Wilco Kroon

A pulse wave propagation model to support decision-making in vascular access planning in the clinic

The preferred vascular access for hemodialysis is an autologous arteriovenous fistula (AVF) in the arm: a surgically created connection between an artery and vein. The surgeon selects the AVF location based on experience and preoperative diagnostics. However, 20-50% of all lower arm AVFs are hampered by a too low access flow, whereas complications associated with too high flows are observed in 20% of all upper arm AVFs. We hypothesize that a pulse wave propagation model fed by patient-specific data has the ability to assist the surgeon in selecting the optimal AVF configuration by predicting direct postoperative flow. Previously, a 1D wave propagation model (spectral elements) was developed in which an approximated velocity profile was assumed based on boundary layer theory. In this study, we derived a distributed lumped parameter implementation of the pulse wave propagation model. The elements of the electrical analog for a segment are based on the approximated velocity profiles and dependent on the Womersley number. We present the application of the lumped parameter pulse wave propagation model to vascular access surgery and show how a patient-specific model is able to predict the hemodynamical impact of AVF creation and might assist in vascular access planning. The lumped parameter pulse wave propagation model was able to select the same AVF configuration as an experienced surgeon in nine out of ten patients. In addition, in six out of ten patients predicted postoperative flows were in the same order of magnitude as measured postoperative flows. Future research should quantify uncertainty in model predictions and measurements.

Computational modeling of volumetric soft tissue growth: application to the cardiac left ventricle

As an initial step to investigate stimulus–response relations in growth and remodeling (G&R) of cardiac tissue, this study aims to develop a method to simulate 3D-inhomogeneous volumetric growth. Growth is regarded as a deformation that is decomposed into a plastic component which describes unconstrained growth and an elastic component to satisfy continuity of the tissue after growth. In current growth models, a single reference configuration is used that remains fixed throughout the entire growth process. However, considering continuous turnover to occur together with growth, such a fixed reference is unlikely to exist in reality. Therefore, we investigated the effect of tissue turnover on growth by incrementally updating the reference configuration. With both a fixed reference and an updated reference, strain-induced cardiac growth in magnitude of 30% could be simulated. However, with an updated reference, the amplitude of the stimulus for growth decreased over time, whereas with a fixed reference this amplitude increased. We conclude that, when modeling volumetric growth, the choice of the reference configuration is of great importance for the computed growth.

Computational analysis of the myocardial structure: Adaptation of cardiac myofiber orientations through deformation

Deformation and structure of the cardiac wall can be assessed non-invasively by imaging techniques such as magnetic resonance imaging. Understanding the (patho-)physiology that underlies the observed deformation and structure is critical for clinical diagnosis. However, much about the genesis of deformation and structure is unknown. In the present computational model study, we hypothesize that myofibers locally adapt their orientation to achieve minimal fiber-cross fiber shear strain during the cardiac cycle. This hypothesis was tested in a 3D finite element model of left ventricular (LV) mechanics by computation of tissue deformations and subsequent adaptation of initial myofiber orientations towards those in the deformed tissue. As a consequence of adaptation, local tissue peak stress, strain during ejection and stroke work density were all found to increase by at least 10%, as well as to become 50% more homogeneous throughout the wall. Global LV work (peak systolic pressure, stroke volume and stroke work) increased significantly as well (>9%). The model-predicted myofiber orientations were found to be similar to those in experiments. To the best of our knowledge the presented model is the first that is able to simultaneously predict a realistic myocardial structure as well as to account for the experimentally observed homogeneity in local mechanics.

Determinants of left ventricular shear strain

Mathematical models of cardiac mechanics can potentially be used to relate abnormal cardiac deformation, as measured noninvasively by ultrasound strain rate imaging or magnetic resonance tagging (MRT), to the underlying pathology. However, with current models, the correct prediction of wall shear strain has proven to be difficult, even for the normal healthy heart. Discrepancies between simulated and measured strains have been attributed to 1) inadequate modeling of passive tissue behavior, 2) neglecting active stress development perpendicular to the myofiber direction, or 3) neglecting crossover of myofibers in between subendocardial and subepicardial layers. In this study, we used a finite-element model of left ventricular (LV) mechanics to investigate the sensitivity of midwall circumferential-radial shear strain (E(cr)) to settings of parameters determining passive shear stiffness, cross-fiber active stress development, and transmural crossover of myofibers. Simulated time courses of midwall LV E(cr) were compared with time courses obtained in three healthy volunteers using MRT. E(cr) as measured in the volunteers during the cardiac cycle was characterized by an amplitude of approximately 0.1. In the simulations, a realistic amplitude of the E(cr) signal could be obtained by tuning either of the three model components mentioned above. However, a realistic time course of E(cr), with virtually no change of E(cr) during isovolumic contraction and a correct base-to-apex gradient of E(cr) during ejection, could only be obtained by including transmural crossover of myofibers. Thus, accounting for this crossover seems to be essential for a realistic model of LV wall mechanics.

