine left ventricular growth model. The heart chambers were modeled as time-varying elastances coupled to a circuit model of the circulation. Circulation parameters were allometrically scaled and adjusted for maturation to simulate birth through 3 yrs of age. Ventricular growth was driven by perturbations in myocyte strain. The model successfully matched clinical measurements of pressures, ventricular and atrial volumes, and ventricular thicknesses within two standard deviations of multiple infant studies. To test the model, we input 10th and 90th percentile infant weights. Predicted volumes and thicknesses decreased and increased within normal ranges and pressures were unchanged. When we simulated coarctation of the aorta, systemic blood pressure, left ventricular thickness, and left ventricular volume all increased, following trends in clinical data. Our model enables a greater understanding of somatic and pathological growth in infants with congenital heart defects. Its flexibility and computational efficiency when compared to models employing more complex geometries allow for rapid analysis of pathological mechanisms affecting cardiac growth and hemodynamics.

Individual variability in animal-specific hemodynamic compensation following myocardial infarction.

Ventricular enlargement and heart failure are common in patients who survive a myocardial infarction (MI). There is striking variability in the degree of post-infarction ventricular remodeling, however, and no one factor or set of factors have been identified that predicts heart failure risk well. Sympathetic activation directly and indirectly modulates hypertrophic stimuli by altering both neurohormonal milieu and ventricular loading. In a recent study, we developed a method to identify the balance of reflex compensatory mechanisms employed by individual animals following MI based on measured hemodynamics. Here, we conducted prospective studies of acute myocardial infarction in rats to test the degree of variability in reflex compensation as well as whether responses to pharmacologic agents targeted at those reflex mechanisms could be anticipated in individual animals. We found that individual animals use very different mixtures of reflex compensation in response to experimental coronary ligation. Some of these mechanisms were related - animals that compensated strongly with venoconstriction tended to exhibit a decrease in the contractility of the surviving myocardium and those that increased contractility tended to exhibit venodilation. Furthermore, some compensatory mechanisms - such as venoconstriction - increased the extent of predicted ventricular enlargement. Unfortunately, initial reflex responses to infarction were a poor predictor of subsequent responses to pharmacologic agents, suggesting that customizing pharmacologic therapy to individuals based on an initial response will be challenging.

Characterizing Tissue Remodeling and Mechanical Heterogeneity in Cerebral Aneurysms.

Accurately assessing the complex tissue mechanics of cerebral aneurysms (CAs) is critical for elucidating how CAs grow and whether that growth will lead to rupture. The factors that have been implicated in CA progression - blood flow dynamics, immune infiltration, and extracellular matrix remodeling - all occur heterogeneously throughout the CA. Thus, it stands to reason that the mechanical properties of CAs are also spatially heterogeneous. Here, we present a new method for characterizing the mechanical heterogeneity of human CAs using generalized anisotropic inverse mechanics, which uses biaxial stretching experiments and inverse analyses to determine the local Kelvin moduli and principal alignments within the tissue. Using this approach, we find that there is significant mechanical heterogeneity within a single acquired human CA. These results were confirmed using second harmonic generation imaging of the CA's fiber architecture and a correlation was observed. This approach provides a single-step method for determining the complex heterogeneous mechanics of CAs, which has important implications for future identification of metrics that can improve accuracy in prediction risk of rupture.

Trajectory of right ventricular indices is an early predictor of outcomes in hypoplastic left heart syndrome.

