Towards patient-specific modeling of brain tumor growth and formation of secondary nodes guided by DTI-MRI

Abstract

Previous studies to simulate brain tumor progression, often investigate either temporal changes in cancer cell density or the overall tissue-level growth of the tumor mass. Here, we developed a computational model to bridge these two approaches. The model incorporates the tumor biomechanical response at the tissue level and accounts for cellular events by modeling cancer cell proliferation, infiltration to surrounding tissues, and invasion to distant locations. Moreover, acquisition of high resolution human data from anatomical magnetic resonance imaging, diffusion tensor imaging and perfusion imaging was employed within the simulations towards a realistic and patient specific model. The model predicted the intratumoral mechanical stresses to range from 20 to 34 kPa, which caused an up to 4.5 mm displacement to the adjacent healthy tissue. Furthermore, the model predicted plausible cancer cell invasion patterns within the brain along the white matter fiber tracts. Finally, by varying the tumor vascular density and its invasive outer ring thickness, our model showed the potential of these parameters for guiding the timing (83-90 days) of cancer cell distant invasion as well as the number (0-2 sites) and location (temportal and/or parietal lobe) of the invasion sites.

Keywords: Biomechanics; Brain; DTI-MRI; Glioblastoma; Tumor distant invasion; Tumor growth; Tumor perfusion.

Fig. 1

(Left) Three-dimensional representation of the computational mesh showing the individual domains for the grey (green), white (purple) matter and tumor seed (light green). (Right) Computational finite element mesh employed in the present study consisting of 777,397 tetrahedral and 202,349 triangular elements. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 2

(Left) Typical relative Cerebral Blood Volume (rCBV) maps extracted from perfusion MRI. (Right) rCBV as a function of tumor volume along with the performed 5^th order fit used to correlate the vascular density and the tumor size within the simulation setup according to the equation rCBV = 1.0 + (7.8 × 10⁻⁴)V_t − (3.4 × 10⁻⁷)V_t² + (5.8 × 10⁻¹¹)V_t³ − (4.4 × 10⁻¹⁵)V_t⁴ + (1.2 × 10⁻¹⁹)Vt⁵.

Fig. 3

(Left y-axis) Tumor volume as a function of time for the tumor domain and the three isosurfaces corresponding to different cell densities infiltrating the proximal tissues. (Right y-axis) Cell density as a function of time for the tumor domain showing the proliferation of cancer cells as the tumor grows. The dashed grey arrows connect each curve with its corresponding vertical axis.

Fig. 4

(Top) Displacement maps and (bottom) stress $\overline{\sigma }=\left({\sigma }_{\mathit{rr}}^s+{\sigma }_{\mathit{\theta \theta }}^s+{\sigma }_{\mathit{\phi \phi }}^s\right)/3$ for the host tissue presented over the reference configuration (right), and for the tumor presented over the final/deformed mesh configuration (left).

Fig. 5

Sagittal and axial surface plots of cancer cell density showing inhomogeneous distribution within the tumor and anisotropic infiltration at the proximal tissue, owing to the inhomogeneous and anisotropic geometry and diffusion tensors. Distant invasion of cancer cells to the right temporal node formed satellite lesion indicated by the yellow arrow in the zoomed region. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 6

(Α) Tumor volume as a function of time (Left y-axis) for the tumor domain and the 2.5% isosurface of cancer cell density, along with the tumor domain's cell density as a function of time (right y-axis) for the additional runs of the parametric study. The dashed grey arrows connect each curve with its corresponding vertical axis. (Β) Sagittal view of T_cell outside the tumor domain showing secondary nodes (yellow arrows) only in the right temporal lobe for the 1.5, 2.5 mm thickness tumor outer rings. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 7

Intratumoral oxygen concentration as a function of time for varying tumoral outer ring and vascular density conditions. Low and high vascular density corresponds to values 50% and 150% of that of the baseline, respectively.

Fig. 8

(Α) Tumor volume as a function of time (Left y-axis) for the tumor domain and the 2.5% isosurface of cancer cell density, along with the tumor domain's cell density as a function of time (right y-axis) for the additional runs of the parametric study. (Β) Sagittal view of T_cell outside the tumor domain showing secondary nodes (yellow arrows) the right temporal posterior parietal lobe for the 50% vascular density run and the only the right temporal lobe for the 150% vascular density run. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)

Fig. 9

(A, C) Tractography depicting numerous fiber tracts connecting the initial tumor location with the secondary nodes. (B, E) Distant invasion of cancer cells at distant locations within the brain, forming secondary nodes at the right posterior parietal lobe (B) and the right temporal lobe (E) (yellow arrows) along with the intermediate “cell pool” (D). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)