Mathematical Modelling of Haemodialysis by Leszek Pstras & Jacek Waniewski

Author:Leszek Pstras & Jacek Waniewski
Language: eng
Format: epub
ISBN: 9783030214104
Publisher: Springer International Publishing

2.7 Computational Implementation

The model is based on the set of 330 ordinary differential equations (describing the time changes of all state variables, i.e. the total volumes and water volumes of all 26 compartments, the number of RBCs in each blood compartment, the quantities of the 10 analysed solutes in all 26 compartments and the variables controlled by the baroreflex), circa 800 auxiliary linear or nonlinear algebraic equations and around 150 parameters (the relatively high number of equations results mainly from the repetition of the equations discussed in this chapter for all individual solutes and all compartments analysed in the model). The computer version of the model was implemented in Matlab® (The Mathworks Inc.).

All simulations are performed using the Matlab built-in solver for stiff systems of ordinary differential equations (ode15s). The absolute and relative tolerances of the ODE solver were set to 10−3, except for the sensitivity analysis, for which both the absolute and relative tolerances were set to 10−6.

The auxiliary numerical procedures for establishing the initial steady-state conditions for the healthy subject and the initial pre-dialysis steady-state conditions for the reference patient are based on minimising the sum of squared deviations from the steady-state conditions or deviations from the desired levels of certain variables in the patient before dialysis, as described in Sect. 2.5. As already mentioned, these tasks were realised using the unconstrained Matlab built-in function fminsearch, which uses the Nelder-Mead simplex direct search algorithm [174].

Table 2.12 summarises all steps involved in the proposed modelling approach divided into three stages – the definition of the model for the healthy subject, the simulation of fluid overload in the dialysis patient and the simulation of the whole HD procedure.Table 2.12Simulation steps and timing used in the proposed modelling approach

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