ODE Parameter Estimation Using Optimization

MATLAB tool for estimating unknown parameters in ODE models using optimization with known time-varying inputs.

Why We Made This Code

This MATLAB code estimates the parameters of a three-element Windkessel (WK3) model from an input flow waveform by solving the governing ODE and performing optimization.

The code was originally developed as part of the following paper:

A fast approach to estimating Windkessel model parameters for patient-specific multi-scale CFD simulations of aortic flow

https://www.sciencedirect.com/science/article/abs/pii/S0045793023001196

In that work, this code provides a fast approach for identifying Windkessel parameters so that the resulting pressure waveform satisfies prescribed physiological targets (e.g., systolic and diastolic pressure).

Quick Start

1. Prepare input data

Place your waveform in `flowrate.csv` with

- Column 1 — time

- Column 2 — flow rate

2. Run the MATLAB script

Open MATLAB in this folder and run `windkessel_model_parameters_estimation`

3. Check outputs

The script

- estimates the Windkessel parameters

- prints the optimized parameters in MATLAB

- generates the reconstructed pressure waveform

General Idea Behind the Code

Although this code was originally developed for Windkessel parameter estimation, the underlying idea can be generalized to many modeling and simulation problems.

The framework can be used when:

- a governing ODE is known

- some coefficients (parameters) are unknown

- a time-varying input waveform is available

- the goal is to determine the unknown parameters so that the resulting output waveform satisfies certain desired properties

For example, the objective may require the output waveform to match

- specific maximum and minimum values

- a desired amplitude

- other waveform characteristics defined through an objective function

In such cases, the workflow becomes:

1. define the governing ODE

2. provide an input waveform

3. define an objective function describing the desired waveform properties

4. use optimization to identify the unknown parameters

To apply this framework to other problems, users mainly need to modify

- the input waveform

- the ODE definition

- the objective function

Acknowledgment

Many thanks to my Ph.D. advisor Dr. Wenbin Mao, who mentored me during the development of this code.

The original framework was implemented during our research work, and I later learned from it and extended parts of the code.

More Information

More detailed explanation, background, and documentation can be found on my project page:

https://zongze-li-pon.github.io/completed-projects/2023-06-15-windkessel-parameter-estimation-matlab-code/

The methodology used in this implementation is described in the paper:

A fast approach to estimating Windkessel model parameters for patient-specific multi-scale CFD simulations of aortic flow

https://www.sciencedirect.com/science/article/abs/pii/S0045793023001196