Eoin R. Hyde

A novel porous mechanical framework for modelling the interaction between coronary perfusion and myocardial mechanics

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.

A computationally efficient framework for the simulation of cardiac perfusion using a multi‐compartment Darcy porous‐media flow model

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.

Mechanistic insights into the benefits of multisite pacing in cardiac resynchronization therapy: The importance of electrical substrate and rate of left ventricular activation.

BACKGROUNDnMultisite pacing (MSP) of the left ventricle is proposed as an alternative to conventional single-site LV pacing in cardiac resynchronization therapy (CRT). Reports on the benefits of MSP have been conflicting. A paradigm whereby not all patients derive benefit from MSP is emerging.nnnOBJECTIVEnWe sought to compare the hemodynamic and electrical effects of MSP with the aim of identifying a subgroup of patients more likely to derive benefit from MSP.nnnMETHODSnSixteen patients with implanted CRT systems incorporating a quadripolar LV pacing lead were studied. Invasive hemodynamic and electroanatomic assessment was performed during the following rhythms: baseline (non-CRT); biventricular (BIV) pacing delivered via the implanted CRT system (BIV(implanted)); BIV pacing delivered via an alternative temporary LV lead (BIV(alternative)); dual-vein MSP delivered via 2 LV leads; MultiPoint Pacing delivered via 2 vectors of the quadripolar LV lead.nnnRESULTSnSeven patients had an acute hemodynamic response (AHR) of <10% over baseline rhythm with BIV(implanted) and were deemed nonresponders. AHR in responders vs nonresponders was 21.4% ± 10.4% vs 2.0% ± 5.2% (P < .001). In responders, neither form of MSP provided incremental hemodynamic benefit over BIV(implanted). Dual-vein MSP (8.8% ± 5.7%; P = .036 vs BIV(implanted)) and MultiPoint Pacing (10.0% ± 12.2%; P = .064 vs BIV(implanted)) both improved AHR in nonresponders. Seven of 9 responders to BIV(implanted) had LV endocardial activation characterized by a functional line of block during intrinsic rhythm that was abolished with BIV pacing. All these patients met strict criteria for left bundle branch block (LBBB). No nonresponders exhibited this line of block or met strict criteria for LBBB.nnnCONCLUSIONnPatients not meeting strict criteria for LBBB appear most likely to derive benefit from MSP.

Beneficial Effect on Cardiac Resynchronization From Left Ventricular Endocardial Pacing Is Mediated by Early Access to High Conduction Velocity Tissue: Electrophysiological Simulation Study

Background—Cardiac resynchronization therapy (CRT) delivered via left ventricular (LV) endocardial pacing (ENDO-CRT) is associated with improved acute hemodynamic response compared with LV epicardial pacing (EPI-CRT). The role of cardiac anatomy and physiology in this improved response remains controversial. We used computational electrophysiological models to quantify the role of cardiac geometry, tissue anisotropy, and the presence of fast endocardial conduction on myocardial activation during ENDO-CRT and EPI-CRT. Methods and Results—Cardiac activation was simulated using the monodomain tissue excitation model in 2-dimensional (2D) canine and human and 3D canine biventricular models. The latest activation times (LATs) for LV endocardial and biventricular epicardial tissue were calculated (LVLAT and TLAT), as well the percentage decrease in LATs for endocardial (en) versus epicardial (ep) LV pacing (defined as %dLV=100×(LVLATep−LVLATen)/LVLATep and %dT=100×(TLATep−TLATen)/TLATep, respectively). Normal canine cardiac anatomy is responsible for %dLV and %dT values of 7.4% and 5.5%, respectively. Concentric and eccentric remodeled anatomies resulted in %dT values of 15.6% and 1.3%, respectively. The 3D biventricular-paced canine model resulted in %dLV and %dT values of −7.1% and 1.5%, in contrast to the experimental observations of 16% and 11%, respectively. Adding fast endocardial conduction to this model altered %dLV and %dT to 13.1% and 10.1%, respectively. Conclusions—Our results provide a physiological explanation for improved response to ENDO-CRT. We predict that patients with viable fast-conducting endocardial tissue or distal Purkinje network or both, as well as concentric remodeling, are more likely to benefit from reduced ATs and increased synchrony arising from endocardial pacing.

