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Table 3 A: Summary of q vector element derivation in the modified nodal analysis (MNA)

From: A precision medicine framework for personalized simulation of hemodynamics in cerebrovascular disease

Type of node

Q-vector node

Q-vector incident node

A

Source

\(q_{s} = - P_{0} \cdot \sum {G_{s,i} }\)

Gs,connected∙P0

Supply area

− Qs,is

Qs,is

Junction

0

0

Element

Value

 

B

 

\(G(i,i)\)

\(\sum\limits_{i \ne j}^{N} {G_{i,j} }\)

 

\(G(i,j)\)

\(- G_{i,j}\)

 
  1. B: Summary of the algorithm for the creation and determination of the G-matrix. The edge conductivity is described by Eq. (13). Here, the edge conductivity between a supply node and the sink is determined by the auto-regulation function