Add time-varying resistance coronary RCRCR boundary condition

[mrp089]

Problem

The resistance of the coronary arteries varies strongly during cardiac contraction

From Young et al., J Biomech (2025)

Solution

Young et al., J Biomech (2025) proposes a time-varying resistance model that's related to the time-varying elastance model for cardiac chambers. It follows the established RCRCR model for coronary arteries (Kim et al.), but with a variable microvascular resistance:

$$ R_{\text{micro}}(t) = \left[ \left( \sqrt{R_{\text{micro,max}}} - \sqrt{R_{\text{micro,min}}} \right) e(t) + \sqrt{R_{\text{micro,min}}} \right]^2 $$

with

$$ \begin{align*} e(t) = \begin{cases} \dfrac{1}{2}\left[ 1 - \cos\left( \pi \dfrac{t}{T_{vc}} \right) \right], & 0 \le t \le T_{vc}, \\ \dfrac{1}{2}\left[ 1 + \cos\left( \pi \dfrac{t - T_{vc}}{T_{vr}} \right) \right], & T_{vc} < t \le T_{vc} + T_{vr}, \\ 0, & T_{vc} + T_{vr} < t \le T. \end{cases} \end{align*} $$

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