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Cerebrospinal fluid (CSF) dynamics
I have been working with the Brain Physics Lab at the University of Cambridge on a computational project to optimize the mathematical model of cerebrospinal fluid (CSF) dynamics and improve diagnostics for CSF disorders.
Our team analyzes CSF infusion studies using mathematical modeling to estimate diagnostic parameters such as reference intracranial pressure (ICP), CSF formation rate, resistance to CSF outflow and brain elastance coefficient. We use an analytical solution to the non-linear differential equation describing the Marmarou model and optimize the parameters. However, this process can produce estimated values that fall outside of physiologically acceptable ranges due to local minima.
To address this, we propose an improvement to the gradient descent methods used in ICM+ by utilizing advanced optimization techniques, ensuring that the results fall within physiologically acceptable ranges.
Furthermore, we have developed a Bayesian method to more accurately estimate diagnostic parameters. The method uses Bayesian statistics to combine prior knowledge with new observations and provides uncertainty estimates on the optimized parameter values. Information about the level of uncertainty is crucial when making clinical decisions and offers a more robust and informative way to model data, providing more accurate predictions.
In addition, the uncertainty predictions of the new method can be applied in the design and interpretation of future clinical studies, allowing for more accurate predictions by considering variations in parameters. Overall, this new Bayesian method is a powerful tool that provides more accurate diagnostic parameter estimates with uncertainty predictions, aiding in the diagnosis of CSF disorders and informed clinical decisions.
The figure illustrates an output of our model when applied to data on intracranial pressure. One major benefit of the method we developed is that it gives us estimates of uncertainty for the optimized parameter values.
