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A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects

View Article: PubMed Central - PubMed

ABSTRACT

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer).

No MeSH data available.


Indicative results of the segmentation in gray scale. Black color (red, green, blue [RGB] [0, 0, 0]) corresponds to anything outside the inner surface of the skull that defines the cranial cavity. This implies that black color can represent cranial bones, air, etc. White color (RGB [255, 255, 255]) corresponds to white matter, RGB (128, 128, 128) corresponds to gray matter, and RGB (160, 160, 160) corresponds to cerebrospinal fluid.
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f8-10.1177_1176935116684824: Indicative results of the segmentation in gray scale. Black color (red, green, blue [RGB] [0, 0, 0]) corresponds to anything outside the inner surface of the skull that defines the cranial cavity. This implies that black color can represent cranial bones, air, etc. White color (RGB [255, 255, 255]) corresponds to white matter, RGB (128, 128, 128) corresponds to gray matter, and RGB (160, 160, 160) corresponds to cerebrospinal fluid.

Mentions: To accelerate the calculations without any loss of information, part of the image corresponding to air surrounding the skull has been cropped. Furthermore, because the discretization of the problem assumes a cubic lattice, a new cubic discretization of the data set–based anatomic region of interest has been performed. The new cubic voxel has a dimension of 1 mm × 1 mm × 1 mm. In addition, the resolution has been reduced to 8 bits per pixel using the ImageJ software.49 Indicative sections of the reconstructed anatomic region of interest in gray scale are depicted in Figure 8. Because only the inner surface of the skull is used in the simulation executions, the 3D flat bone structure of the skull has been removed.


A Numerical Handling of the Boundary Conditions Imposed by the Skull on an Inhomogeneous Diffusion-Reaction Model of Glioblastoma Invasion Into the Brain: Clinical Validation Aspects
Indicative results of the segmentation in gray scale. Black color (red, green, blue [RGB] [0, 0, 0]) corresponds to anything outside the inner surface of the skull that defines the cranial cavity. This implies that black color can represent cranial bones, air, etc. White color (RGB [255, 255, 255]) corresponds to white matter, RGB (128, 128, 128) corresponds to gray matter, and RGB (160, 160, 160) corresponds to cerebrospinal fluid.
© Copyright Policy - open-access
Related In: Results  -  Collection

License 1 - License 2
Show All Figures
getmorefigures.php?uid=PMC5392020&req=5

f8-10.1177_1176935116684824: Indicative results of the segmentation in gray scale. Black color (red, green, blue [RGB] [0, 0, 0]) corresponds to anything outside the inner surface of the skull that defines the cranial cavity. This implies that black color can represent cranial bones, air, etc. White color (RGB [255, 255, 255]) corresponds to white matter, RGB (128, 128, 128) corresponds to gray matter, and RGB (160, 160, 160) corresponds to cerebrospinal fluid.
Mentions: To accelerate the calculations without any loss of information, part of the image corresponding to air surrounding the skull has been cropped. Furthermore, because the discretization of the problem assumes a cubic lattice, a new cubic discretization of the data set–based anatomic region of interest has been performed. The new cubic voxel has a dimension of 1 mm × 1 mm × 1 mm. In addition, the resolution has been reduced to 8 bits per pixel using the ImageJ software.49 Indicative sections of the reconstructed anatomic region of interest in gray scale are depicted in Figure 8. Because only the inner surface of the skull is used in the simulation executions, the 3D flat bone structure of the skull has been removed.

View Article: PubMed Central - PubMed

ABSTRACT

A novel explicit triscale reaction-diffusion numerical model of glioblastoma multiforme tumor growth is presented. The model incorporates the handling of Neumann boundary conditions imposed by the cranium and takes into account both the inhomogeneous nature of human brain and the complexity of the skull geometry. The finite-difference time-domain method is adopted. To demonstrate the workflow of a possible clinical validation procedure, a clinical case/scenario is addressed. A good agreement of the in silico calculated value of the doubling time (ie, the time for tumor volume to double) with the value of the same quantity based on tomographic imaging data has been observed. A theoretical exploration suggests that a rough but still quite informative value of the doubling time may be calculated based on a homogeneous brain model. The model could serve as the main component of a continuous mathematics-based glioblastoma oncosimulator aiming at supporting the clinician in the optimal patient-individualized design of treatment using the patient’s multiscale data and experimenting in silico (ie, on the computer).

No MeSH data available.