Part 4 of ScienceJournalJourneys – Hi I am your SG pharmacometrician, an early career researcher here to share my expertise and learnings about everything pharmacometrics.

For any PK/PD modeler, ODEs are a staple in our models that help us to describe the dynamic processes of absorption, distribution and elimination. To a computer scientist though, ODEs are great for introducing structure into neural networks as neural ODEs, helping these models handle time series predictions much better. See https://lnkd.in/dhyBeVy3

What about the benefit of adding a neural network to our ODE structure though? Neural networks allow for more flexible model fitting for highly nonlinear dynamics. I am interested in seeing how it could benefit PD modeling, where biological response tends to be nonlinear, and therefore harder to capture when the drug’s full mechanism of action may not be well described.

The main downside is that most of these models are done in either Python or Julia, while pharmacometricians prefer to work in NONMEM. This brings us to today’s paper by DS Baram et al. https://lnkd.in/dJqB3PzH, a tutorial on how to implement neural ODEs in popular modeling softwares NONMEM and Monolix. They also compared the fitting of neural ODEs against traditional ODE fits using mean squared error (MSE), which tells you how close the model’s predictions are to the actual values. In this case, I was surprised to see that the MSE was rather similar in both neural ODE and regular ODEs as some claim neural ODEs tend to give better fits. This could be because their example data is rather clean (see Fig 4), and because this is a low dimensional neural ODE, meaning that it may not capture as many complex relationships as a high dimensional neural ODE would.

I will still be interested to try this out though, especially to see if a low dimensional neural ODE can help me to capture more complex PD relationships without being computationally too expensive, or if I should move to python to do higher dimensional analysis.

Example code is available in their supplementary material too if you are interested in trying it out.

Are you using neural ODEs in your PK/PD workflow? Comment down below!

Pic credit: Dall.E an “Ode to Neural ODE”—a fusion of neural networks, differential equations, and cosmic inspiration.