At the heart of computational modelling

Neural Network Approaches for Soft Biological Tissue and Organ Simulations

Given the functional complexities of soft tissues and organs, it is clear that computational simulations are critical in their understanding and for the rational basis for the development of therapies and replacements. A key aspect of such simulations is accounting for their complex, nonlinear, anisotropic mechanical behaviors. While soft tissue material models have developed to the point of high fidelity, in-silico implementation is typically done using the finite element (FE) method, which remains impractically slow for translational clinical time frames. As a potential path toward addressing the development of high fidelity simulations capable of performing in clinically relevant time frames, we review the use of neural networks (NN) for soft tissue and organ simulation using two approaches. In the first approach, we show how a NN can learn the responses for a detailed meso-structural soft tissue material model. The NN material model not only reproduced the full anisotropic mechanical responses but also demonstrated a considerable efficiency improvement, as it was trained over a range of realizable fibrous structures. In the second approach, we go a step further with the use of a physics-based surrogate model to directly learn the displacement field solution without the need for raw training data or FE simulation datasets. In this approach we utilize a finite element mesh to define the domain and perform the necessary integrations, but not the finite element method (FEM) itself. We demonstrate with this approach, termed neural network finite element (NNFE), results in a trained NNFE model with excellent agreement with the corresponding "ground truth" FE solutions over the entire physiological deformation range on a cuboidal myocardium specimen. More importantly, the NNFE approach provided a significantly decreased computational time for a range of finite element mesh sizes. Specifically, as the FE mesh size increased from 2744 to 175,615 elements, the NNFE computational time increased from 0.1108 s to 0.1393 s, while the "ground truth" FE model increased from 4.541 s to 719.9 s, with the same effective accuracy. These results suggest that NNFE run times are significantly reduced compared with the traditional large-deformation-based finite element solution methods. We then show how a nonuniform rational B-splines (NURBS)-based approach can be directly integrated into the NNFE approach as a means to handle real organ geometries. While these and related approaches are in their early stages, they offer a method to perform complex organ-level simulations in clinically relevant time frames without compromising accuracy.

Frank-Starling mechanism, fluid responsiveness, and length-dependent activation: Unravelling the multiscale behaviors with an in silico analysis

The Frank-Starling mechanism is a fundamental regulatory property which underlies the cardiac output adaptation to venous filling. Length-dependent activation is generally assumed to be the cellular origin of this mechanism. At the heart scale, it is commonly admitted that an increase in preload (ventricular filling) leads to an increased cellular force and an increased volume of ejected blood. This explanation also forms the basis for vascular filling therapy. It is actually difficult to unravel the exact nature of the relationship between length-dependent activation and the Frank-Starling mechanism, as three different scales (cellular, ventricular and cardiovascular) are involved. Mathematical models are powerful tools to overcome these limitations. In this study, we use a multiscale model of the cardiovascular system to untangle the three concepts (length-dependent activation, Frank-Starling, and vascular filling). We first show that length-dependent activation is required to observe both the Frank-Starling mechanism and a positive response to high vascular fillings. Our results reveal a dynamical length dependent activation-driven response to changes in preload, which involves interactions between the cellular, ventricular and cardiovascular levels and thus highlights fundamentally multiscale behaviors. We show however that the cellular force increase is not enough to explain the cardiac response to rapid changes in preload. We also show that the absence of fluid responsiveness is not related to a saturating Frank-Starling effect. As it is challenging to study those multiscale phenomena experimentally, this computational approach contributes to a more comprehensive knowledge of the sophisticated length-dependent properties of cardiac muscle.

Modeling individual differences in cardiovascular response to gravitational stress using a sensitivity analysis

