Measuring microvascular flow characteristics with myocardial DCE-MRI perfusion data using a model-independent, multi-resolution spline approach in patients at stress
Karl P Kunze1, Christoph Rischpler1, Markus Schwaiger1, and Stephan G Nekolla1

1Department of Nuclear Medicine, Klinikum rechts der Isar der TU München, Munich, Germany

Synopsis

This abstract proposes a new B-spline based approach for model-independent deconvolution of myocardial DCE-MRI perfusion data and the reconstruction of the vascular transit time distribution function. It allows the model-independent quantification of vascular mean transit time and vascular transit time heterogeneity, whose relationship is of importance in understanding the implications of different ischemic microvascular disease patterns. The presented algorithm was tested in simulations and showed stability for the range of perfusion parameters expected under stress conditions. 12 DCE-MRI patient datasets from adenosine stress examinations were analyzed, showing a steady increase of heterogeneity with mean transit time.

Introduction

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 (Tc), vascular plasma volume (vp) and vascular transit time heterogeneity (CTH). It has recently been hypothesized that the relationship of Tc 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 Tc and CTH from adenosine stress DCE-MRI perfusion data.

Methods

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 4th 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 Re 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 ve were globally fixed to values of E=55% and ve = 18% as expected at pharmacological stress.4 The part of hv corresponding to vascular indicator kinetics was integrated to yield Tc and CTH, which are defined as mean and standard deviation of hv respectively. Mean and standard deviation of the preceding negative part of hv corresponding to bolus dispersion were calculated to correct Tc for the bolus arrival time. The algorithm is schematically depicted in Fig. 2. To validate the resulting parameters, a simulation was executed varying Tc and CTH using a gamma-distributed transit-time (GCTT) model.5 Parameters vp, ve, 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

Results

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 Tc and CTH than seen in the patient data. The average results from the patient study were: Tc = 3.10s and CTH = 1.21s leading to an average Tc/CTH ratio of 2.55. The individual results in Fig. 4 show a relatively stable increase of CTH with Tc for the investigated range. One dataset was rejected due to a CTH estimate lower than the time resolution of the scan.

Conclusion

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 Tc and CTH from DCE-MRI perfusion data.

Acknowledgements

This work was funded in part by Deutsche Forschungsgemeinschaft (DFG), grant number: 8810001759.

References

1. Østergaard L, Kristiansen SB, Angleys H, et al. The role of capillary transit time heterogeneity in myocardial oxygenation and ischemic heart disease. Basic Res Cardiol 2014;109:409.

2. Jerosch-Herold M, Swingen C, Seethamraju RT. Myocardial blood flow quantification with MRI by model-independent deconvolution. Med Phys 2002;29:886-897.

3. Koh TS, Zeman V, Darko J, et al. The inclusion of capillary distribution in the adiabatic tissue homogeneity model of blood flow. Phys Med Biol 2001;46:1519-1538.

4. Broadbent DA, Biglands JD, Larghat A, et al. Myocardial blood flow at rest and stress measured with dynamic contrast-enhanced MRI: Comparison of a distributed parameter model with a fermi function model. Magn Reson Med 2013;70:1591-1597.

5. Schabel MC. A unified impulse response model for DCE-MRI. Magn Reson Med 2012;68:1632-1646.

6. Zhang HS, Rischpler C, Langwieser et al. Proc ISMRM (2013) 0576

Figures

Visualization of spline-based deconvolution, the thin coloured lines represent the respective basis splines. All three parts of the used knot sequence are shown in their generic forms with hints to their respective domains in the response function.

Schematic depiction of the iterative determination of knot sequences and calculation of hv.

Simulation results showing the relative bias of Tc (a) and CTH (b) estimates for various combinations of both parameters. The black regions indicate situations with CTH larger or equal to Tc, which were deemed unrealistic for the in-vivo data at hand and thus not simulated.

Estimates for individual Tc and CTH in all 12 patient datasets. Despite the relatively small variations in Tc due to the stress condition, a steady increase of CTH with increasing Tc is visible. The red dot marks the excluded case.



Proc. Intl. Soc. Mag. Reson. Med. 24 (2016)
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