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. 2013 Apr 2:3:62.
doi: 10.3389/fonc.2013.00062. eCollection 2013.

From patient-specific mathematical neuro-oncology to precision medicine

Affiliations

From patient-specific mathematical neuro-oncology to precision medicine

A L Baldock et al. Front Oncol. .

Abstract

Gliomas are notoriously aggressive, malignant brain tumors that have variable response to treatment. These patients often have poor prognosis, informed primarily by histopathology. Mathematical neuro-oncology (MNO) is a young and burgeoning field that leverages mathematical models to predict and quantify response to therapies. These mathematical models can form the basis of modern "precision medicine" approaches to tailor therapy in a patient-specific manner. Patient-specific models (PSMs) can be used to overcome imaging limitations, improve prognostic predictions, stratify patients, and assess treatment response in silico. The information gleaned from such models can aid in the construction and efficacy of clinical trials and treatment protocols, accelerating the pace of clinical research in the war on cancer. This review focuses on the growing translation of PSM to clinical neuro-oncology. It will also provide a forward-looking view on a new era of patient-specific MNO.

Keywords: clinical modeling; glioma; individualized health care; mathematical modeling; patient-specific; personalized medicine.

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Figures

Figure 1
Figure 1
(A) Concentrations of tumor cells contributing to a gradient of diffusely invading glioma cells extending well beyond the threshold of detection. The PI model characterizes the net rates of growth and invasion of the glioma cells contributing to this overall profile, a sum of individual cell behaviors. Swanson et al. have demonstrated that D and ρ can be calculated on a patient-specific basis and can vary widely, even for patients within the same histological grade (Harpold et al., ; Swanson et al., ; Szeto et al., ; Wang et al., ; Rockne et al., 2010). (B) A simulation of the reaction-diffusion mathematical model on an anatomically accurate brain phantom (Cocosco et al., 2004) with differential motility in gray and white matter as proposed by Swanson (1999). The MRI-detectable edge of the lesion is superimposed as a dark gray contour emphasizing the extent of invasion well beyond the threshold of detection. From Wang et al. (2009) with permission from Cancer Research.
Figure 2
Figure 2
Three dimensional simulation of diffuse tumor invasion and proliferation predicted by the PI model which accounts for differential motility of tumor cells in gray and white matter. Malignant glioma cells can migrate up to 100-fold faster in white matter than in gray, characterizing the extent of invisible subclinical disease.
Figure 3
Figure 3
Decision process for patient-specific model validation and translation to clinically applicable analysis. Courtesy: Neal and Kerckhoffs (2010), by permission of Oxford University Press.
Figure 4
Figure 4
“Example screenshots from glioma growth model simulations with varied points of origin. Images at four time points each for three simulated lesions provided in the sagittal, coronal, and axial planes for lesion start points at the anterior dorsolateral subventricular zone, anterior deep white matter, and anterior superficial white matter. Green area reflects estimated T2-weighted image abnormality on magnetic resonance; red area reflects estimated T1-weighted image post-gadolinium abnormality.” Courtesy: Bohman et al. (2010).
Figure 5
Figure 5
Scatter plot of relative hypoxia (RH, the ratio of hypoxic volume to T2-weighted MRI volume) versus ρ/D for n = 11 glioblastoma patients. RH was determined over a variety of tissue to blood (T/B) tracer levels, ranging from 1.1 to 1.6 in increments of 0.1. A strong linear relationship between the variables is shown for all thresholds; correlations were statistically significant for all T/B levels considered. From Szeto et al. (2009b), with permission from Nature Publishing Group, Cancer Research.
Figure 6
Figure 6
Simulated FMISO-PET and actual FMISO-PET. Hypoxia is predicted by the PIHNA model and an imaging reconstruction algorithm produces the simulated FMISO-PET. Pixel intensity distribution is not statistically different between the two images, providing model-based predictions of tumor hypoxia which is otherwise obscured by PET image acquisition and reconstruction. Courtesy: Gu et al. (2012), by permission of Oxford University Press.
Figure 7
Figure 7
Comparisons between untreated virtual controls and post-treatment MRI scans. First row: post-treatment MRI. Second row: contours showing measured tumor on T1-Gd-enhanced scan (red) and UVC prediction of T1-Gd area (aqua). Third row: UVC tumor cell densities overlaid (white, high cell density; red, low cell density) on scan with T1-Gd measured tumor outline (black).
Figure 8
Figure 8
(A) Survival curves for actual glioblastoma patients (asterisks) and virtual patients (squares) subjected to biopsy or subtotal resection (BX/STR, N = 38). Inset shows a close-up of the survival curves near the median survival times of 32.4 and 36.5 weeks. (B) Survival curves on a longer time scale following gross total resection (GTR, N = 32) in actual patients (asterisks) defined by the absence of residual tumor on post-operative enhanced CT. The virtual patients (matched to actual pre-operative T1-Gd volume and D/ρ ratio derived from the T1-Gd and T2 volumes) were subjected to no resection (BX/STR, squares), to resection of 100% of the T1-Gd volumes or radii, rT1 (circles), and to resection of 125% of the T1-Gd volumes or radii, 1.25 rT1 (diamonds). Inset shows a close-up of the survival curves near the median survival times of 44.9, 55, 62, and 66.9 weeks.” Reprinted from Swanson et al. (2008b) with permission from Nature Publishing Group, British Journal of Cancer.
Figure 9
Figure 9
(A) “Response to therapy is conventionally assessed by determining changes in gross tumor volume (GTV) on MRI prior to and after the administration of therapy. Post-contrast T1-weighted MRI images are shown for two glioblastoma patients that would typically be separated into generic groups: responder and stable disease. The radiation response parameter α gives an additional quantification of radiation response for each patient.” (B) “Relationship between radiation response and tumor proliferation rate parameters α (Gy−1) and ρ (1/year), respectively, with α calculated relative to changes in T2 GTV post therapy r = 0.89, ρ ≪ 0.05, N = 9. Error bars on ρ are calculated by propagation of error in pre-treatment GTV as assessed by inter-observer variability of ±1 mm in equivalent spherical radius. Error bars in α are computed by taking the maximum and minimum values of α in a leave one out cross validation (LOOCV) technique.” Courtesy: Rockne et al. (2010), with permission from IOP Publishing Ltd.

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