I am working on a cardiovascular model that uses circuit diagram as an approximation and this is the circuit of a bifurcation but I got troubles determining the voltage on the capacitors and the current through the branches.
I got a following diagram where the parameter of the elements are known and a time-varying input current is defined
After I applied the KVL, I end up with the following differential equations:
$$\frac{di_2}{dt}=-\frac{(R_2+R_3)}{L_2} i_2-\frac{V_{C1}}{L_2}-\frac{R_1}{L_2} i_1 - \frac{L_1}{L_2} \frac{di_1}{dt} + V_I$$ $$\frac{dV_{C1}}{dt} = \frac{i_2}{C_1} - \frac{V_{C1}}{C_1 R_4}$$ $$\frac{di_3}{dt}=-\frac{(R_5+R_6)}{L_3} i_3-\frac{V_{C2}}{L_3}-\frac{R_1}{L_3} i_1 - \frac{L_1}{L_3} \frac{di_1}{dt} + V_I$$ $$\frac{dV_{C2}}{dt} = \frac{i_3}{C_2} - \frac{V_{C2}}{C_2 R_7}$$
where \$i_2\$ and \$i_3\$ are currents on the branches, \$V_I\$ is the voltage on the source. However that's where I am stuck and don't know how to proceed as I am a bit confused about the \$V_I\$ term how to determine it.
Am I missing anything information or did I forgot a step? Thank you very much for help.