Control of Whole Heart Geometry by Intramyocardial Mechano-Feedback: A Model Study

Geometry of the heart adapts to mechanical load, imposed by pressures and volumes of the cavities. We regarded preservation of cardiac geometry as a homeostatic control system. The control loop was simulated by a chain of models, starting with geometry of the cardiac walls, sequentially simulating circulation hemodynamics, myofiber stress and strain in the walls, transfer of mechano-sensed signals to structural changes of the myocardium, and finalized by calculation of resulting changes in cardiac wall geometry. Instead of modeling detailed mechano-transductive pathways and their interconnections, we used principles of control theory to find optimal transfer functions, representing the overall biological responses to mechanical signals. As biological responses we regarded tissue mass, extent of contractile myocyte structure and extent of the extra-cellular matrix. Mechano-structural stimulus-response characteristics were considered to be the same for atrial and ventricular tissue. Simulation of adaptation to self-generated hemodynamic load rendered physiologic geometry of all cardiac cavities automatically. Adaptation of geometry to chronic hypertension and volume load appeared also physiologic. Different combinations of mechano-sensors satisfied the condition that control of geometry is stable. Thus, we expect that for various species, evolution may have selected different solutions for mechano-adaptation.

Patient-specific modelling of cardiac electrophysiology in heart-failure patients

Aims Left-ventricular (LV) conduction disturbances are common in heart-failure patients and a left bundle-branch block (LBBB) electrocardiogram (ECG) type is often seen. The precise cause of this pattern is uncertain and is probably variable between patients, ranging from proximal interruption of the left bundle branch to diffuse distal conduction disease in the working myocardium. Using realistic numerical simulation methods and patient-tailored model anatomies, we investigated different hypotheses to explain the observed activation order on the LV endocardium, electrogram morphologies, and ECG features in two patients with heart failure and LBBB ECG. Methods and results Ventricular electrical activity was simulated using reaction–diffusion models with patient-specific anatomies. From the simulated action potentials, ECGs and cardiac electrograms were computed by solving the bidomain equation. Model parameters such as earliest activation sites, tissue conductivity, and densities of ionic currents were tuned to reproduce the measured signals. Electrocardiogram morphology and activation order could be matched simultaneously. Local electrograms matched well at some sites, but overall the measured waveforms had deeper S-waves than the simulated waveforms. Conclusion Tuning a reaction–diffusion model of the human heart to reproduce measured ECGs and electrograms is feasible and may provide insights in individual disease characteristics that cannot be obtained by other means.

Patient-Specific Computational Modeling of Upper Extremity Arteriovenous Fistula Creation: Its Feasibility to Support Clinical Decision-Making

Introduction Inadequate flow enhancement on the one hand, and excessive flow enhancement on the other hand, remain frequent complications of arteriovenous fistula (AVF) creation, and hamper hemodialysis therapy in patients with end-stage renal disease. In an effort to reduce these, a patient-specific computational model, capable of predicting postoperative flow, has been developed. The purpose of this study was to determine the accuracy of the patient-specific model and to investigate its feasibility to support decision-making in AVF surgery. Methods Patient-specific pulse wave propagation models were created for 25 patients awaiting AVF creation. Model input parameters were obtained from clinical measurements and literature. For every patient, a radiocephalic AVF, a brachiocephalic AVF, and a brachiobasilic AVF configuration were simulated and analyzed for their postoperative flow. The most distal configuration with a predicted flow between 400 and 1500 ml/min was considered the preferred location for AVF surgery. The suggestion of the model was compared to the choice of an experienced vascular surgeon. Furthermore, predicted flows were compared to measured postoperative flows. Results Taken into account the confidence interval (25th and 75th percentile interval), overlap between predicted and measured postoperative flows was observed in 70% of the patients. Differentiation between upper and lower arm configuration was similar in 76% of the patients, whereas discrimination between two upper arm AVF configurations was more difficult. In 3 patients the surgeon created an upper arm AVF, while model based predictions allowed for lower arm AVF creation, thereby preserving proximal vessels. In one patient early thrombosis in a radiocephalic AVF was observed which might have been indicated by the low predicted postoperative flow. Conclusions Postoperative flow can be predicted relatively accurately for multiple AVF configurations by using computational modeling. This model may therefore be considered a valuable additional tool in the preoperative work-up of patients awaiting AVF creation.

