Fig 1.
Segmentation of the magnetic resonance image dataset featuring the inner (yellow) and outer (red) cortical surfaces for three orthogonal planes.
Sulci and gyri can be appreciated in the zoomed-in area performed over the fronto-lateral view.
Fig 2.
Preparation of the initial vascular network.
Left: ADAN model. Right top: Selection of the initial vascular sub-networks ,
and
corresponding to the ACA, MCA and PCA territories, respectively. Right bottom: Non-linear co-registration of initial sub-networks on top of the pial surface.
Fig 3.
Pial space and vascular territories.
Top: Generation of the pial space (in blue, with transparency) by extrusion of the pial surface
(in gray), and details of the pial space in different locations. Bottom: Definition of the ACA (red), MCA (green), and PCA (blue) vascular territories, by Boolean operations with the reference territorial solids
,
and
. These vascular spaces are denoted by
,
and
, respectively. The corresponding pial surfaces are denoted by
,
, and
.
Fig 4.
Decomposition into sub-domains for the ACA (top row), MCA (middle row) and PCA (bottom row) territories.
Each color represents a sub-domain. The projections from the lateral, ventral, and caudal directions are shown in each case.
Table 1.
Parameters to configure the multi-staged vascularization using the PDCCO algorithm.
For the definition of parameters, see Section Vascularization stages.
Table 2.
Data and parameters regarding inter-territorial pressure distribution equalization.
: flow rate at the inlet,
: inlet vessel radius given in ADAN model,
: proportionality constant in Murray’s law for ADAN model, fS scaling factor for vessel diameters,
: inlet vessel radius after equalization, and
: proportionality constant in Murray’s law for the scaled network after equalization.
Fig 5.
Pial vascular network built with the proposed multi-stage approach.
Top panel: Orthogonal projections on transverse, coronal and sagittal planes, and ventro-lateral perspective, with color-code given by vessel diameter in . Mid panel: Multi-staged vascularization of the pial space. From left to right: initial sub-networks from the ADAN model (totaling 450 vessel segments), first and second sequential vascularization stages with different cost functions (totaling 8 390 and 40 390 vessel segments, respectively), and third vascularization stage after merging the parallelized sub-domain networks (totaling 234 344 vessel segments). Bottom panel: Distribution of vessel diameters D, vessel lengths L, and their joint kernel density estimate distribution in the pial networks for each of the three territories,
(red),
(green), and
(blue), and also for the entire pial network
(gray). All distributions are in logarithmic scale.
Table 3.
Multiplication factors for the modification of parameters in the hypertensive scenario.
Table 4.
Statistics for vessel diameter D and vessel length L in the pial vascular networks for the different territories and for the entire network.
: mean value,
: standard deviation,
: median value,
: lower and upper quartiles. LT: cumulative vessel length,
: cumulative vascular volume,
: number of vessels.
Fig 6.
Hemodynamics in the cerebral cortex for the normotensive scenario.
Flow rate is reported in logarithmic scale. Top panel: Distribution of mean blood pressure over time , mean flow rate over time
, and their joint kernel density estimate distribution in the pial networks for each of the three territories
(red),
(green), and
(blue), and also for the entire pial network
(gray). Mid panel: Pressure (top left inset) and flow rate (top right inset) waveforms along four evenly spaced locations placed in three arbitrarily chosen paths with length L (one per territory); pressure through space is characterized in the space-time domain (bottom left inset, isolines in white), and using the maximum, mean and minimum temporal values of the pressure waveforms along each path (bottom right inset) from the corresponding territory root to the terminal point at distance L. Bottom panel: Visualization of the blood pressure in each vessel along the entire cortex network for five different time-instants during the cardiac cycle.
Table 5.
Descriptive statistics for temporal mean pressure and mean flow rate
in the pial vascular networks for the different territories and for the entire network in the normotensive scenario.
: mean value,
: standard deviation,
: median value,
: lower and upper quartiles.
: number of vessels.
Table 6.
Comparison of the systolic , mean
and diastolic
pressure values at different locations for the normotensive and hypertensive scenarios.
BA: brachial artery, l. ICA: left internal carotid artery, p.: proximal, d.: distal, : median value computed for the vessels in each territory that meet the criteria of diameter D and distance to the territory root L.
Fig 7.
Comparison of the hemodynamics in the cerebral cortex between the normotensive and hypertensive scenarios using pulse-related indexes.
Left panel: Pulse pressure across the entire cortex network as a field (top insets) and distribution of the pulse pressure in the different territories (bottom insets). Right panel: Pulsatility (flow rate-based) index across the entire cortex network as a field (top insets) and distribution of the index in the different territories (bottom insets). Statistics are shown for networks (red),
(green), and
(blue), and also for the entire pial network
(gray), considering both scenarios, normotensive (left plots) and hypertensive (right plots).
Table 7.
Descriptive statistics for pulse pressure , the pulsatility index
, and the damping factors obtained from these two indexes (
and
) in the pial vascular networks for the different territories and for the entire network in the normotensive (top half) and hypertensive (bottom half) scenarios.
: median value,
: lower and upper quartiles. The number of vessels
is reported in Table 5.
Fig 8.
Transport-level hemodynamics (top-half) along randomly chosen vascular paths per vascular territory, and perfusion-level hemodynamics (bottom-half) defined at all terminal vessels.
The transport-level quantities along the path are shown with a thick black line. Colorbar indicates vessel diameter values in the perfusion-level panels. Left panels: Pulsatility index (PI) as a function of the distance to the territory root. Right panels: Mean blood pressure as a function of the distance to the territory root. In each panel, each row corresponds to a given territory: (red),
(green), and
(blue). In each panel, the normotensive (left) and the hypertensive (right) scenarios are displayed.
Fig 9.
Effect of viscoelasticity in the normotensive (top panel) and hypertensive (bottom panel) scenarios.
Pressure and flow rate waveforms at two different sites along the selected path through the MCA territory (left plots) and pulsatility index at transport and perfusion levels (right plots) in the ACA territory.
Table 8.
Descriptive statistics for mean pressure , pulse pressure
and the pulsatility index
for the entire network in the normotensive and hypertensive scenarios considering different modeling ingredients.
: median value,
: lower and upper quartiles. The number of vessels is
.
Table 9.
Model ingredients adopted in the studies available in the literature.