Recently, Dr. Yoo-Seong Jeong et al., published an article about how to compose 'slow' or 'rapid' tissue in a bottom-up approach in a minimal PBPK model in the AAPS Journal (2022a and 2022b; AAPS J).

The content of the work was also interesting, but the 'Tissue Lumping Calculator' provided as supplementary material was more interesting for me.

Usually, it is difficult to obtain an analytical solution of a differential equation for a PBPK model, so numerical solutions are handled after numerical integration. In the case of the Tissue Lumping Calculator, it doesn't use numerical integration like the Runge-Kutta method. Instead, the integration was attempted using linear algebraic theory in the absence of a nonlinear rate equation such as the Michelis-Menten equation.

It seems that the way Python's matrix library finds the inverse matrix is ​​to find an approximate value, but it was interesting for me that it shows the result as the sum of exponential functions.

It might not be very interesting to those who are good at math, but... because I'm weak at math! 😉

Tissue Lumping Calculator can be used at https://sukjae.snu.ac.kr/tlc/.