A numerical method of reduced complexity for simulating vascular hemodynamics using coupled 0D lumped and 1D wave propagation models.

A computational method of reduced complexity is developed for simulating vascular hemodynamics by combination of one-dimensional (1D) wave propagation models for the blood vessels with zero-dimensional (0D) lumped models for the microcirculation. Despite the reduced dimension, current algorithms used to solve the model equations and simulate pressure and flow are rather complex, thereby limiting acceptance in the medical field. This complexity mainly arises from the methods used to combine the 1D and the 0D model equations. In this paper a numerical method is presented that no longer requires additional coupling methods and enables random combinations of 1D and 0D models using pressure as only state variable. The method is applied to a vascular tree consisting of 60 major arteries in the body and the head. Simulated results are realistic. The numerical method is stable and shows good convergence.

In vivo electromechanical assessment of heart failure patients with prolonged QRS duration

BACKGROUND Combined measurement of electrical activation and mechanical dyssynchrony in heart failure (HF) patients is scarce but may contain important mechanistic and diagnostic clues. OBJECTIVE The purpose of this study was to characterize the electromechanical (EM) coupling in HF patients with prolonged QRS duration. METHODS Ten patients with QRS width >120 ms underwent left ventricular (LV) electroanatomic contact mapping using the Noga® XP system (Biosense Webster). Recorded voltages during the cardiac cycle were converted to maps of depolarization time (TD). Electrode positions were tracked and converted into maps of time-to-peak shortening (TPS) using custom-made deformation analysis software. Correlation analysis was performed between the 2 maps to quantify EM coupling. Simulations with the CircAdapt cardiovascular system model were performed to mechanistically unravel the observed relation between TD and TPS. RESULTS The delay between earliest LV electrical activation and peak shortening differed considerably between patients (TPSmin-TDmin = 360 ± 73 ms). On average, total mechanical dyssynchrony exceeded total electrical activation (ΔTPS = 177 ± 47 ms vs ΔTD = 93 ± 24 ms, P <.001), but a large interpatient variability was observed. The TD and TPS maps correlated strongly in all patients (median R = 0.87, P <.001). These correlations were similar for regions with unipolar voltages above and below 6mV (Mann-Whitney U test, P = .93). Computer simulations revealed that increased passive myocardial stiffness decreases ΔTPS relative to ΔTD and that lower contractility predominantly increases TPSmin-TDmin. CONCLUSION EM coupling in HF patients is maintained, but the relationship between TD and TPS differs strongly between patients. Intra-individual and inter-individual differences may be explained by local and global differences in passive and contractile myocardial properties.

Structure and torsion of the normal and situs inversus totalis cardiac left ventricle. I: Experimental data in humans

In 1926, the famous American pediatric cardiologist, Dr. Helen B. Taussig, observed that in situs inversus totalis (SIT) main gross anatomical structures and the deep muscle bundles of the ventricles were a mirror image of the normal structure, while the direction of the superficial muscle bundles remained unchanged (H. B. Taussig, Bull Johns Hopkins Hosp 39: 199-202, 1926). She and we wondered about the implication of this observation for left ventricular (LV) deformation in SIT. We used magnetic resonance tagging to obtain information on LV deformation, rotation, and torsion from a series of tagged images in five evenly distributed, parallel, short-axis sections of the heart of nine controls and eight persons with SIT without other structural (cardiac) defect. In the controls, during ejection, the apex rotated counterclockwise with respect to the base, when looking from the apex. Furthermore, the base-to-apex gradient in rotation (torsion) was negative and similar at all longitudinal levels of the LV. In SIT hearts, torsion was positive near the base, indicating mirrored myofiber orientations compared with the normal LV. Contrary to expectations, torsion in the apical regions of SIT LVs was as in normal ones, reflecting a normal internal myocardial architecture. The transition zone with zero torsion, found between the apex and base, suggests that the heart structure in SIT is essentially different from that in the normal heart. This provides a unique possibility to study regulatory mechanisms for myocardial fiber orientation and mechanical load, which has been dealt with in the companion paper by Kroon et al.