Wouter Huberts

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.

A benchmark study of numerical schemes for one-dimensional arterial blood flow modelling

Haemodynamical simulations using one-dimensional (1D) computational models exhibit many of the features of the systemic circulation under normal and diseased conditions. Recent interest in verifying 1D numerical schemes has led to the development of alternative experimental setups and the use of three-dimensional numerical models to acquire data not easily measured in vivo. In most studies to date, only one particular 1D scheme is tested. In this paper, we present a systematic comparison of six commonly used numerical schemes for 1D blood flow modelling: discontinuous Galerkin, locally conservative Galerkin, Galerkin least-squares finite element method, finite volume method, finite difference MacCormack method and a simplified trapezium rule method. Comparisons are made in a series of six benchmark test cases with an increasing degree of complexity. The accuracy of the numerical schemes is assessed by comparison with theoretical results, three-dimensional numerical data in compatible domains with distensible walls or experimental data in a network of silicone tubes. Results show a good agreement among all numerical schemes and their ability to capture the main features of pressure, flow and area waveforms in large arteries. All the information used in this study, including the input data for all benchmark cases, experimental data where available and numerical solutions for each scheme, is made publicly available online, providing a comprehensive reference data set to support the development of 1D models and numerical schemes.

Experimental validation of a pulse wave propagation model for predicting hemodynamics after vascular access surgery

Hemodialysis patients require a vascular access that is, preferably, surgically created by connecting an artery and vein in the arm, i.e. an arteriovenous fistula (AVF). The site for AVF creation is chosen by the surgeon based on preoperative diagnostics, but AVFs are still compromised by flow-associated complications. Previously, it was shown that a computational 1D-model is able to describe pressure and flow after AVF surgery. However, predicted flows differed from measurements in 4/10 patients. Differences can be attributed to inaccuracies in Doppler measurements and input data, to neglecting physiological mechanisms or to an incomplete physical description of the pulse wave propagation after AVF surgery. The physical description can be checked by validating against an experimental setup consisting of silicone tubes mimicking the aorta and arm vasculature both before and after AVF surgery, which is the aim of the current study. In such an analysis, the output uncertainty resulting from measurement uncertainty in model input should be quantified. The computational model was fed by geometrical and mechanical properties collected from the setup. Pressure and flow waveforms were simulated and compared with experimental waveforms. The precision of the simulations was determined by performing a Monte Carlo study. It was concluded that the computational model was able to simulate mean pressures and flows accurately, whereas simulated waveforms were less attenuated than experimental ones, likely resulting from neglecting viscoelasticity. Furthermore, it was found that in the analysis output uncertainties, resulting from input uncertainties, cannot be neglected and should thus be considered.

A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous fistula surgery. Part A: Identification of most influential model parameters

Previously, a pulse wave propagation model was developed that has potential in supporting decision-making in arteriovenous fistula (AVF) surgery for hemodialysis. To adapt the wave propagation model to personalized conditions, patient-specific input parameters should be available. In clinics, the number of measurable input parameters is limited which results in sparse datasets. In addition, patient data are compromised with uncertainty. These uncertain and incomplete input datasets will result in model output uncertainties. By means of a sensitivity analysis the propagation of input uncertainties into output uncertainty can be studied which can give directions for input measurement improvement. In this study, a computational framework has been developed to perform such a sensitivity analysis with a variance-based method and Monte Carlo simulations. The framework was used to determine the influential parameters of our pulse wave propagation model applied to AVF surgery, with respect to parameter prioritization and parameter fixing. With this we were able to determine the model parameters that have the largest influence on the predicted mean brachial flow and systolic radial artery pressure after AVF surgery. Of all 73 parameters 51 could be fixed within their measurement uncertainty interval without significantly influencing the output, while 16 parameters importantly influence the output uncertainty. Measurement accuracy improvement should thus focus on these 16 influential parameters. The most rewarding are measurement improvements of the following parameters: the mean aortic flow, the aortic windkessel resistance, the parameters associated with the smallest arterial or venous diameters of the AVF in- and outflow tract and the radial artery windkessel compliance.

