Mathematical modeling of metabolism and hemodynamics

Partial differential model of lactate neuro-energetics: analytic results and numerical simulations

Interfaces play a key role on diseases development because they dictate the energy inflow of nutrients from the surrounding tissues. What is underestimated by existing mathematical models is the biological fact that cells are able to use different resources through nonlinear mechanisms. Among all nutrients, lactate appears to be a sensitive metabolic when talking about brain tumours or neurodegenerative diseases. Here we present a partial differential model to investigate the lactate exchanges between cells and the vascular network in the brain. By extending an existing kinetic model for lactate neuro-energetics, we first provide analytical proofs of the uniqueness and the derivation of precise bounds on the solutions of the problem including diffusion of lactate in a representative volume element comprising the interface between a capillary and cells. We further perform finite element simulations of the model in two test cases, discussing the relevant physical parameters governing the lactate dynamics.

Treatment Response Assessment in IDH-Mutant Glioma Patients by Noninvasive 3D Functional Spectroscopic Mapping of 2-Hydroxyglutarate

PURPOSE

Measurements of objective response rates are critical to evaluate new glioma therapies. The hallmark metabolic alteration in gliomas with mutant isocitrate dehydrogenase (IDH) is the overproduction of oncometabolite 2-hydroxyglutarate (2HG), which plays a key role in malignant transformation. 2HG represents an ideal biomarker to probe treatment response in IDH-mutant glioma patients, and we hypothesized a decrease in 2HG levels would be measureable by in vivo magnetic resonance spectroscopy (MRS) as a result of antitumor therapy.

EXPERIMENTAL DESIGN

We report a prospective longitudinal imaging study performed in 25 IDH-mutant glioma patients receiving adjuvant radiation and chemotherapy. A newly developed 3D MRS imaging was used to noninvasively image 2HG. Paired Student t test was used to compare pre- and posttreatment tumor 2HG values. Test-retest measurements were performed to determine the threshold for 2HG functional spectroscopic maps (fSM). Univariate and multivariate regression were performed to correlate 2HG changes with Karnofsky performance score (KPS).

RESULTS

We found that mean 2HG (2HG/Cre) levels decreased significantly (median = 48.1%; 95% confidence interval = 27.3%-56.5%;P= 0.007) in the posttreatment scan. The volume of decreased 2HG correlates (R(2)= 0.88,P= 0.002) with clinical status evaluated by KPS.

CONCLUSIONS

We demonstrate that dynamic measurements of 2HG are feasible by 3D fSM, and the decrease of 2HG levels can monitor treatment response in patients with IDH-mutant gliomas. Our results indicate that quantitative in vivo 2HG imaging may be used for precision medicine and early response assessment in clinical trials of therapies targeting IDH-mutant gliomas.

Low-grade gliomas: the challenges of imaging

WHO grade II gliomas are a major challenge for magnetic resonance imaging (MRI) due to their delayed anaplastic transformation. Today it is possible to individually characterize tumor progression from diagnosis to anaplastic transformation based on the many parameters identified in studies in the literature and the possibility of integrating these data into mathematical models. Early identification of negative morphological and metabolic factors, as well as treatment follow-up, help identify predictive factors of tumor progression, as well as determine treatment response to adapt management of this disease.