Despite the growing role of myocardial perfusion flow measurements using DCE-MRI to assess the significance of suspected coronary artery disease (CAD), myocardial DCE-MRI data contain also quantitative information on microvascular perfusion parameters such as vascular mean transit time (T_c), vascular plasma volume (v_p) and vascular transit time heterogeneity (CTH). It has recently been hypothesized that the relationship of T_c and CTH plays a crucial role in regulating the availability of oxygen to the myocardium, and that different ischemic (non-CAD) disease patterns may in fact be understood as pathological changes in these microvascular parameters.¹ We introduce a model-independent deconvolution approach based on B-splines for obtaining the transit time distribution h and use it to estimate T_c and CTH from adenosine stress DCE-MRI perfusion data.

In addition to standard Tikhonov regularization, model-independent deconvolution techniques using singular value decomposition (SVD) support the application of further constraints, such as requiring that the solution be represented in terms of a 4^th degree B-spline basis.² By controlling the placement and overall number of knots, i.e. the grid on which the resulting spline (the response function R) is evaluated, different portions of that spline may be forced to exhibit different degrees of smoothness. The approach presented here is based on a sequence with varying knot density, accommodating the expected features of a response curves in DCE-MRI data. The exact placement of knots is determined using essentially two criteria: First, the assumption of a global minimal transit time (0.25s), which is supposed to represents a lower boundary to transit time information contained in data with the time resolution of usual DCE-MRI measurements. Second, the constraint that the response curve be monotonous as required by basic indicator-dilution theory. After determination of the knot sequence, oscillations in h, i.e. the negative derivative of R, are minimized by adjusting the corresponding (Thikonov) regularization parameter. After finding a suitable spline representation of R (Fig. 1), an iterative method to estimate the contribution R_e made to R by the extravascular kinetics of Gd-DTPA was implemented, assuming an adiabatic exchange condition:³

$$R_e^i=Ee^{-\frac{EF_p}{v_e}t}\int_{0}^{t} h_v^i(t') e^{\frac{EF_p}{v_e}t'}dt'\\h^{i+1}_v=-\frac{\partial}{\partial t}R_v=-\frac{\partial}{\partial t}(R-R^i_e)$$

Extraction fraction E and extravascular distribution volume v_e were globally fixed to values of E=55% and ve = 18% as expected at pharmacological stress.⁴ The part of h_v corresponding to vascular indicator kinetics was integrated to yield T_c and CTH, which are defined as mean and standard deviation of h_v respectively. Mean and standard deviation of the preceding negative part of h_v corresponding to bolus dispersion were calculated to correct T_c for the bolus arrival time. The algorithm is schematically depicted in Fig. 2. To validate the resulting parameters, a simulation was executed varying T_c and CTH using a gamma-distributed transit-time (GCTT) model.⁵ Parameters v_p, v_e, and E were fixed at 8, 18 and 55% respectively. The simulated GCTT response was convolved with a measured input function after convolution with a gaussian kernel to simulate bolus dispersion and delay. Noise was added to the resulting tissue curve for an SNR of 50. To test the algorithm in vivo, 12 DCE-MRI stress perfusion datasets from a previous study were analyzed. Data were acquired using an ECG-gated SR-FLASH sequence on a 3T PET/MRI scanner (Biograph mMR, Siemens, Erlangen), with a study protocol as given by Zhang et al.⁶

The results of the simulation are summarized in Fig. 3. The algorithm was reliable for CTH as low as 1s, however more likely to overestimate very small CTH. The algorithm was least reliable if confronted with combinations of much higher T_c and CTH than seen in the patient data. The average results from the patient study were: T_c = 3.10s and CTH = 1.21s leading to an average T_c/CTH ratio of 2.55. The individual results in Fig. 4 show a relatively stable increase of CTH with T_c for the investigated range. One dataset was rejected due to a CTH estimate lower than the time resolution of the scan.A new algorithm has been presented to estimate myocardial mean transit time and transit time heterogeneity from DCE-MRI perfusion data without the necessity to assume a specific vascular model. The presented approach is able to account for and potentially also quantify bolus dispersion and delay, as well as to account for the extravascular contributions in the transit time distribution function h while making only minor assumptions on tissue structure and experimental design. To the best of the authors knowledge, the in-vivo results represent the first model-independent assessment of myocardial T_c and CTH from DCE-MRI perfusion data.