Optimized Left Ventricular Endocardial Stimulation Is Superior to Optimized Epicardial Stimulation in Ischemic Patients With Poor Response to Cardiac Resynchronization Therapy: A Combined Magnetic Resonance Imaging, Electroanatomic Contact Mapping, and Hemodynamic Study to Target Endocardial Lead Placement

Objectives The purpose of this study was to identify the optimal pacing site for the left ventricular (LV) lead in ischemic patients with poor response to cardiac resynchronization therapy (CRT). Background LV endocardial pacing may offer benefit over conventional CRT in ischemic patients. Methods We performed cardiac magnetic resonance, invasive electroanatomic mapping (EAM), and measured the acute hemodynamic response (AHR) in patients with existing CRT systems. Results In all, 135 epicardial and endocardial pacing sites were tested in 8 patients. Endocardial pacing was superior to epicardial pacing with respect to mean AHR (% change in dP/dtmax vs. baseline) (11.81 [-7.2 to 44.6] vs. 6.55 [-11.0 to 19.7]; p = 0.025). This was associated with a similar first ventricular depolarization (Q-LV) (75 ms [13 to 161 ms] vs. 75 ms [25 to 129 ms]; p = 0.354), shorter stimulation–QRS duration (15 ms [7 to 43 ms] vs. 19 ms [5 to 66 ms]; p = 0.010) and shorter paced QRS duration (149 ms [95 to 218 ms] vs. 171 ms [120 to 235 ms]; p < 0.001). The mean best achievable AHR was higher with endocardial pacing (25.64 ± 14.74% vs. 12.64 ± 6.76%; p = 0.044). Furthermore, AHR was significantly greater pacing the same site endocardially versus epicardially (15.2 ± 10.7% vs. 7.6 ± 6.3%; p = 0.014) with a shorter paced QRS duration (137 ± 22 ms vs. 166 ± 30 ms; p < 0.001) despite a similar Q-LV (70 ± 38 ms vs. 79 ± 34 ms; p = 0.512). Lack of capture due to areas of scar (corroborated by EAM and cardiac magnetic resonance) was associated with a poor AHR. Conclusions In ischemic patients with poor CRT response, biventricular endocardial pacing is superior to epicardial pacing. This may reflect accessibility to sites that cannot be reached via coronary sinus anatomy and/or by access to more rapidly conducting tissue. Furthermore, guidance to the optimal LV pacing site may be aided by modalities such as cardiac magnetic resonance to target delayed activating sites while avoiding scar.

Multi-Scale Parameterisation of a Myocardial Perfusion Model Using Whole-Organ Arterial Networks

A method to extract myocardial coronary permeabilities appropriate to parameterise a continuum porous perfusion model using the underlying anatomical vascular network is developed. Canine and porcine whole-heart discrete arterial models were extracted from high-resolution cryomicrotome vessel image stacks. Five parameterisation methods were considered that are primarily distinguished by the level of anatomical data used in the definition of the permeability and pressure-coupling fields. Continuum multi-compartment porous perfusion model pressure results derived using these parameterisation methods were compared quantitatively via a root-mean-square metric to the Poiseuille pressure solved on the discrete arterial vasculature. The use of anatomical detail to parameterise the porous medium significantly improved the continuum pressure results. The majority of this improvement was attributed to the use of anatomically-derived pressure-coupling fields. It was found that the best results were most reliably obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. This paper presents the first continuum perfusion model where all parameters were derived from the underlying anatomical vascular network.

Parameterisation of multi-scale continuum perfusion models from discrete vascular networks