The human cardiovascular (CV) system elicits a physiological response to gravitational environments, with significant variation between different individuals. Computational modeling can predict CV response, however model complexity and variation of physiological parameters in a normal population makes it challenging to capture individual responses. We conducted a sensitivity analysis on an existing 21-compartment lumped-parameter hemodynamic model in a range of gravitational conditions to 1) investigate the influence of model parameters on a tilt test CV response and 2) to determine the subset of those parameters with the most influence on systemic physiological outcomes. A supine virtual subject was tilted to upright under the influence of a constant gravitational field ranging from 0 g to 1 g. The sensitivity analysis was conducted using a Latin hypercube sampling/partial rank correlation coefficient methodology with subsets of model parameters varied across a normal physiological range. Sensitivity was determined by variation in outcome measures including heart rate, stroke volume, central venous pressure, systemic blood pressures, and cardiac output. Results showed that model parameters related to the length, resistance, and compliance of the large veins and parameters related to right ventricular function have the most influence on model outcomes. For most outcome measures considered, parameters related to the heart are dominant. Results highlight which model parameters to accurately value in simulations of individual subjects' CV response to gravitational stress, improving the accuracy of predictions. Influential parameters remain largely similar across gravity levels, highlighting that accurate model fitting in 1 g can increase the accuracy of predictive responses in reduced gravity.NEW & NOTEWORTHY Computational modeling is used to predict cardiovascular responses to altered gravitational environments. However, considerable variation between subjects and model complexity makes accurate parameter assignment for individuals challenging. This computational effort studies sensitivity in cardiovascular model outcomes due to varying parameters across a normal physiological range. This allows determination of which parameters have the largest influence on outcomes, i.e., which parameters must be most carefully selected to give accurate predictions of individual responses.

Multi-scale approaches for the simulation of cardiac electrophysiology: II - Tissue-level structure and function

Computational models of the heart, from cell-level models, through one-, two- and three-dimensional tissue-level simplifications, to biophysically-detailed three-dimensional models of the ventricles, atria or whole heart, allow the simulation of excitation and propagation of this excitation, and have provided remarkable insight into the normal and pathological functioning of the heart. In this article we present equations for modelling cellular excitation (i.e. the cell action potential) from both a phenomenological and a biophysical perspective. Hodgkin-Huxley formalism is discussed, along with the current generation of biophysically-detailed cardiac cell models. Alternative Markovian formulations for modelling ionic currents are also presented. Equations describing propagation of this cellular excitation, through one-, two- and three-dimensional idealised or realistic tissues, are then presented. For all types of model, from cell to tissue, methods for discretisation and integration of the underlying equations are discussed. The article finishes with a discussion of two tissue-level experimental imaging techniques - diffusion tensor magnetic resonance imaging and optical imaging - that can be used to provide data for parameterisation and validation of cell- and tissue-level cardiac models.

Comparing two sequential Monte Carlo samplers for exact and approximate Bayesian inference on biological models

Bayesian methods are advantageous for biological modelling studies due to their ability to quantify and characterize posterior variability in model parameters. When Bayesian methods cannot be applied, due either to non-determinism in the model or limitations on system observability, approximate Bayesian computation (ABC) methods can be used to similar effect, despite producing inflated estimates of the true posterior variance. Owing to generally differing application domains, there are few studies comparing Bayesian and ABC methods, and thus there is little understanding of the properties and magnitude of this uncertainty inflation. To address this problem, we present two popular strategies for ABC sampling that we have adapted to perform exact Bayesian inference, and compare them on several model problems. We find that one sampler was impractical for exact inference due to its sensitivity to a key normalizing constant, and additionally highlight sensitivities of both samplers to various algorithmic parameters and model conditions. We conclude with a study of the O'Hara-Rudy cardiac action potential model to quantify the uncertainty amplification resulting from employing ABC using a set of clinically relevant biomarkers. We hope that this work serves to guide the implementation and comparative assessment of Bayesian and ABC sampling techniques in biological models.

Potassium currents in the heart: functional roles in repolarization, arrhythmia and therapeutics

This is the second of the two White Papers from the fourth UC Davis Cardiovascular Symposium Systems Approach to Understanding Cardiac Excitation-Contraction Coupling and Arrhythmias (3-4 March 2016), a biennial event that brings together leading experts in different fields of cardiovascular research. The theme of the 2016 symposium was 'K⁺ channels and regulation', and the objectives of the conference were severalfold: (1) to identify current knowledge gaps; (2) to understand what may go wrong in the diseased heart and why; (3) to identify possible novel therapeutic targets; and (4) to further the development of systems biology approaches to decipher the molecular mechanisms and treatment of cardiac arrhythmias. The sessions of the Symposium focusing on the functional roles of the cardiac K⁺ channel in health and disease, as well as K⁺ channels as therapeutic targets, were contributed by Ye Chen-Izu, Gideon Koren, James Weiss, David Paterson, David Christini, Dobromir Dobrev, Jordi Heijman, Thomas O'Hara, Crystal Ripplinger, Zhilin Qu, Jamie Vandenberg, Colleen Clancy, Isabelle Deschenes, Leighton Izu, Tamas Banyasz, Andras Varro, Heike Wulff, Eleonora Grandi, Michael Sanguinetti, Donald Bers, Jeanne Nerbonne and Nipavan Chiamvimonvat as speakers and panel discussants. This article summarizes state-of-the-art knowledge and controversies on the functional roles of cardiac K⁺ channels in normal and diseased heart. We endeavour to integrate current knowledge at multiple scales, from the single cell to the whole organ levels, and from both experimental and computational studies.

