تجزیه و تحلیل حساسیت از یک مدل پالس موج انتشار شخصی شده برای عمل جراحی فیستول شریانی وریدی. بخش A: شناسایی پارامترهای مدل تاثیرگذارترین

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.

A well-functioning vascular access is crucial for successful hemodialysis therapy. Such a vascular access is used to connect the patient's circulation to the artificial kidney and should provide the blood flow rate of 300 ml/min required for efficient treatment [1] and [2]. The best option for a vascular access is an arteriovenous fistula (AVF) in the arm, which is a surgically created permanent connection between an artery and vein [1] and [2] resulting in a five- to thirtyfold flow increase and vessel dilation and remodeling. An AVF can be created at several positions in the arm and the optimal location is preoperatively selected by a vascular surgeon. Functioning lower arm AVFs have statistically better long-term patency rates and lower complication rates than upper arm AVFs [1] and [2] and are therefore preferred. However, for a significant number of patients (up to 50%), the resulting blood flow after creation of a lower arm AVF can be too low to enable hemodialysis [3], [4] and [5]. Conversely, the blood flow in upper arm AVFs may be too high, leading to cardiac problems and/or distal hand ischemia in 20% of all upper arm AVFs [2], [3], [4] and [6]. In addition to the high blood flow, also a low systolic finger pressure after AVF creation is indicative for the development of distal ischemia [1], [2] and [4]. In previous work, a distributed lumped parameter pulse wave propagation model was presented that simulates the hemodynamical conditions directly after AVF creation [7]. In order to make personalized predictions that might assist the surgeon during vascular access planning, the model parameters were adapted to patient-specific conditions and the model was able to select the same AVF configuration (upper or lower arm) as an experienced surgeon (more than 1000 interventions) in nine out of ten patients. Furthermore, the predictions of the mean brachial flows were similar to ultrasound flow measurements in six out of ten patients [7]. Although these preliminary results were promising, to further optimize the use of this personalized pulse wave propagation model we need to be able to deal with the uncertainty in and incompleteness of input datasets obtained by clinical measurements. This uncertainty in input parameters will propagate to the pressure and flow predictions and therefore it is necessary to analyse the uncertainty in the predictions before inferences with the model can be made reliably. The knowledge of which model parameters influence output uncertainty the most can be used to determine which clinical measurements are most important for obtaining reliable predictions. Developing more accurate measurement methods for these model parameters will be most rewarding as this will result in the best improvement of the predictions (parameter prioritization). Model parameters that hardly influence the output uncertainty can be fixed within their measurement uncertainty interval (parameter fixing), and improving measurements of these parameters is not beneficial for a more reliable output (i.e. reduction in output uncertainty). To select which model parameters can be fixed and which model parameters need to be prioritized for measurement improvements, a sensitivity analysis needs to be performed [8] and [9]. A sensitivity analysis can either be local or global [8], [9], [10] and [11]. In a local sensitivity analysis, changes in the output are investigated by varying one input parameter around its initial value, while all other input parameters are kept fixed. The conclusions, therefore, only hold when the input conditions are kept around the initial state and neglect the influence of interactions between input parameters. In a global sensitivity analysis, sensitivity measures are determined while all model parameters are changed simultaneously and thus the complete input domain is sampled and interactions between model parameters are taken into account. Because the wave propagation model is nonlinear and interactions between parameters are expected, a global sensitivity analysis is the most suitable for our application. Xiu et al. [12] performed uncertainty and sensitivity analysis in a wave propagation model of a human arterial tree based on generalized polynomial chaos expansion. The uncertain model parameters were modeled as random variables directly within the governing equations, transforming them into stochastic equations. This method gives a global description of the effect of model parameter uncertainties on the output. However, the deterministic properties of the model are lost and therefore apportioning the output uncertainty to the input uncertainties is not easy. An alternative is a Monte Carlo approach, in which the input parameters are randomly varied within their uncertainty domain [8] and [9]. Leguy et al. [13] used Monte Carlo simulations to perform a global sensitivity analysis of a wave propagation model and showed that the majority of model parameters affected the output significantly. However, Leguy et al. used the Pearson correlation coefficient and the ranked Spearmann correlation coefficient as sensitivity measures [13]. These correlation coefficients can only be applied for monotonic models and do not reveal interactions between model parameters [8], [9], [14] and [11]. Variance-based methods are independent of the model's behavior with respect to linearity, monotonicity or additivity, and these methods also take into account possible interactions between parameters. Wenk et al. [15] used a variance-based method in their application of finite element stress analysis of atherosclerotic plaques. However, they only had a limited number of three input parameters. To our knowledge, variance-based methods have not yet been applied to wave propagation models which typically have 50 parameters. The aim of this study is to identify the influential and (non)-influential model parameters of our pulse wave propagation model for AVF surgery. A variance-based method and Monte Carlo simulations are used, which is considered to be the current best available practice to perform a global sensitivity analysis [8], [9] and [16]. This analysis will generate more insight into the model and into which model parameters should be determined more accurately to reduce output uncertainty. It is important to realize that the parameters to prioritize and which parameters to fix depend on the specific output parameter of interest. Here the output parameters are the mean brachial flow and systolic radial artery pressure distal to the anastomosis after AVF creation. These outputs are chosen as mean brachial flow is related to AVF short-term failure, while distal systolic pressure in the radial artery is used as measure for finger pressure, which is related to distal ischemia [1], [2] and [4]. Radial pressure is chosen as it is difficult to assess vessel diameters and lengths in the hand vasculature. In this paper, we briefly describe the distributed lumped parameter pulse wave propagation model, and, thereafter, present the variance-based global sensitivity analysis. In the description of the global sensitivity analysis, an overview of the model parameters and their uncertainty intervals are given. In addition, the computational framework to calculate the sensitivity indices is presented. Results with regard to mean brachial flow and finger pressure are presented and conclusions on how to improve the measurement protocol to obtain the most reliable model outcomes are drawn.

In summary, we developed a computational framework to perform a sensitivity analysis with a variance-based method and Monte Carlo simulations within a reasonable amount of time. The framework was used to determine which parameters of our distributed lumped parameter wave propagation model for AVF surgery are the most important for a reliable outcome. Of all 73 parameters, 16 parameters were identified which are rewarding to be measured as accurately as possible in order to reduce the uncertainty in the output predictions. The most rewarding model parameters were the aortic windkessel resistance, the mean aortic flow, the parameters associated with the smallest arterial or venous diameters of the AVF in- and outflow tract and the radial artery windkessel compliance.