Stereotactic radiosurgery (SRS) is the preferred treatment option for patients with brain metastasis¹. Assessing tumor response early after treatment allows for adjusting the therapy. Current response evaluation criteria (i.e. RANO-BM²) rely on changes in tumor size. However, it may take weeks or months before significant changes in tumor size occur, by which the therapeutic window may be lost. Quantitative MRI techniques that are sensitive to radiation-induces changes such as apoptosis, which occur within days post-treatment, have a potential to accurately evaluate tumor response early after treatment. Apoptosis leads to higher cell membrane permeability and larger surface-to-volume ratio of the cell, both of which increase the water exchange between intracellular and extracellular compartments³. We hypothesize that intracellular-extracellular water exchange may provide more accurate assessment of brain metastases response to SRS as early as one-week post-treatment.

Acquisition: A total of $$$24$$$ patients with brain metastases were scanned before SRS, one-week post-SRS, and one-month post-SRS on a $$$3T$$$ Philips Achieva system under ethics board approved protocols. DCE-MRI was acquired using 3D-SPGR ($$$TR/TE=4/2ms$$$, $$$FA=15^o$$$, $$$FOV=25.6\times25.6cm$$$, slice thickness=$$$8mm$$$). Pre-contrast $$$T_{1}/B_{1}$$$ mapping was performed using Method of Slopes⁷ with $$$FA=3,14,130,150^o$$$.

Tumor volume was measured from post-Gd $$$T_{1}$$$-weighted MRI and was used for determining response. Based on RANO-BM, patients were divided into three cohorts: $$$16$$$ with partial response $$$(PR)$$$, $$$4$$$ with stable disease $$$(SD)$$$, and $$$4$$$ with progressing disease $$$(PD)$$$.

Modeling: A three water compartment model of tissue longitudinal relaxation was used^4–6. Briefly, each compartment (vascular, $$$V$$$, extracellular extravascular, $$$E$$$, intracellular, $$$I$$$) in a voxel was assumed to contain a fraction of its total water content proportional to the compartment volume fraction $$$(M_{0,V},M_{0,E},M_{0,I})$$$. Water was assumed to move from intracellular to extracellular extravascular compartment with exchange rate constant, $$$k_{IE}$$$, and no water exchange was assumed between vascular and extracellular extravascular compartments. Bloch equations describing longitudinal magnetization recovery from perturbation in each compartment are (assuming negligible $$$T_{2}$$$ decay): $$\begin{cases}\frac{\text{d}M_{Z,V}(t)}{\text{d}t}=R_{1,V}(M_{0,V}-M_{Z,V}(t))\\\frac{\text{d}M_{Z,I}(t)}{\text{d}t}=R_{1,I}(M_{0,I}-M_{Z,I}(t))-k_{IE}M_{Z,I}(t)+k_{EI}M_{Z,E}(t)\\\frac{\text{d}M_{Z,E}(t)}{\text{d}t}=R_{1,E}(M_{0,E}-M_{Z,E}(t))-k_{EI}M_{Z,E}(t)+k_{IE}M_{Z,I}(t)\end{cases}$$

The vascular enhancement of DCE-MRI was separated from total DCE-MRI using independent component analysis. Then, the Bloch equations were fit to DCE-MRI data, and model parameters $$$(k_{IE},M_{0,V},M_{0,E},M_{0,I})$$$ were calculated.

Classification: Support vector machines (SVM), which have superior performance when the sample size is small^8,9, were used in classifying the patients. Two SVM classifiers were built with radial basis function kernels for: a) separating the $$$PR$$$ patients from $$$SD+PD$$$ patients, b) separating the $$$PD$$$ patients from $$$PR+SD$$$ patients. The classifiers were build with feature vectors containing: 1) only the change in tumor volume one-week post-treatment, 2) only change in $$$k_{IE}$$$ one-week post-treatment, 3) Combining pre-treatment $$$k_{IE}$$$, one-week post-treatment $$$k_{IE}$$$, and tumor volume change one-week post-treatment. Note that the first two classifiers are equivalent of selecting a threshold value for classification. Accuracy of each classifier was determined using leave-one-out cross-validation technique.

Tumor volume change one-week post-treatment was compared to its change one-month post-treatment (Fig.1) and there was no correlation between these two parameters $$$(R=-0.02,p=0.92)$$$. The water exchange quantification technique was applied to DCE-MRI of all $$$24$$$ patients. Among all model parameters the intracellular-extracellular water exchange rate constant provided the highest correlation $$$(R=-0.64,p<0.001)$$$ with tumor volume change one-month post-treatment (Fig.2). Table 1 reports the accuracy of the SVM classifiers in separating the $$$PR$$$ patients from $$$PD+SD$$$ patients, as well as separating $$$PD$$$ patients from $$$PR+SD$$$ patients, demonstrating the superior performance of SVM with the three parameters compared to individual parameters.The weak correlation in Fig.1 shows the early tumor volume change was unable to predict treatment response. It was also unable to separate $$$PR$$$ from $$$SD+PD$$$ (accuracy=$$$58\%$$$) or separate $$$PD$$$ from $$$PR+SD$$$ (accuracy=$$$42\%$$$), as reported in Table 1. Intracellular-extracellular water exchange rate constant one-week post-treatment demonstrated strong correlation with tumor volume change one-month post-treatment. However, a threshold value could not be selected for this parameter to accurately separate patient groups. As reported in Table 1, the SVM using only $$$k_{IE}$$$ resulted in $$$83\%$$$ accuracy in separating patients with PR and $$$75\%$$$ in separating patients with PD. The last column of Table 1 shows combining the information provided by pre-treatment $$$k_{IE}$$$, one-week post-treatment $$$k_{IE}$$$, and tumor volume change one-week post-treatment provided the highest accuracy in separating partial response patients from other groups ($$$92\%$$$). It also provided the highest accuracy in separating patients with progressing disease ($$$92\%$$$).Intracellular-extracellular water exchange rate constant is a promising biomarker of radiation-induced changes (i.e. apoptosis) in brain metastases. Combining the information provided by this parameter and changes in tumor volume was capable of accurately classifying patients into $$$PR,SD$$$, and $$$PD$$$ cohorts within one-week post-treatment. Such early classification may allow the physician to identify non-responders and alter/adjust their treatment.