Frans van de Vosse

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  Personalization of 1D Wave Propagation Models of the Cardiovascular System
  Frans van de Vosse

  One of the main di?culties in the translation of mathematical models to the clinic for supporting clinical decision-making is assessing patient-speci?c values for the model parameters, the boundary and the initial conditions. Measurement modalities or data are not always available for all model parameters. In addition, the precision and accuracy of clinical measurements are hampered by large (biological) variations. Consequently, a balance is needed between the uncertainty resulting from model input parameters and the uncertainty resulting from model assumptions. For this, it is essential to quantify the uncertainty resulting from model input and to determine whether the complexity of the model is su?cient for the application of interest.

  
  

  The aim of this study is to investigate model personalization (parameter ?xing and prioritization), model output uncertainty, and the number of runs required to reach convergence of their sensitivity estimates (i.e. computational cost) in case of a 1D pulse wave propagation model that was developed to support vascular access surgery planning [1].

  
  

  The most common and straightforward method is to use crude Monte Carlo simulations in which the model is executed multiple times to estimate the sensitivity indices. This method, however, requires a lot of computational e?ort. Saltelli et al. [2] introduced a method that is computationally less demanding. This makes the method better applicable to computational expensive models or models with many model parameters. However, large computing resources are still required when applying the method to models with many model parameters. Finally, the method of Morris [3] is a global sensitivity analysis that is able to identify the few important model parameters among the many model parameters in the model with a relatively small number of model evaluations.

  
  

  Our specific aim was to investigate whether model personalization could be performed by ?rst applying the Morris screening method that identi?es the non-important parameters and subsequently applying the Saltelli method to the resulting subset of important parameters. As this is expected to reduce the computational cost of the uncertainty and sensitivity analysis, this might improve clinical applicability. In addition the uncertainty of the model outputs was quantified using the same data that was generated for the sensitivity analysis.

  
  

  The Saltelli method, which in general requires many model runs, is found to be a robust method for model personalization. Screening for the important parameters using the Morris method is found to work well for the complex cardiovascular wave propagation model for vascular access. The Morris method can therefore be used for parameter ?xing. However, it does not o?er any information in the setting of parameter prioritization, i.e. in identifying which parameters are most rewarding to measure as accurately as possible. The subsets of important parameters identi?ed for the output of interest lead to a significant complexity reduction.

  
  

  We conclude that for model personalization of complex models it is advised to perform a screening for the important parameters using the method of Morris ?rst, and then perform a variance-based sensitivity analysis on the subset with only important parameters. For this purpose a Saltelli method can be used. Alternative and more computationally e?cient estimation methods not presented in this study are stochastic collocation methods based on polynomial chaos expansion.

  
  

  [1]W. Huberts, C de Jonge, W.P.M. van der Linden, M.A Inda, J.H.M. Tordoir, F.N. van de Vosse, and E.M.H. Bosboom. A sensitivity analysis of a personalized pulse wave propagation model for arteriovenous ?stula surgery. Part A: Identi?cation of most in?uential model parameters. Med Eng Phys., 35(6):810–26, 2013.

  
  

  [2]A. Saltelli. Making best use of model evaluations to compute sensitivity indices. Comp Phys Comm, 145:280–297, 2002.

  
  

  [3]M.D. Morris. Factorial sampling plans for preliminary computational experiments. Technometrics, 33(2):161–174, 1991.