BACKGROUND: Children with hypoplastic left heart syndrome (HLHS) have risk for mortality and/or transplantation. Previous studies have associated right ventricular (RV) indices in a single echocardiogram with survival, but none have related serial measurements to outcomes. This study sought to determine whether the trajectory of RV indices in the first year of life was associated with transplant-free survival to stage 3 palliation (S3P). METHODS: HLHS patients at a single center who underwent stage 1 palliation (S1P) between 2000 and 2015 were reviewed. Echocardiographic indices of RV size and function were obtained before and following S1P and stage 2 palliation (S2P). The association between these indices and transplant-free survival to S3P was examined. RESULTS: There were 61 patients enrolled in the study with 51 undergoing S2P, 20 S3P, and 18 awaiting S3P. In the stage 1 perioperative period, indexed RV end-systolic area increased in patients who died or needed transplant following S2P, and changed little in those surviving to S3P (3.37 vs -0.04 cm2 /m2 , P = .017). Increased indexed RV end-systolic area was associated with worse transplant-free survival. (OR = 0.815, P = .042). In the interstage period, indexed RV end-diastolic area increased less in those surviving to S3P (3.6 vs 9.2, P = .03). CONCLUSION: Change in indexed RV end-systolic area through the stage 1 perioperative period was associated with transplant-free survival to S3P. Neither the prestage nor poststage 1 indexed RV end-systolic area was associated with transplant-free survival to S3P. Patients with death or transplant before S3P had a greater increase in indexed RV end-diastolic area during the interstage period. This suggests earlier serial changes in RV size which may provide prognostic information beyond RV indices in a single study.

The Impact of Hemodynamic Reflex Compensation Following Myocardial Infarction on Subsequent Ventricular Remodeling.

Patients who survive a myocardial infarction (MI) are at high risk for ventricular dilation and heart failure. While infarct size is an important determinant of post-MI remodeling, different patients with the same size infarct often display different levels of left ventricular (LV) dilation. The acute physiologic response to MI involves reflex compensation, whereby increases in heart rate (HR), arterial resistance, venoconstriction, and contractility of the surviving myocardium act to maintain mean arterial pressure (MAP). We hypothesized that variability in reflex compensation might underlie some of the reported variability in post-MI remodeling, a hypothesis that is difficult to test using experimental data alone because some reflex responses are difficult or impossible to measure directly. We, therefore, employed a computational model to estimate the balance of compensatory mechanisms from experimentally reported hemodynamic data. We found a strikingly wide range of compensatory reflex profiles in response to MI in dogs and verified that pharmacologic blockade of sympathetic and parasympathetic reflexes nearly abolished this variability. Then, using a previously published model of postinfarction remodeling, we showed that observed variability in compensation translated to variability in predicted LV dilation consistent with published data. Treatment with a vasodilator shifted the compensatory response away from arterial and venous vasoconstriction and toward increased HR and myocardial contractility. Importantly, this shift reduced predicted dilation, a prediction that matched prior experimental studies. Thus, postinfarction reflex compensation could represent both a source of individual variability in the extent of LV remodeling and a target for therapies aimed at reducing that remodeling.

Predicting the Time Course of Ventricular Dilation and Thickening Using a Rapid Compartmental Model.

The ability to predict long-term growth and remodeling of the heart in individual patients could have important clinical implications, but the time to customize and run current models makes them impractical for routine clinical use. Therefore, we adapted a published growth relation for use in a compartmental model of the left ventricle (LV). The model was coupled to a circuit model of the circulation to simulate hemodynamic overload in dogs. We automatically tuned control and acute model parameters based on experimentally reported hemodynamic data and fit growth parameters to changes in LV dimensions from two experimental overload studies (one pressure, one volume). The fitted model successfully predicted the reported time course of LV dilation and thickening not only in independent studies of pressure and volume overload but also following myocardial infarction. Implemented in MATLAB on a desktop PC, the model required just 6 min to simulate 3 months of growth.

Failure of the Porcine Ascending Aorta: Multidirectional Experiments and a Unifying Microstructural Model.

The ascending thoracic aorta is poorly understood mechanically, especially its risk of dissection. To make better predictions of dissection risk, more information about the multidimensional failure behavior of the tissue is needed, and this information must be incorporated into an appropriate theoretical/computational model. Toward the creation of such a model, uniaxial, equibiaxial, peel, and shear lap tests were performed on healthy porcine ascending aorta samples. Uniaxial and equibiaxial tests showed anisotropy with greater stiffness and strength in the circumferential direction. Shear lap tests showed catastrophic failure at shear stresses (150-200 kPa) much lower than uniaxial tests (750-2500 kPa), consistent with the low peel tension (∼60 mN/mm). A novel multiscale computational model, including both prefailure and failure mechanics of the aorta, was developed. The microstructural part of the model included contributions from a collagen-reinforced elastin sheet and interlamellar connections representing fibrillin and smooth muscle. Components were represented as nonlinear fibers that failed at a critical stretch. Multiscale simulations of the different experiments were performed, and the model, appropriately specified, agreed well with all experimental data, representing a uniquely complete structure-based description of aorta mechanics. In addition, our experiments and model demonstrate the very low strength of the aorta in radial shear, suggesting an important possible mechanism for aortic dissection.