Heart Valve Biomechanics and Underlying Mechanobiology

Heart valves control unidirectional blood flow within the heart during the cardiac cycle. They have a remarkable ability to withstand the demanding mechanical environment of the heart, achieving lifetime durability by processes involving the ongoing remodeling of the extracellular matrix. The focus of this review is on heart valve functional physiology, with insights into the link between disease-induced alterations in valve geometry, tissue stress, and the subsequent cell mechanobiological responses and tissue remodeling. We begin with an overview of the fundamentals of heart valve physiology and the characteristics and functions of valve interstitial cells (VICs). We then provide an overview of current experimental and computational approaches that connect VIC mechanobiological response to organ- and tissue-level deformations and improve our understanding of the underlying functional physiology of heart valves. We conclude with a summary of future trends and offer an outlook for the future of heart valve mechanobiology, specifically, multiscale modeling approaches, and the potential directions and possible challenges of research development. © 2016 American Physiological Society. Compr Physiol 6:1743-1780, 2016.

There and back again: Iterating between population-based modeling and experiments reveals surprising regulation of calcium transients in rat cardiac myocytes

While many ion channels and transporters involved in cardiac cellular physiology have been identified and described, the relative importance of each in determining emergent cellular behaviors remains unclear. Here we address this issue with a novel approach that combines population-based mathematical modeling with experimental tests to systematically quantify the relative contributions of different ion channels and transporters to the amplitude of the cellular Ca(2+) transient. Sensitivity analysis of a mathematical model of the rat ventricular cardiomyocyte quantified the response of cell behaviors to changes in the level of each ion channel and transporter, and experimental tests of these predictions were performed to validate or invalidate the predictions. The model analysis found that partial inhibition of the transient outward current in rat ventricular epicardial myocytes was predicted to have a greater impact on Ca(2+) transient amplitude than either: (1) inhibition of the same current in endocardial myocytes, or (2) comparable inhibition of the sarco/endoplasmic reticulum Ca(2+) ATPase (SERCA). Experimental tests confirmed the model predictions qualitatively but showed some quantitative disagreement. This guided us to recalibrate the model by adjusting the relative importance of several Ca(2+) fluxes, thereby improving the consistency with experimental data and producing a more predictive model. Analysis of human cardiomyocyte models suggests that the relative importance of outward currents to Ca(2+) transporters is generalizable to human atrial cardiomyocytes, but not ventricular cardiomyocytes. Overall, our novel approach of combining population-based mathematical modeling with experimental tests has yielded new insight into the relative importance of different determinants of cell behavior.

Improving cardiomyocyte model fidelity and utility via dynamic electrophysiology protocols and optimization algorithms

Mathematical models of cardiac electrophysiology are instrumental in determining mechanisms of cardiac arrhythmias. However, the foundation of a realistic multiscale heart model is only as strong as the underlying cell model. While there have been myriad advances in the improvement of cellular-level models, the identification of model parameters, such as ion channel conductances and rate constants, remains a challenging problem. The primary limitations to this process include: (1) such parameters are usually estimated from data recorded using standard electrophysiology voltage-clamp protocols that have not been developed with model building in mind, and (2) model parameters are typically tuned manually to subjectively match a desired output. Over the last decade, methods aimed at overcoming these disadvantages have emerged. These approaches include the use of optimization or fitting tools for parameter estimation and incorporating more extensive data for output matching. Here, we review recent advances in parameter estimation for cardiomyocyte models, focusing on the use of more complex electrophysiology protocols and global search heuristics. We also discuss future applications of such parameter identification, including development of cell-specific and patient-specific mathematical models to investigate arrhythmia mechanisms and predict therapy strategies.

