Fig 1.
Longitudinal dynamics of the 3D reconstructions of a brain metastasis treated with SRS showing radiation necrosis.
Dots correspond to the measured volumes together with their 3D reconstructions and the solid line is the result of interpolating longitudinal volumetric data (shown only to guide the eye). The patient was a 50-year-old male with a non-small-cell lung cancer primary, who underwent a single session SRS with a dose of 20 Gy. In this case, the inflammatory lesion exhibited its peak volumetric expansion around 12 months after treatment. The solid line is a cubic spline interpolation shown to guide the eye.
Fig 2.
Schematic representation of the populations involved in the response to SRS.
The post-treatment scenario represents the growth of radiation necrosis events as defined in Eq (1). After SRS healthy cells around the tumor become damaged and die by necrotic catastrophe. The appearance of necrosis stimulates immune cells leading to an apparent growth of the lesion.
Table 1.
Summary of parameters for the compartmental model.
Fig 3.
A Slice of a tumor simulation before SRS with DSBMS, mapping the distribution of cell density.
A representation of the populations of healthy (blue), tumor (red) and necrotic (black) cells within a voxel according to their location is shown. B. Example of a single-shot treatment plan for a virtual simulation of SRS. The target is outlined in yellow, and it is the area most affected by SRS. The green line encloses another area affected with less intensity. C. Spatial distribution of cell populations just before and after SRS. Voxels may be occupied by more than one cell population but the dominant populations per voxel are shown.
Table 2.
Notation and description of the cell populations in the DSBMS model.
Table 3.
Summary of parameter values used for the stochastic model.
Fig 4.
Results of simulations of the compartmental model Eq (1).
a. Example of a simulation of model Eq (1) showing the typical dynamics observed post-SRS in the context of RN events. The simulation illustrates the evolution of each cell type, with the initial number of tumor cells set to NT = 5 ⋅ 107, and parameter values ρ = 0.07 days−1, λN = 2.3 ⋅ 10−11 days−1, γ = 1.9 ⋅ 10−7 days−1 and θ = 0.17 days−1. b. Fittings using Eq (1) (solid lines) for the longitudinal volumetric growth data (circles) for five patients diagnosed with RN. The parameters used for the fitting process are shown in Table 4. c. Distribution of growth exponents, β values obtained for simulations with varying initial volumes ranging from 0.5 to 3.0 cm3 by simulating 500 RN events per volume using a randomized approach where model parameters took values in the predefined range. Note that values of β between 1 and 2 were obtained systematically.
Table 4.
Model Eq (1) parameters best fitting the longitudinal dynamics of RN events. Volumetric data were taken from Ref. [43] and lesions 1 to 5 correspond to patients ID numbers: 30031, 40024, 40001, 40176, and 40042, respectively.
Fig 5.
The dynamics of brain metastases (BMs) recurrences and radiation necrosis (RN) events are captured by the stochastic mesoscopic model.
a. Recurrent BM. b. RN event. White points represent the total tumor volume at different time points, and black lines depict interpolations between the points (provided as visual guidance). Additionally, spatial distribution of the four cell populations illustrate the dynamic shifts in dominance among cell types for both scenarios. The dominant population per voxel is shown.
Fig 6.
DSBMS simulations of longitudinal tumor growth dynamics after SRS.
The first column (A,C,E) shows the dynamics of the total populations of proliferating cells (red lines), damaged cells (orange lines), necrotic cells (violet lines), immune cells (green lines) and total tumor cells (blue lines). The second column (B,D,F) shows the longitudinal tumor volumetric dynamics. Blue lines inside the zoom box represent different fits of β exponent solving Eq (7) and the mean is shown. Subplots (A-B) correspond with a tumor simulation with no damage to healthy tissue (Sn = 1,
), subplots (E-F) correspond with small damage to healthy tissue (Sn = 0.7,
) and subplots (C-D) correspond with high damage to healthy tissue (Sn = 0.1,
). Basal rate parameters for simulations in this figure are
h,
h,
h,
h,
h,
h,
h and
h.
Fig 7.
Comparison of box plots for the growth exponents β calculated for virtual BMs performed with the DSBMS.
A. Growth exponents β values computed for the group of 200 simulations with Sn = 1 and . B. Growth exponents β values computed for the group of 200 simulations with 0.1 ≤ Sn ≤ 0.7 and
. C. Scatter plot that shows the β median calculated for the virtual BMs which were simulated with different values of (
, Sn). Basal rate parameters for the simulations are shown in Table 3.
Fig 8.
A. Box plots showing the comparison of the growth exponents between the different simulated BMs: relapse group (R), whose response is characterized by tumor progression (
, Sn = 1), relapse and inflammation group (R & I), whose response is characterized by tumor progression and inflammation (
, 0.1 ≤ Sn ≤ 0.7) and inflammation group (I), whose response is characterized by inflammation (
, 0.1 ≤ Sn ≤ 0.7). B. ROC curve for the discrimination between tumor progression (R and R&I groups) and inflammatory response (I group) according to the growth exponent
.
Fig 9.
Exploring the correlation between the AUC of the ROC curve and ranging the Sf bound from 0.04 to 0.4.
The colorbar illustrates the corresponding calculated β* threshold.