A Comparison of Phenomenologic Growth Laws for Myocardial Hypertrophy.

The heart grows in response to changes in hemodynamic loading during normal development and in response to valve disease, hypertension, and other pathologies. In general, a left ventricle subjected to increased afterload (pressure overloading) exhibits concentric growth characterized by thickening of individual myocytes and the heart wall, while one experiencing increased preload (volume overloading) exhibits eccentric growth characterized by lengthening of myocytes and dilation of the cavity. Predictive models of cardiac growth could be important tools in evaluating treatments, guiding clinical decision making, and designing novel therapies for a range of diseases. Thus, in the past 20 years there has been considerable effort to simulate growth within the left ventricle. While a number of published equations or systems of equations (often termed "growth laws") can capture some aspects of experimentally observed growth patterns, no direct comparisons of the various published models have been performed. Here we examine eight of these laws and compare them in a simple test-bed in which we imposed stretches measured during in vivo pressure and volume overload. Laws were compared based on their ability to predict experimentally measured patterns of growth in the myocardial fiber and radial directions as well as the ratio of fiber-to-radial growth. Three of the eight laws were able to reproduce most key aspects of growth following both pressure and volume overload. Although these three growth laws utilized different approaches to predict hypertrophy, they all employed multiple inputs that were weakly correlated during in vivo overload and therefore provided independent information about mechanics.

A nonlinear anisotropic inverse method for computational dissection of inhomogeneous planar tissues.

Quantification of the mechanical behavior of soft tissues is challenging due to their anisotropic, heterogeneous, and nonlinear nature. We present a method for the 'computational dissection' of a tissue, by which we mean the use of computational tools both to identify and to analyze regions within a tissue sample that have different mechanical properties. The approach employs an inverse technique applied to a series of planar biaxial experimental protocols. The aggregated data from multiple protocols provide the basis for (1) segmentation of the tissue into regions of similar properties, (2) linear analysis for the small-strain behavior, assuming uniform, linear, anisotropic behavior within each region, (3) subsequent nonlinear analysis following each individual experimental protocol path and using local linear properties, and (4) construction of a strain energy data set W(E) at every point in the material by integrating the differential stress-strain functions along each strain path. The approach has been applied to simulated data and captures not only the general nonlinear behavior but also the regional differences introduced into the simulated tissue sample.

Automatic Segmentation of Mechanically Inhomogeneous Tissues Based on Deformation Gradient Jump.

Variations in properties, active behavior, injury, scarring, and/or disease can all cause a tissue's mechanical behavior to be heterogeneous. Advances in imaging technology allow for accurate full-field displacement tracking of both in vitro and in vivo deformation from an applied load. While detailed strain fields provide some insight into tissue behavior, material properties are usually determined by fitting stress-strain behavior with a constitutive equation. However, the determination of the mechanical behavior of heterogeneous soft tissue requires a spatially varying constitutive equation (i.e., one in which the material parameters vary with position). We present an approach that computationally dissects the sample domain into many homogeneous subdomains, wherein subdomain boundaries are formed by applying a betweenness based graphical analysis to the deformation gradient field to identify locations with large discontinuities. This novel partitioning technique successfully determined the shape, size and location of regions with locally similar material properties for: (1) a series of simulated soft tissue samples prescribed with both abrupt and gradual changes in anisotropy strength, prescribed fiber alignment, stiffness, and nonlinearity, (2) tissue analogs (PDMS and collagen gels) which were tested biaxially and speckle tracked (3) and soft tissues which exhibited a natural variation in properties (cadaveric supraspinatus tendon), a pathologic variation in properties (thoracic aorta containing transmural plaque), and active behavior (contracting cardiac sheet). The routine enables the dissection of samples computationally rather than physically, allowing for the study of small tissues specimens with unknown and irregular inhomogeneity.