Hodgkin-Huxley revisited: reparametrization and identifiability analysis of the classic action potential model with approximate Bayesian methods

As cardiac cell models become increasingly complex, a correspondingly complex 'genealogy' of inherited parameter values has also emerged. The result has been the loss of a direct link between model parameters and experimental data, limiting both reproducibility and the ability to re-fit to new data. We examine the ability of approximate Bayesian computation (ABC) to infer parameter distributions in the seminal action potential model of Hodgkin and Huxley, for which an immediate and documented connection to experimental results exists. The ability of ABC to produce tight posteriors around the reported values for the gating rates of sodium and potassium ion channels validates the precision of this early work, while the highly variable posteriors around certain voltage dependency parameters suggests that voltage clamp experiments alone are insufficient to constrain the full model. Despite this, Hodgkin and Huxley's estimates are shown to be competitive with those produced by ABC, and the variable behaviour of posterior parametrized models under complex voltage protocols suggests that with additional data the model could be fully constrained. This work will provide the starting point for a full identifiability analysis of commonly used cardiac models, as well as a template for informative, data-driven parametrization of newly proposed models.

An integrated electromechanical-growth heart model for simulating cardiac therapies

An emerging class of models has been developed in recent years to predict cardiac growth and remodeling (G&R). We recently developed a cardiac G&R constitutive model that predicts remodeling in response to elevated hemodynamics loading, and a subsequent reversal of the remodeling process when the loading is reduced. Here, we describe the integration of this G&R model to an existing strongly coupled electromechanical model of the heart. A separation of timescale between growth deformation and elastic deformation was invoked in this integrated electromechanical-growth heart model. To test our model, we applied the G&R scheme to simulate the effects of myocardial infarction in a realistic left ventricular (LV) geometry using the finite element method. We also simulate the effects of a novel therapy that is based on alteration of the infarct mechanical properties. We show that our proposed model is able to predict key features that are consistent with experiments. Specifically, we show that the presence of a non-contractile infarct leads to a dilation of the left ventricle that results in a rightward shift of the pressure volume loop. Our model also predicts that G&R is attenuated by a reduction in LV dilation when the infarct stiffness is increased.

Human cardiac systems electrophysiology and arrhythmogenesis: iteration of experiment and computation

Human cardiac electrophysiology (EP) is a unique system for computational modelling at multiple scales. Due to the complexity of the cardiac excitation sequence, coordinated activity must occur from the single channel to the entire myocardial syncytium. Thus, sophisticated computational algorithms have been developed to investigate cardiac EP at the level of ion channels, cardiomyocytes, multicellular tissues, and the whole heart. Although understanding of each functional level will ultimately be important to thoroughly understand mechanisms of physiology and disease, cardiac arrhythmias are expressly the product of cardiac tissue-containing enough cardiomyocytes to sustain a reentrant loop of activation. In addition, several properties of cardiac cellular EP, that are critical for arrhythmogenesis, are significantly altered by cell-to-cell coupling. However, relevant human cardiac EP data, upon which to develop or validate models at all scales, has been lacking. Thus, over several years, we have developed a paradigm for multiscale human heart physiology investigation and have recovered and studied over 300 human hearts. We have generated a rich experimental dataset, from which we better understand mechanisms of arrhythmia in human and can improve models of human cardiac EP. In addition, in collaboration with computational physiologists, we are developing a database for the deposition of human heart experimental data, including thorough experimental documentation. We anticipate that accessibility to this human heart dataset will further human EP computational investigations, as well as encourage greater data transparency within the field of cardiac EP.

β-adrenergic effects on cardiac myofilaments and contraction in an integrated rabbit ventricular myocyte model

A five-state model of myofilament contraction was integrated into a well-established rabbit ventricular myocyte model of ion channels, Ca(2+) transporters and kinase signaling to analyze the relative contribution of different phosphorylation targets to the overall mechanical response driven by β-adrenergic stimulation (β-AS). β-AS effect on sarcoplasmic reticulum Ca(2+) handling, Ca(2+), K(+) and Cl(-) currents, and Na(+)/K(+)-ATPase properties was included based on experimental data. The inotropic effect on the myofilaments was represented as reduced myofilament Ca(2+) sensitivity (XBCa) and titin stiffness, and increased cross-bridge (XB) cycling rate (XBcy). Assuming independent roles of XBCa and XBcy, the model reproduced experimental β-AS responses on action potentials and Ca(2+) transient amplitude and kinetics. It also replicated the behavior of force-Ca(2+), release-restretch, length-step, stiffness-frequency and force-velocity relationships, and increased force and shortening in isometric and isotonic twitch contractions. The β-AS effect was then switched off from individual targets to analyze their relative impact on contractility. Preventing β-AS effects on L-type Ca(2+) channels or phospholamban limited Ca(2+) transients and contractile responses in parallel, while blocking phospholemman and K(+) channel (IKs) effects enhanced Ca(2+) and inotropy. Removal of β-AS effects from XBCa enhanced contractile force while decreasing peak Ca(2+) (due to greater Ca(2+) buffering), but had less effect on shortening. Conversely, preventing β-AS effects on XBcy preserved Ca(2+) transient effects, but blunted inotropy (both isometric force and especially shortening). Removal of titin effects had little impact on contraction. Finally, exclusion of β-AS from XBCa and XBcy while preserving effects on other targets resulted in preserved peak isometric force response (with slower kinetics) but nearly abolished enhanced shortening. β-AS effects on XBCa and XBcy have greater impact on isometric and isotonic contraction, respectively.

