Table 1 Overview of the test cases setup: model configuration and comparisons. The column “Figure” lists all figure references with the corresponding plot labels (if applicable) in the column “Label”. Figure references may appear multiple times if different coupling configurations are compared within the same plot. The columns under “Model component” list the components from Fig. 1a, their corresponding operators and time formulations (if applicable) with references to the Methods section. A 
indicates that the corresponding component is active in the coupling framework, while a 
indicates it is deactivated. The notation “vs.” denotes that two variants of the same component are compared within the test case. For \({\mathscr {M}}\), 
corresponds to the rigid approach, and 
to EMUM. The steady formulation of \({\mathscr {B}}\) is used by default, except for the first two rows (indicated by *), where the time-averaged (time-avg.) one is required by the corresponding variants of \(\varvec{\theta }_\text {hemo}\) and \({\mathscr {C}}_b\). The flow rate profiles imposed on \(\Gamma _{\text {in}}\) are shown in Fig. 3b, with Q(t) used for time-avg. and \(\bar{Q}\) for steady. The column “Parameter variation” remarks which parameters are varied within a specific model component for comparison purposes. The curves for \(F_{B2}\) and \(f_{B2}\) are represented in Fig. 3e. The definitions of \(C_{bw}^D\) and \(\epsilon\) are given in (8) and (5), respectively.
