Multi-scale parameterisation of static and dynamic continuum porous perfusion models using discrete anatomical data

The aim of this thesis is to replace the intractable problem of using discrete flow models within large vascular networks with a suitably parameterised and tractable continuum perfusion model. Through this work, we directly address the hypothesis that discrete vascular data can be incorporated within continuum perfusion models via spatially-averaged parameterisation techniques. Chapter 1 reviews biological perfusion from both clinical and computational modelling perspectives, with a particular focus on myocardial perfusion. In Chapter 2, a synthetic 3D vascular network was constructed, which was controllable in terms of its size and properties. A multi-compartment static Darcy perfusion model of this discrete system was parameterised via a number of techniques. Permeabilities were derived using: (i) porosity-scaled isotropic (ϕI); (ii) Huyghe and Van Campen (HvC); and (iii) projected-PCA parameterisation methods. It was found that HvC permeabilities and pressure-coupling fields derived from the discrete data produced the best comparison to the spatially-averaged Poiseuille pressure. In Chapter 3, the construction and analysis of high-resolution anatomical arterial vascular models was undertaken. In Chapter 4, various anatomically-derived vascular networks were used to parameterise our perfusion model, including a microCT-derived rat capillary network, a single arterial subtree, and canine and porcine whole-organ arterial models. Allowing for general-connectivity (as opposed to strictly-hierarchical connectivity) yielded a significant improvement on the continuum model pressure. For the whole-organ model however, it was found that the best results were obtained by using porosity-scaled isotropic permeabilities and anatomically-derived pressure-coupling fields. It was also discovered that naturally occurring small length but relatively large radius vessels were not suitable for the HvC method. In Chapter 5, the suitability of derived parameters for use within a dynamic perfusion model was examined. It was found that the parameters derived from the original static network were adequate for application throughout the cardiac cycle. Chapter 6 presents a concluding discussion, highlighting limitations and future directions to be investigated.</p

Factors determining the magnitude of the pre-ejection leftward septal motion in left bundle branch block

AIMS: An abnormal large leftward septal motion prior to ejection is frequently observed in left bundle branch block (LBBB) patients. This motion has been proposed as a predictor of response to cardiac resynchronization therapy (CRT). Our goal was to investigate factors that influence its magnitude. METHODS AND RESULTS: Left (LVP) and right ventricular (RVP) pressures and left ventricular (LV) volume were measured in eight canines. After induction of LBBB, LVP and, hence, the transmural septal pressure (P(LV–RV) = LVP–RVP) increased more slowly (P < 0.01) during the phase when septum moved leftwards. A biventricular finite-element LBBB simulation model confirmed that the magnitude of septal leftward motion depended on reduced rise of P(LV–RV). The model showed that leftward septal motion was decreased with shorter activation delay, reduced global or right ventricular (RV) contractility, septal infarction, or when the septum was already displaced into the LV at end diastole by RV volume overload. Both experiments and simulations showed that pre-ejection septal hypercontraction occurs, in part, because the septum performs more of the work pushing blood towards the mitral valve leaflets to close them as the normal lateral wall contribution to this push is lost. CONCLUSIONS: Left bundle branch block lowers afterload against pre-ejection septal contraction, expressed as slowed rise of P(LV–RV), which is a main cause and determinant of the magnitude of leftward septal motion. The motion may be small or absent due to septal infarct, impaired global or RV contractility or RV volume overload, which should be kept in mind if this motion is to be used in evaluation of CRT response

Improvement of Right Ventricular Hemodynamics with Left Ventricular Endocardial Pacing during Cardiac Resynchronization Therapy

BACKGROUND: Cardiac resynchronization therapy (CRT) with biventricular epicardial (BV‐CS) or endocardial left ventricular (LV) stimulation (BV‐EN) improves LV hemodynamics. The effect of CRT on right ventricular function is less clear, particularly for BV‐EN. Our objective was to compare the simultaneous acute hemodynamic response (AHR) of the right and left ventricles (RV and LV) with BV‐CS and BV‐EN in order to determine the optimal mode of CRT delivery. METHODS: Nine patients with previously implanted CRT devices successfully underwent a temporary pacing study. Pressure wires measured the simultaneous AHR in both ventricles during different pacing protocols. Conventional epicardial CRT was delivered in LV‐only (LV‐CS) and BV‐CS configurations and compared with BV‐EN pacing in multiple locations using a roving decapolar catheter. RESULTS: Best BV‐EN (optimal AHR of all LV endocardial pacing sites) produced a significantly greater RV AHR compared with LV‐CS and BV‐CS pacing (P < 0.05). RV AHR had a significantly increased standard deviation compared to LV AHR (P < 0.05) with a weak correlation between RV and LV AHR (Spearman r(s) = −0.06). Compromised biventricular optimization, whereby RV AHR was increased at the expense of a smaller decrease in LV AHR, was achieved in 56% of cases, all with BV‐EN pacing. CONCLUSIONS: BV‐EN pacing produces significant increases in both LV and RV AHR, above that achievable with conventional epicardial pacing. RV AHR cannot be used as a surrogate for optimizing LV AHR; however, compromised biventricular optimization is possible. The beneficial effect of endocardial LV pacing on RV function may have important clinical benefits beyond conventional CRT

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

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

The impact of beat-to-beat variability in optimising the acute hemodynamic response in cardiac resynchronisation therapy

Background: Acute indicators of response to cardiac resynchronisation therapy (CRT) are critical for developing lead optimisation algorithms and evaluating novel multi-polar, multi-lead and endocardial pacing protocols. Accounting for beat-to-beat variability in measures of acute haemodynamic response (AHR) may help clinicians understand the link between acute measurements of cardiac function and long term clinical outcome. Methods and results: A retrospective study of invasive pressure tracings from 38 patients receiving an acute pacing and electrophysiological study was performed. 602 pacing protocols for left ventricle (LV) (n = 38), atria–ventricle (AV) (n = 9), ventricle–ventricle (VV) (n = 12) and endocardial (ENDO) (n = 8) optimisation were performed. AHR was measured as the maximal rate of LV pressure development (dP/dtMx) for each beat. The range of the 95% confidence interval (CI) of mean AHR was ~7% across all optimisation protocols compared with the reported CRT response cut off value of 10%. A single clear optimal protocol was identifiable in 61%, 22%, 25% and 50% for LV, AV, VV and ENDO optimisation cases, respectively. A level of service (LOS) optimisation that aimed to maximise the expected AHR 5th percentile, minimising variability and maximising AHR, led to distinct optimal protocols from conventional mean AHR optimisation in 34%, 78%, 67% and 12.5% of LV, AV, VV and ENDO optimisation cases, respectively. Conclusion: The beat-to-beat variation in AHR is significant in the context of CRT cut off values. A LOS optimisation offers a novel index to identify the optimal pacing site that accounts for both the mean and variation of the baseline measurement and pacing protocol

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×(LVLAT ep −LVLAT en )/LVLAT ep and %dT=100×(TLAT ep −TLAT en )/TLAT ep , 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. </jats:sec