Partial Volume MR Fingerprinting (PVMRF)^1,2 aims to quantify partial volumes of multiple tissues present within a single voxel by modeling the mixed-species voxel signal as a weighted sum of known MRF signal evolutions, stored in a subdictionary. The subdictionary includes MRF signals of several tissues which may be present, where we assume to know the tissues a priori. Previous PVMRF calculations solved the least squares problem between the subdictionary and mixed signal, taking the magnitude of the complex solution and scaling the weights to sum to one². However, taking the magnitude will remove information and can allow for an erroneous weight contribution when the solution is negative. One way to avoid this is to construct a synthetic partial volume (PV) dictionary comprised of known fraction combinations of the selected dictionary entries. This work examines the possibility of enforcing consistency with a physical model of tissue mixture, in which the weights are forced to be positive and real.Normal volunteers were scanned at 3T (Skyra, Siemens Medical, Erlangen, Germany) using a FISP MRF sequence³. This study is IRB-approved and volunteers provided written consent prior to participation. To individualize the method to each subject, MRF T1 and T2 results were clustered using the k-means algorithm to infer representative T1 and T2 values for CSF, gray matter, and white matter using the cluster centroids. As shown previously, subvoxel tissue components were estimated by forming a subset dictionary where each entry is a weighted sum of selected subvoxel tissues (such as CSF, gray matter and white matter). Only positive real fractions that summed to one were considered. Fractions range from 0 to 1 in steps of 0.02. The full MRF dictionary contains 5,552 entries, while the subset dictionary contains 1,326 entries. The subset dictionary was matched to the full MRF dictionary to obtain the effective T1 and T2 for each mixed entry. The effective T1 and T2 values in the synthetic PV dictionary are shown in Figure 1. Signals from the volunteer study were matched to the synthetic PV dictionary to identify the fractions at each pixel for each of the representative tissues as well as the effective T1, T2, and proton density (M0) maps. The residual norm was computed as a metric of the fit between the signals and their dictionary matches, scaled by the magnitude of the computed M0 values.For the results discussed here, the T1, T2 pairs used for the partial volume dictionary are as follows: CSF: T1 3000, T2 790, gray matter: T1 1360, T2 55 , and white matter: T1 840, T2 35. All units are in milliseconds. The range of effective T1 and T2 values in the PV dictionary are shown in Figure 1. Figure 2 illustrates the T1, T2 and M0 maps generated from pattern matching with the full MRF dictionary and the PV dictionary. Fraction maps using the PV dictionary and fraction maps computed from the magnitude of pseudoinverse weights as presented previously¹ are provided for comparison in Figure 3. Fractions are quantified in various gray matter and white matter structures. Figure 4 maps the model preference between the full MRF dictionary and the synthetic PV dictionary as measured by residual norms between the pixel signal evolution and the matched dictionary entry. Preference for the full MRF dictionary is indicated in blue while preference for the PV dictionary is indicated in copper.Matching the PV dictionary to the full MRF dictionary limits the combinations of effective T1 and T2 values, however, it has the advantage that non-physiological pairs are removed and may aid in reducing noise from the T1, T2, and M0 maps. Computing fractions with the synthetic dictionary prevents a misinterpretation of negative weights, as is the case in regions such as the thalamus, where the pseudoinverse model shows a significant fraction of CSF. Regions where the PV dictionary model is preferred are where this three tissue model is most accurate.We have presented a method to compute fraction maps of tissue types using a subset of three dictionary entries chosen specifically for each individual. Enforcing consistency with a physical tissue model removes erroneous partial volumes in the fraction maps, and reduces noise and distortions in T1, T2, and M0 maps, correcting tissue identification errors in the fraction calculation.