Decision-making in vascular access surgery for hemodialysis can be supported by a pulse wave propagation model that is able to simulate pressure and flow changes induced by the creation of a vascular access. To personalize such a model, patient-specific input parameters should be chosen. However, the number of input parameters that can be measured in clinical routine is limited. Besides, patient data are compromised with uncertainty. Incomplete and uncertain input data will result in uncertainties in model predictions. In part A, we analyzed how the measurement uncertainty in the input propagates to the model output by means of a sensitivity analysis. Of all 73 input parameters, 16 parameters were identified to be worthwhile to measure more accurately and 51 could be fixed within their measurement uncertainty range, but these latter parameters still needed to be measured. Here, we present a methodology for assessing the model input parameters that can be taken constant and therefore do not need to be measured. In addition, a method to determine the value of this parameter is presented. For the pulse wave propagation model applied to vascular access surgery, six patient-specific datasets were analyzed and it was found that 47 out of 73 parameters can be fixed on a generic value. These model parameters are not important for personalization of the wave propagation model. Furthermore, we were able to determine a generic value for 37 of the 47 fixable model parameters.
A vascular access (VA) is required for end-stage renal disease (ESRD) patients undergoing hemodialysis therapy. The vascular access is the site at the body where blood is withdrawn to the dialyzer and returned after filtration. Preferably, a vascular access is created surgically by connecting an artery and vein in the arm, i.e. an arteriovenous fistula (AVF).
Planning the optimal location for AVF surgery by the surgeon could be improved if a quantitative measure of the postoperative vascular access flow (brachial artery inflow) and of the postoperative systolic pressure distal to the anastomosis were available before surgery [1], [2] and [3]. Therefore, we developed a distributed lumped parameter pulse wave propagation model that can make an individualized prediction of the postoperative mean brachial flow and the systolic pressure distal to the anastomosis [4].
To use distributed wave propagation models in individualized treatment planning, model input parameters should be adapted to patient-specific conditions and therefore measurements on patients are needed. However, in clinical practice, measurements are associated with relatively large measurement uncertainties compared to in vitro measurements resulting from restrictions in measurement time, limited facilities and available modalities. These inaccurate and incomplete datasets will result in output uncertainties and, therefore, insight into the propagation of measurement uncertainties to output uncertainty is needed. To this end, a global sensitivity analysis can be applied [5], [6] and [7]. The insight obtained by such a global sensitivity analysis can be used to determine the model parameters that are most rewarding to measure more accurately, as accurate measurements of these parameters will result in the largest reduction in the uncertainty of the predicted mean brachial flow and distal systolic pressure (parameter prioritization). Moreover, the global sensitivity analysis can be used to determine model parameters that can be fixed onto a constant value (parameter fixing), because they do not significantly influence the output uncertainty. Therefore in part A [8], we set-up a framework and used this to execute a variance-based sensitivity analysis on our wave propagation model. Parameters were varied within their measurement uncertainty and in this way we determined which model parameters should be measured more accurately to reduce the uncertainty in the prediction of mean brachial flow and distal systolic pressure (parameter prioritization), and which parameters could be fixed within their measurement uncertainty domain. We found that improving measurements was only rewarding for 16 out of 73 model parameters, whereas 51 parameters could be fixed within their measurement uncertainty domain. Improving measurements of these 51 model parameters are therefore not beneficial in order to obtain a reduction in output uncertainty and, moreover, fixing these 51 parameters within their measurement uncertainty domain still means that these parameters need to be measured or estimated for each patient. In this paper (part B), we will present a methodology to identify model input parameters, for which a constant generic value can be taken. As a result, the number of required patient-specific measurements will be reduced. Parameter fixing used to reduce the number of model parameters is amongst others described by Saltelli et al. [5] and [6].
An intuitive strategy to determine which model parameters can be fixed is to first define model parameters for an average patient and, thereafter, perform a sensitivity analysis, comparable to the analysis in part A, but now while each model parameter is varied within its population uncertainty domain. However, defining parameters for an average patient is not trivial, because, to compute reliable mean values for the model parameters, a large number of patients is required. In addition, model parameters might be grouped within the complete input space, for example as a result of gender differences or because of a relation between the parameter and age or body-mass-index (BMI). Since in a sensitivity analysis all model parameters are varied within the complete population uncertainty domain, a sensitivity analysis for parameter fixing should be performed within each (sub)group to avoid non-physiological combinations of input parameters. For non-physiological parameter combinations, the model will not converge which will hamper the sensitivity analysis. Therefore, in this study we performed a sensitivity analysis by segmenting the input parameter space. For this we selected patient-specific datasets and applied the population uncertainty on each individual set. This approach reduces the chance of non-physiological input, while the relevant part of the input space is still covered.
The outline of this paper is as follows. First, we describe our distributed wave propagation model and the global sensitivity method that is used in this study. Thereafter, we describe the input parameters that are selected as possible candidates for parameter fixing and we define their uncertainty domains based on the variation within the patient population. Furthermore, the Monte Carlo experiments executed for the global sensitivity analysis are described. Finally, the parameters are discussed that can be fixed and generically chosen.
In this manuscript, we presented a self-learning approach that was able to identify 47 out of 73 model input parameters that could be fixed within their uncertainty domain. Furthermore, we found generic values for 37 of these 47 model parameters onto which the model parameters could be fixed. Our proposed methodology can be used to determine generic values for fixable model parameters as long as the applied uncertainty domains are close to the population spread. For model personalization, a sensitivity analysis is essential since the number of model parameters that needs to be measured patient-specifically can significantly be reduced.