Fibroblast-myocyte electrotonic coupling: does it occur in native cardiac tissue?

Heterocellular electrotonic coupling between cardiac myocytes and non-excitable connective tissue cells has been a long-established and well-researched fact in vitro. Whether or not such coupling exists in vivo has been a matter of considerable debate. This paper reviews the development of experimental insight and conceptual views on this topic, describes evidence in favour of and against the presence of such coupling in native myocardium, and identifies directions for further study needed to resolve the riddle, perhaps less so in terms of principal presence which has been demonstrated, but undoubtedly in terms of extent, regulation, patho-physiological context, and actual relevance of cardiac myocyte–non-myocyte coupling in vivo. This article is part of a Special Issue entitled "Myocyte-Fibroblast Signalling in Myocardium."

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Electrical coupling of cardiomyocytes and fibroblasts is well-established in vitro

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Whether such hetero-cellular coupling exists in vivo has been a matter of debate

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We review the development of experimental and conceptual insight into the topic

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Conclusion 1: hetero-cellular coupling in heart tissue has been shown in principle

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Conclusion 2: extent, regulation, context, and relevance remain to be established

Toward GPGPU accelerated human electromechanical cardiac simulations

In this paper, we look at the acceleration of weakly coupled electromechanics using the graphics processing unit (GPU). Specifically, we port to the GPU a number of components of CHeart--a CPU-based finite element code developed for simulating multi-physics problems. On the basis of a criterion of computational cost, we implemented on the GPU the ODE and PDE solution steps for the electrophysiology problem and the Jacobian and residual evaluation for the mechanics problem. Performance of the GPU implementation is then compared with single core CPU (SC) execution as well as multi-core CPU (MC) computations with equivalent theoretical performance. Results show that for a human scale left ventricle mesh, GPU acceleration of the electrophysiology problem provided speedups of 164 × compared with SC and 5.5 times compared with MC for the solution of the ODE model. Speedup of up to 72 × compared with SC and 2.6 × compared with MC was also observed for the PDE solve. Using the same human geometry, the GPU implementation of mechanics residual/Jacobian computation provided speedups of up to 44 × compared with SC and 2.0 × compared with MC.

Perfusion territories subtended by penetrating coronary arteries increase in size and decrease in number toward the subendocardium

Blood flow distribution within the myocardium and the location and extent of areas at risk in case of coronary artery disease are dependent on the distribution and morphology of intramural vascular crowns. Knowledge of the intramural vasculature is essential in novel multiscale and multiphysics modeling of the heart. For this study, eight canine hearts were analyzed with an imaging cryomicrotome, developed to acquire high-resolution spatial data on three-dimensional vascular structures. The obtained vasculature was skeletonized, and for each penetrating artery starting from the epicardium, the dependent vascular crown was defined. Three-dimensional Voronoi tessellation was applied with the end points of the terminal segments as center points. The centroid of end points in each branch allowed classification of the corresponding perfusion territories in subendocardial, midmyocardial, and subepicardial. Subendocardial regions have relatively few territories of about 0.5 ml in volume having their own penetrating artery at the epicardium, whereas the subepicardium is perfused by a multitude of small perfusion territories, in the order of 0.01 ml. Vascular volume density of small arteries up till 400 μm was 3.2% at the subendocardium territories but only 0.8% in the subepicardium territories. Their higher volume density corresponds to compensation for flow impeding forces by cardiac contraction. These density differences result in different scaling law properties of vascular volume and tissue mass per territory type. This novel three-dimensional quantitative analysis may form the basis for patient-specific computational models on coronary perfusion and aid the interpretation of image-based clinical methods for assessing the transmural perfusion distribution.