Clinical study protocol for the ARCH project - Computational modeling for improvement of outcome after vascular access creation

Despite clinical guidelines and the possibility of diagnostic vascular imaging, creation and maintenance of a vascular access (VA) remains problematic: avoiding short- and long-term VA dysfunction is challenging. Although prognostic factors for VA dysfunction have been identified in previous studies, their potential interplay at a systemic level is disregarded. Consideration of multiple prognostic patient specific factors and their complex interaction using dedicated computational modeling tools might improve outcome after VA creation by enabling a better selection of VA configuration. These computational modeling tools are developed and validated in the ARCH project: a joint initiative of four medical centers and three industrial partners (FP7-ICT-224390). This paper reports the rationale behind computational modeling and presents the clinical study protocol designed for calibrating and validating these modeling tools. The clinical study is based on the pre-operative collection of structural and functional data at a vascular level, as well as a VA functional evaluation during the follow-up period. The strategy adopted to perform the study and for data collection is also described here.

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.

Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model: Applicability of the polynomial chaos expansion method for personalization of a cardiovascular pulse wave propagation model

Patient-specific modeling requires model personalization, which can be achieved in an efficient manner by parameter fixing and parameter prioritization. An efficient variance-based method is using generalized polynomial chaos expansion (gPCE), but it has not been applied in the context of model personalization, nor has it ever been compared with standard variance-based methods for models with many parameters. In this work, we apply the gPCE method to a previously reported pulse wave propagation model and compare the conclusions for model personalization with that of a reference analysis performed with Saltellis efficient Monte Carlo method. We furthermore differentiate two approaches for obtaining the expansion coefficients: one based on spectral projection (gPCE-P) and one based on least squares regression (gPCE-R). It was found that in general the gPCE yields similar conclusions as the reference analysis but at much lower cost, as long as the polynomial metamodel does not contain unnecessary high order terms. Furthermore, the gPCE-R approach generally yielded better results than gPCE-P. The weak performance of the gPCE-P can be attributed to the assessment of the expansion coefficients using the Smolyak algorithm, which might be hampered by the high number of model parameters and/or by possible non-smoothness in the output space.

Computational model for simulation of vascular adaptation following vascular access surgery in haemodialysis patients.

An important number of surgical procedures for creation of vascular access (VA) in haemodialysis patients still results in non-adequate increase in blood flow (non-maturation). The rise in blood flow in arteriovenous shunts depends on vascular remodelling. Computational tools to predict the outcome of VA surgery would be important in this clinical context. The aim of our investigation was then to develop a 0D/1D computational model of arm vasculature able to simulate vessel wall remodelling and related changes in blood flow. We assumed that blood vessel remodelling is driven by peak wall shear stress. The model was calibrated with previously reported values of radial artery diameter and blood flow after end-to-end distal fistula creation. Good agreement was obtained between predicted changes in VA flow and in arterial diameter after surgery and corresponding measured values. The use of this computational model may allow accurate vascular surgery planning and ameliorate VA surgery outcomes.

A guide to uncertainty quantification and sensitivity analysis for cardiovascular applications

As we shift from population-based medicine towards a more precise patient-specific regime guided by predictions of verified and well-established cardiovascular models, an urgent question arises: how sensitive are the model predictions to errors and uncertainties in the model inputs? To make our models suitable for clinical decision-making, precise knowledge of prediction reliability is of paramount importance. Efficient and practical methods for uncertainty quantification (UQ) and sensitivity analysis (SA) are therefore essential. In this work, we explain the concepts of global UQ and global, variance-based SA along with two often-used methods that are applicable to any model without requiring model implementation changes: Monte Carlo (MC) and polynomial chaos (PC). Furthermore, we propose a guide for UQ and SA according to a six-step procedure and demonstrate it for two clinically relevant cardiovascular models: model-based estimation of the fractional flow reserve (FFR) and model-based estimation of the total arterial compliance (CT ). Both MC and PC produce identical results and may be used interchangeably to identify most significant model inputs with respect to uncertainty in model predictions of FFR and CT . However, PC is more cost-efficient as it requires an order of magnitude fewer model evaluations than MC. Additionally, we demonstrate that targeted reduction of uncertainty in the most significant model inputs reduces the uncertainty in the model predictions efficiently. In conclusion, this article offers a practical guide to UQ and SA to help move the clinical application of mathematical models forward. Copyright