Experimental data and advanced imaging techniques are increasingly enabling the extraction of detailed vascular anatomy from biological tissues. Incorporation of anatomical data within perfusion models is non-trivial, due to heterogeneous vessel density and disparate radii scales. Furthermore, previous idealised networks have assumed a spatially repeating motif or periodic canonical cell, thereby allowing for a flow solution via homogenisation. However, such periodicity is not observed throughout anatomical networks. In this study, we apply various spatial averaging methods to discrete vascular geometries in order to parameterise a continuum model of perfusion. Specifically, a multi-compartment Darcy model was used to provide vascular scale separation for the fluid flow. Permeability tensor fields were derived from both synthetic and anatomically realistic networks using (1) porosity-scaled isotropic, (2) Huyghe and Van Campen, and (3) projected-PCA methods. The Darcy pressure fields were compared via a root-mean-square error metric to an averaged Poiseuille pressure solution over the same domain. The method of Huyghe and Van Campen performed better than the other two methods in all simulations, even for relatively coarse networks. Furthermore, inter-compartment volumetric flux fields, determined using the spatially averaged discrete flux per unit pressure difference, were shown to be accurate across a range of pressure boundary conditions. This work justifies the application of continuum flow models to characterise perfusion resulting from flow in an underlying vascular network.

A spatially-distributed computational model to quantify behaviour of contrast agents in MR perfusion imaging

Graphical abstract

Myocardial perfusion distribution and coronary arterial pressure and flow signals:clinical relevance in relation to multiscale modeling, a review

AbstractnnCoronary artery disease, CAD, is associated with both narrowing of the epicardial coronary arteries and microvascular disease, thereby limiting coronary flow and myocardial perfusion. CAD accounts for almost 2 million deaths within the European Union on an annual basis. In this paper, we review the physiological and pathophysiological processes underlying clinical decision making in coronary disease as well as the models for interpretation of the underlying physiological mechanisms. Presently, clinical decision making is based on non-invasive magnetic resonance imaging, MRI, of myocardial perfusion and invasive coronary hemodynamic measurements of coronary pressure and Doppler flow velocity signals obtained during catheterization. Within the euHeart project, several innovations have been developed and applied to improve diagnosis-based understanding of the underlying biophysical processes. Specifically, MRI perfusion data interpretation has been advanced by the gradientogram, a novel graphical representation of the spatiotemporal myocardial perfusion gradient. For hemodynamic data, functional indices of coronary stenosis severity that do not depend on maximal vasodilation are proposed and the Valsalva maneuver for indicating the extravascular resistance component of the coronary circulation has been introduced. Complementary to these advances, model innovation has been directed to the porous elastic model coupled to a one-dimensional model of the epicardial arteries. The importance of model development is related to the integration of information from different modalities, which in isolation often result in conflicting treatment recommendations.n

Multiscale modelling of cardiac perfusion

To elucidate the mechanisms governing coronary blood flow in health and disease requires an understanding of the structure—function relationship of the coronary system, which exhibits distinct characteristics over multiple scales. Given the complexities arising from the multiscale and distributed nature of the coronary system and myocardial mechanical coupling, computational modelling provides an indispensable tool for advancing our understanding. In this work, we describe our strategy for an integrative whole-organ perfusion model, and illustrate a series of examples which apply the framework within both basic science and clinical translation settings. In particular, the one-dimensional reduced approach common in vascular modelling is combined with a new poromechanical formulation of the myocardium that is capable of reproducing the full contractile cycle, to enable simulation of the dynamic coronary and myocardial blood flow. In addition, a methodology for estimating continuum porous medium parameters from discrete network geometry is presented. The benefit of this framework is first demonstrated via an application to coronary wave intensity analysis, a technique developed to study time-dependent aspects of pulse waves invasively measured in the vessels. It is shown that, given experimentally-acquired boundary conditions the 1D model is capable of reproducing a wave behaviour broadly consistent with that observed in vivo, however, its utility is limited to a phenomenological level. The integrated 1D-poromechanical model on the other hand enables a mechanistic investigation of wave generation thus allowing the influence of contractile function and distal hemodynamic states on coronary flow to be described. In addition, when coupled with the advection-diffusion-reaction equation, the integrated model can be used to study the transport of tracers through the vascular network, thus allowing the dependence of noninvasive imaging signal intensities on the diffusive properties of the contrast agent to be quantified. A systematic investigation of the commonly used clinical indices and whole-organ modelling results are illustrated. Taken together, the proposed model provides a comprehensive framework with which to apply quantitative analysis in whole organ coronary artery disease diagnosis using noninvasive perfusion imaging modalities. The added value of the model in clinical practice lies in its ability to combine comprehensive patient-specific information into therapy. In this regard, we close the chapter with a discussion on potential model-aided strategies of disease management.