Verification of Patch2022

In order to verify the Patch2022, a clamp experiment was designed by connecting the Patch2022 object to a PreAfterloadExperiment object. The PreAfterloadExperiment object calculates tension and length based on the stress in the patch. The state variables, \(l_{si}\) and \(C\), are verified separately to facilitate the analytical solution of ordinary differential equations. These tests are also part of the unit tests. All ordinary differential equations can be found in the Patch2022 description section.

Code Verification of the State Variable \(l_{si}\)

The time derivative of the state variable \(l_{si}\) is given by

\[\frac{dl_{si}}{dt} = v_{max} \cdot \left(\frac{l_s - l_{si}}{l_{se0}} - 1 \right)\]

In this benchmark model, the sarcomere length is kept constant. Following this assumption, the analytical solution is as follows:

\[l_{si}(t) = l_s - l_{se0} + \left(l_{si, t=0} - l_s + l_{se0}\right) \cdot e^{-v_{max} \cdot t / l_{se0} }\]

The mean squared error of the numerical solution is depicted in the figure below.

(Source code, png, hires.png, pdf)

Verification of the State Variable \(C\)

The verification of state variable \(C\) has been combined with the verification of the Chamber2022 and Bag, and can be found on this page.