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Estimating Liver Function: A Model-Based Approach

The use of liver-specific contrast agents in combination with magnetic resonance imaging (MRI) has recently emerged as a non-invasive approach to assess liver function. Here, we create a pharmacokinetic model to describe the distribution and transfer rates of contrast agent between different parts of the body. Using MRI data, the model is then calibrated to investigate the quantitative difference between a non-diseased population and diseased patients suffering from liver fibrosis stage 4.

Create Compartmental Biological Models

Create a compartmental model with custom-designed components that describe the pharmacokinetics of the contrast agent.

Perform Monte Carlo simulations

Use Mathematica to define probability distributions corresponding to non-diseased and diseased parameters for contrast-agent uptake in the liver.

Dynamically visualize contrast agent fluxes

Use dynamic diagrams to visualize the comparative amounts of contrast agent flowing between the different compartments.

Watch the Video

Optimized model parameters, describing the different transfer rates between compartments, are obtained by fitting the model to MRI data.
The probability distributions show that the liver's uptake rate of contrast agent is lower for a person suffering from liver fibrosis. Moreover, the rate by which the contrast agent is transported back to the blood plasma is somewhat higher.
The plot shows the means and standard deviations, as well as the individual trajectories, obtained from multiple simulations of the two populations. Patients suffering from fibrosis will have a significantly lower concentration of contrast agent in the liver during the course of the examination.
Dynamic diagrams are a useful feature to visualize model dynamics. Notice how the red arrows between the compartments change direction and thickness to indicate in which direction the contrast agent is currently flowing and in which quantities. Note also how the flow of contrast agent to the liver is lower in the diseased scenario.

Programmatically control simulations

Use WSMSimulate to simulate multiple parameter samples from the non-diseased and diseased populations and compare the contrast agent concentrations in the liver.

M. F. Forsgren, L. Dahlqvist, N. Dahlström, et al., "Physiologically Realistic and Validated Mathematical Liver Model Revels Hepatobiliary Transfer Rates for Gd-EOB-DTPA Using Human DCE-MRI Data," PLOS ONE [online], 9(4), 2014 e95700.