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.
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.
ObjectivesThe 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).BackgroundLV endocardial pacing may offer benefit over conventional CRT in ischemic patients.MethodsWe performed cardiac magnetic resonance, invasive electroanatomic mapping (EAM), and measured the acute hemodynamic response (AHR) in patients with existing CRT systems.ResultsIn 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.ConclusionsIn 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.
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