Multiscale modeling of human cerebrovasculature: A hybrid approach using image-based geometry and a mathematical algorithm
Fig 3
Schematic of the MRC algorithm.
(A) Vascular generation in the multilevel region-confined manner. In the LV1 reconstruction, two arterial structures (red) and one venous (blue) structure are generated from their root edges, where the terminal vertices enter into respective vascular subregions Di. The following arterial and venous structures are then generated while being confined within each subregion Di in the LV2 reconstruction. (B) Definitions of the vascular structure. A single graph is shown with vertices vm and edges en. Also, a schematic of the edge subdivision for en is shown, where the edge is divided by the line segments ln,k with subpoints pn,k. In the representation, the edgewise line segment is given as a straight cylinder with the radius an,k and length Ln,k. (C) Description of the generation of new branches. Four bifurcation patterns (P1, P2, P3, P4) are considered for solving the optimization problem (7) when adding a new terminal vertex vM+1 to the graph with vertices vm and edges en. In the schematic, the edge en is selected as the closest edge of the new vertex, and a branching vertex vM+2 and edges eN+1, eN+2 are newly added. (D) Schematic of the relocation of an edge. Here, the vascular subregions are given on a curved surface Γ, and the reconstruction domain Ω is defined as the extended domain within the lower limit surface Γlow and upper limit surface Γup. As the edge passes across the boundary of Ω (outside of the lower limit Γlow), the edgewise subpoints outside the domain are relocated on the curved surface Γ.