Outcomes of myocardial infarction hydrogel injection therapy in the human left ventricle dependent on injectate distribution

Myocardial infarction therapies involving biomaterial injections have shown benefits in inhibiting progression towards heart failure. However, the underlying mechanisms remain unclear. A finite element model of the human left ventricle was developed from magnetic resonance images. An anteroapical infarct was represented at acute (AI) and fibrotic (FI) stage. Hydrogel injections in the infarct region were modelled with layered (L) and bulk (B) distribution. In the FI, injectates reduced end-systolic myofibre stresses from 291.6% to 117.6% (FI-L) and 115.3% (FI-B) of the healthy value, whereas all AI models exhibited sub-healthy stress levels (AI: 90.9%, AI-L: 20.9%, AI-B: 30.5%). Reduction in end-diastolic infarct stress were less pronounced for both FI (FI: 294.1%, FI-L: 176.5%, FI-B: 188.2%) and AI (AI: 94.1%, AI-L: 35.3%, AI-B: 41.2%). In the border zone, injectates reduced end-systolic fibre stress by 8-10% and strain from positive (AI) and zero (FI) to negative. Layered and bulk injectates increased ejection fraction by 7.4% and 8.4% in AI and 14.1% and 13.7% in FI. The layered injectate had a greater impact on infarct stress and strain at acute stage, whereas the bulk injectate exhibited greater benefits at FI stage. These findings were confirmed by our previous in vivo results.

Combining wet and dry research: experience with model development for cardiac mechano-electric structure-function studies

Since the development of the first mathematical cardiac cell model 50 years ago, computational modelling has become an increasingly powerful tool for the analysis of data and for the integration of information related to complex cardiac behaviour. Current models build on decades of iteration between experiment and theory, representing a collective understanding of cardiac function. All models, whether computational, experimental, or conceptual, are simplified representations of reality and, like tools in a toolbox, suitable for specific applications. Their range of applicability can be explored (and expanded) by iterative combination of 'wet' and 'dry' investigation, where experimental or clinical data are used to first build and then validate computational models (allowing integration of previous findings, quantitative assessment of conceptual models, and projection across relevant spatial and temporal scales), while computational simulations are utilized for plausibility assessment, hypotheses-generation, and prediction (thereby defining further experimental research targets). When implemented effectively, this combined wet/dry research approach can support the development of a more complete and cohesive understanding of integrated biological function. This review illustrates the utility of such an approach, based on recent examples of multi-scale studies of cardiac structure and mechano-electric function.

Benchmarking electrophysiological models of human atrial myocytes

Mathematical modeling of cardiac electrophysiology is an insightful method to investigate the underlying mechanisms responsible for arrhythmias such as atrial fibrillation (AF). In past years, five models of human atrial electrophysiology with different formulations of ionic currents, and consequently diverging properties, have been published. The aim of this work is to give an overview of strengths and weaknesses of these models depending on the purpose and the general requirements of simulations. Therefore, these models were systematically benchmarked with respect to general mathematical properties and their ability to reproduce certain electrophysiological phenomena, such as action potential (AP) alternans. To assess the models' ability to replicate modified properties of human myocytes and tissue in cardiac disease, electrical remodeling in chronic atrial fibrillation (cAF) was chosen as test case. The healthy and remodeled model variants were compared with experimental results in single-cell, 1D and 2D tissue simulations to investigate AP and restitution properties, as well as the initiation of reentrant circuits.

3D Imaging of vascular networks for biophysical modeling of perfusion distribution within the heart

One of the main determinants of perfusion distribution within an organ is the structure of its vascular network. Past studies were based on angiography or corrosion casting and lacked quantitative three dimensional, 3D, representation. Based on branching rules and other properties derived from such imaging, 3D vascular tree models were generated which were rather useful for generating and testing hypotheses on perfusion distribution in organs. Progress in advanced computational models for prediction of perfusion distribution has raised the need for more realistic representations of vascular trees with higher resolution. This paper presents an overview of the different methods developed over time for imaging and modeling the structure of vascular networks and perfusion distribution, with a focus on the heart. The strengths and limitations of these different techniques are discussed. Episcopic fluorescent imaging using a cryomicrotome is presently being developed in different laboratories. This technique is discussed in more detail, since it provides high-resolution 3D structural information that is important for the development and validation of biophysical models but also for studying the adaptations of vascular networks to diseases. An added advantage of this method being is the ability to measure local tissue perfusion. Clinically, indices for patient-specific coronary stenosis evaluation derived from vascular networks have been proposed and high-resolution noninvasive methods for perfusion distribution are in development. All these techniques depend on a proper representation of the relevant vascular network structures.