With heart and cardiovascular diseases continually challenging healthcare systems worldwide, translating basic research on cardiac (patho)physiology into clinical care is essential. Exacerbating this already extensive challenge is the complexity of the heart, relying on its hierarchical structure and function to maintain cardiovascular flow. Computational modelling has been proposed and actively pursued as a tool for accelerating research and translation. Allowing exploration of the relationships between physics, multiscale mechanisms and function, computational modelling provides a platform for improving our understanding of the heart. Further integration of experimental and clinical data through data assimilation and parameter estimation techniques is bringing computational models closer to use in routine clinical practice. This article reviews developments in computational cardiac modelling and how their integration with medical imaging data is providing new pathways for translational cardiac modelling.
Objective
Recent methods for imaging microvascular structures provide geometrical data on networks containing thousands of segments. Prediction of functional properties, such as solute transport, requires information on blood flow rates also, but experimental measurement of many individual flows is difficult. Here, a method is presented for estimating flow rates in a microvascular network based on incomplete information on the flows in the boundary segments that feed and drain the network.
Methods
With incomplete boundary data, the equations governing blood flow form an underdetermined linear system. An algorithm was developed that uses independent information about the distribution of wall shear stresses and pressures in microvessels to resolve this indeterminacy, by minimizing the deviation of pressures and wall shear stresses from target values.
Results
The algorithm was tested using previously obtained experimental flow data from four microvascular networks in the rat mesentery. With two or three prescribed boundary conditions, predicted flows showed relatively small errors in most segments and fewer than 10% incorrect flow directions on average.
Conclusions
The proposed method can be used to estimate flow rates in microvascular networks, based on incomplete boundary data and provides a basis for deducing functional properties of microvessel networks.
There is a need for, and utility in, the acquisition of data sets of cardiac histoanatomy, with the vision of reconstructing individual hearts on the basis of noninvasive imaging, such as MRI, enriched by reference to detailed atlases of serial histology obtained from representative samples. These data sets would be useful not only as a repository of knowledge regarding the specifics of cardiac histoanatomy, but could form the basis for generation of individualized high-resolution cardiac structure-function models. The current article presents a step in this general direction: it illustrates how whole-heart noninvasive imaging can be combined with whole-heart histology in an approach to achieve automated construction of histoanatomically detailed models of cardiac 3D structure and function at hitherto unprecedented resolution and accuracy (based on 26.4 × 26.4 × 24.4 μm MRI voxel size, and enriched by histological detail). It provides an overview of the tools used in this quest and outlines challenges posed by the approach in the light of applications that may benefit from the availability of such data and tools.
We present a method to efficiently simulate coronary perfusion in subject-specific models of the heart within clinically relevant time frames. Perfusion is modelled as a Darcy porous-media flow, where the permeability tensor is derived from homogenization of an explicit anatomical representation of the vasculature. To account for the disparity in length scales present in the vascular network, in this study, this approach is further refined through the implementation of a multi-compartment medium where each compartment encapsulates the spatial scales in a certain range by using an effective permeability tensor. Neighbouring compartments then communicate through distributed sources and sinks, acting as volume fluxes. Although elegant from a modelling perspective, the full multi-compartment Darcy system is computationally expensive to solve. We therefore enhance computational efficiency of this model by reducing the N-compartment system of Darcy equations to N pressure equations, and N subsequent projection problems to recover the Darcy velocity. The resulting 'reduced' Darcy formulation leads to a dramatic reduction in algebraic-system size and is therefore computationally cheaper to solve than the full multi-compartment Darcy system. A comparison of the reduced and the full formulation in terms of solution time and memory usage clearly highlights the superior performance of the reduced formulation. Moreover, the implementation of flux and, specifically, impermeable boundary conditions on arbitrarily curved boundaries such as epicardium and endocardium is straightforward in contrast to the full Darcy formulation. Finally, to demonstrate the applicability of our methodology to a personalized model and its solvability in clinically relevant time frames, we simulate perfusion in a subject-specific model of the left ventricle.
The strong coupling between the flow in coronary vessels and the mechanical deformation of the myocardial tissue is a central feature of cardiac physiology and must therefore be accounted for by models of coronary perfusion. Currently available geometrically explicit vascular models fail to capture this interaction satisfactorily, are numerically intractable for whole organ simulations, and are difficult to parameterise in human contexts. To address these issues, in this study, a finite element formulation of an incompressible, poroelastic model of myocardial perfusion is presented. Using high-resolution ex vivo imaging data of the coronary tree, the permeability tensors of the porous medium were mapped onto a mesh of the corresponding left ventricular geometry. The resultant tensor field characterises not only the distinct perfusion regions that are observed in experimental data, but also the wide range of vascular length scales present in the coronary tree, through a multi-compartment porous model. Finite deformation mechanics are solved using a macroscopic constitutive law that defines the coupling between the fluid and solid phases of the porous medium. Results are presented for the perfusion of the left ventricle under passive inflation that show wall-stiffening associated with perfusion, and that show the significance of a non-hierarchical multi-compartment model within a particular perfusion territory.
Advances in medical imaging and image processing are paving the way for personalised cardiac biomechanical modelling. Models provide the capacity to relate kinematics to dynamics and—through patient-specific modelling—derived material parameters to underlying cardiac muscle pathologies. However, for clinical utility to be achieved, model-based analyses mandate robust model selection and parameterisation. In this paper, we introduce a patient-specific biomechanical model for the left ventricle aiming to balance model fidelity with parameter identifiability. Using non-invasive data and common clinical surrogates, we illustrate unique identifiability of passive and active parameters over the full cardiac cycle. Identifiability and accuracy of the estimates in the presence of controlled noise are verified with a number of in silico datasets. Unique parametrisation is then obtained for three datasets acquired in vivo. The model predictions show good agreement with the data extracted from the images providing a pipeline for personalised biomechanical analysis.
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