Recent dynamic contrast-enhanced MRI studies using the adiabatic tissue homogeneity model have highlighted potential issues of difficulty in convergence during data-fitting and reduced parameter precision, due to discontinuities in the adiabatic tissue homogeneity model. This study presents two solutions (an analytic approach and a discrete correction method) to such convergence problems and show that these problems can be attributed to an inaccurate approximation of the convolution integral based on the standard trapezoidal quadrature. It is further explained that such issues of discontinuity in the impulse residue function do not pertain only to the adiabatic tissue homogeneity model, but are generic to all tracer kinetic models, if the difference in bolus arrival time between the arterial input and tissue voxels were to be accounted for simultaneously during model-fitting. Quantitative estimates of tissue microvascular parameters can be derived from dynamic contrast-enhanced (DCE) MRI data by a model-constrained deconvolution process that involves parametric fitting of a tracer kinetic model. Among the existing tracer kinetic models, the adiabatic approximation to the tissue homogeneity (AATH) model (1) has gained increasing popularity because it allows for simultaneous estimation of tissue blood flow (F) and capillary permeability-surface area product (PS), which are important parameters related to tumor angiogenic potential (2-6). Another advantage of the AATH model is its relative simplicity, as it preserves the vascular properties of the more complicated distributedparameter model in its impulse residue function (7)(8)(9) and approximates the parenchyma backflux phase using an exponential function by assuming adiabatic changes in tracer concentration within the interstitial space (1).However, recent emerging studies have indicated potential issues with convergence and parameter precision when implementing the AATH model due to discontinuities in its impulse residue function (2,5,10). As DCE-MRI data are acquired sequentially at fixed time points, it is believed that these discontinuities in the AATH model pose difficulties in the data-fitting process and could result in large errors for some of the parameters (2,5,10). In this study, we provide two solutions to these issues and demonstrate their feasibility using Monte Carlo simulations. MATERIALS AND METHODSThe operational equation for analysis of DCE MRI data describes the tissue concentration-time curve C tiss (t) as a convolution integral involving the arterial input function (AIF) C A (t) and the impulse residue function R(t):To account for the difference in bolus arrival time between the sampled C A (t) and C tiss (t) curves, a delay t 0 can be imposed in the expression for R(t) (5,8,10). The AATH model can be given bywhere T c denotes the vascular transit time and v e is the fractional extravascular extracellular space (1,10). E denotes the first-pass extraction fraction, and it can be related to capillary permeability PS by the Renkin-Crone equati...

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Background The primary objective was to quantify changes in vascular micro-environment in spinal metastases (SM) patients treated with stereotactic body radiotherapy (SBRT) with multi-parametric dynamic contrast enhanced (DCE) magnetic resonance imaging (MRI). The secondary objective was to study plasma biomarkers related to endothelial apoptosis. Patients and methods Patients were imaged with DCE-MRI at baseline/1-week/12-weeks post-SBRT. Metrics including normalised time-dependent leakage (Ktrans), permeability surface product (PS), fractional plasma volume (Vp), extracellular volume (Ve) and perfusion (F) were estimated using distributed parameter model. Serum acid sphingomyelinase (ASM) and sphingosine-1-phosphate (S1P) were quantified using ELISA. Clinical outcomes including physician-scored and patient-reported toxicity were collected. Results Twelve patients (with varying primary histology) were recruited, of whom 10 underwent SBRT. Nine patients (with 10 lesions) completed all 3 imaging assessment timepoints. One patient died due to pneumonia (unrelated) before follow-up scans were performed. Median SBRT dose was 27 Gy (range: 24–27) over 3 fractions (range: 2–3). Median follow-up for alive patients was 42-months (range: 22.3–54.3), with local control rate of 90% and one grade 2 or higher toxicity (vertebral compression fracture). In general, we found an overall trend of reduction at 12-weeks in all parameters (Ktrans/PS/Vp/Ve/F). Ktrans and PS showed a reduction as early as 1-week. Ve/Vp/F exhibited a slight rise 1-week post-SBRT before reducing below the baseline value. There were no significant changes, post-SBRT, in plasma biomarkers (ASM/S1P). Conclusions Tumour vascular micro-environment (measured by various metrics) showed a general trend towards downregulation post-SBRT. It is likely that vascular-mediated cell killing contributes to excellent local control rates seen with SBRT. Future studies should evaluate the effect of SBRT on primary-specific spinal metastases (e.g., renal cell carcinoma).

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