The most widely used curve-fitting algorithm is the Levenberg-Marquardt algorithm (LM)¹, but Bayesian modeling (Bayes) is an alternative approach² not previously used for DCE. We fit patient- and simulated data by two different hemodynamic models using each of the two fitting algorithms, with the aim to improve parameter accuracy and image quality.

Among the hemodynamic models, the Tofts Extended Model (TOFTs) is the most commonly used. Its leakage parameter, K_trans, is however hampered by the cerebral blood flow, CBF, especially in non-leaky healthy tissue. On the contrary, the two-compartment exchange model (2CX) is potentially able to separate leakage, K₁, and CBF, but K₁ is not well-determined in non-leaky tissue. We suggest that a more robust Bayesian fitting algorithm will provide more accurate values in both healthy and diseased tissue.

Hemodynamic parameters were estimated in 42 glioma patients using both the TOFTs and the 2CX models with each of the two fitting-algorithms, LM and Bayes. Patlak estimates³ were used as the starting guess for the fitting routines. The same approach was pursued in 10.000 simulated data sets for each of 4 disease stages and healthy tissue. Scanner parameters and noise levels were used for the simulations. The hemodynamic parameter maps from the patients were visually rated by two neuro-radiologists. The parameter estimates of simulations were compared to the underlying true values (see fig. 3).

The TOFTs Ktrans estimates have confounding high values from the vessels (see fig. 1 A and B). These are vanishing in K₁ of 2CX (fig. 1 C and D). The vessel contribution is instead visible in the CBF estimates (fig 1 E and F). Using Bayes fitting algorithm (right column) leads to clear separation of healthy and leaky tissue in the K₁ image (fig 1 D). And the number of spurious voxels in the maps of extra-vascular volume, Ve, (fig. 1H) is reduced compared to LM (fig. 1G). The average rater scores for K₁ and V_e were higher for Bayes compared to LM, see fig. 2.

In simulations, TOFTs K_trans estimates reproduced neither K₁ nor CBF in no- or mildly diseased tissue, regardless of fitting algorithm (fig. 3A). Opposing this, 2CX largely reproduced the underlying K₁, CBF and V_e estimates for all disease stages (fig. 3B-D). In simulated healthy tissue, outliers were seen for K₁ for both fitting algorithms, whereas outliers in V_e only were seen when using LM.

Only the 2CX model separates blood flow and leakage for all disease stages. When optimizing the 2CX model parameters, the Bayesian algorithm offers similar accuracy as the Levenberg-Marquardt algorithm with fewer outliers resulting in less image scatter and improved image rating. The Bayesian algorithm may be what is needed for the 2CX model to become clinical applicable.