DSC-MRI: Basics

Amit Mehndiratta¹
¹Indian Institute of Technology Delhi, New Delhi, India

Synopsis

Perfusion imaging using dynamic susceptibility contrast MRI is widely used in management of brain ischemia and stroke. It is based on change in T2* effect arising from local field inhomogeneity as the contrast flow from the tissue capillary network. Quantitative analysis is completely based on the mathematical understanding of the underlying capillary network model, either a simplified model based approach or a complex model free methods have been used in literature. There are pros and cons of each method, this lecture will discuss few of these important methods and there benefits and limitations.

Perfusion MRI: Basics of Dynamic Susceptibility Contrast MRI, Physiological Model and Analysis Methods

Measuring tissue blood perfusion is important in planning treatment for disease such as in brain ischemia and stroke. Computed Tomography (CT), Positron Emission Tomography (PET) and Magnetic Resonance Imaging (MRI) can measure brain perfusion non-invasively. Tissue perfusion is a dynamic process and Gadolinium based contrast based MRI are used to measure blood flow. The flow of the Gadolinium through the tissue capillary bed allows to measure change in tissue susceptibility as a marker of tissue perfusion. This imaging technique is called Dynamic Susceptibility Contrast MRI (DSC-MRI). Analysis of the images from DSC-MRI is typically based on an understanding of cerebral microvascular hemodynamics. DSC, also called bolus tracking imaging is based on T2* effects that arise from local field inhomogeneity induced by a Gadolinium contrast agent in the vessels. Gadolinium contrast agents are aqueous solutions of heavy metal Gadolinium based complexes that are injected intravenously. With the flow of the contrast the transverse relation (R2*) of the tissue is alters that causes a change in MR signal as a measure of tissue perfusion ¹. This effect is highly significant in areas where contrast is compartmentalized in the vessels only, also known as single compartmental model.
Perfusion analysis is based on Tracer Kinetic Theory², where capillary vessels are modeled as a complex branching tubular network. As the bolus arrives in the capillary bed, there is distribution of bolus across multiple paths, and the individual transit times through this bed can be described in the form of a probability density function, h(t). As bolus is continuously flowing through the capillary bed, at any instance of time, t, the fraction of contrast present in the tissue is presented a function called residue function, R(t):
$$R(t)= 1 - \int_{0}^{t} h(t) dt$$
Fundamentally residue function is a monotonically decreasing function starting from R(0)=1. The contrast concentration, C(t), in the tissue is not only proportional to total blood flow to the tissue CBF (Cerebral Blood Flow) as well the tissue capillary hemodynamic properties i.e. the residue function, but also dependent on how the bolus injection is performed i.e. the Arterial Input Function (AIF) ^3,4:
$$C (t)= \frac{ρ}{k_{H}}· CBF · (Ca (t)⊗ R (t)) d\tau$$
$$= \frac{ρ}{k_{H}}· CBF · \int_{0}^{t} Ca (\tau) · R (t-\tau)d\tau$$
where, it is a convolution operation between is the AIF and tissue residue function. The proportionality constant, ρ is the density of brain tissue (needed to provide the correct flow units) and k_H accounts for the difference in hematocrit between capillaries and large vessels.
The total blood supply to this tissue network can be measured as Cerebral Blood Volume (CBV, in ml/100g of tissue), Cerebral Blood Flow (CBF, in ml/100g of tissue/min) according to the indicator dilution theory ^2,4–7. These two parameters are related through the central volume theorem ^4,6:
$$CBV=CBF·MTT$$
where MTT is the Mean Transit Time measured in minutes.
The Analysis for DSC perfusion MRI is broadly classified into two categories: model-based and model-free methods. Various deconvolution methods have been proposed under both model-based and model-free analysis methodologies. These include: I) Model based methods⁸, where a specific analytical expression or shape of R(t) is assumed, such as: a) Exponential ^4,6,9, b) Fermi ¹⁰, c) Vascular Model ¹¹ and II) Model-free methods, where no assumption of the underlying response function is made, such as: a) Frequency domain deconvolution (Fourier Transform) ^5,12, b) Singular Value Decomposition (SVD) ³, c) Block-circulant SVD (oSVD) ¹³, d) Tikhonov Regularization (tkSVD) ¹⁴, e) Maximum Likelihood ¹⁵, f) Gaussian Processes Deconvolution ¹⁶, g) Nonlinear Stochastic Regularization ¹⁷, h) Control Point Interpolation Method ^18,19.
The perfusion analysis problem can, at least in theory, be circumvented by performing parametric (model based) OR non-parametric (model-free) deconvolution with or without a priori knowledge of R(t) respectively. In model-free approaches, the tissue response function, i.e. the flow and shape of R(t), are determined from the data.
Model based methods are easy to implement and the estimated parameters has an added value to clinical decision making as these parameter are physiologically relevant. However, these methods always has a limitation of assumptions that are made for analysis which might divert under patho-physiological variations. Model free methods learn from data and can accommodate patho-physiological variation in estimation process, but these methods are mostly computationally expensive and the estimated parameters might not always have relevant physiological meaning.
Another key issue in DSC analysis the dispersion effects in bolus. The arterial input function is often measured at a larger distant artery from tissue of interest, however as bolus reaches the tissue of interest it is ‘smeared out’ during the transit which is called bolus dispersion ^20–22. Not to consider this effect in analysis can always give underestimation in perfusion values which can have serious implications in clinical decision making. The dispersion effect can be modeled in the mathematical equations of perfusion in the form of ‘Vascular Transport Function (VTF)’ ^23–26.

Acknowledgements

Acknowledgment: The material for this abstract and presentation is adopted from my own work as presented in thesis ¹⁹.

References

1 Villringer A, Rosen BR, Belliveau JW, Ackerman JL, Lauffer RB, Buxton RB et al. Dynamic imaging with lanthanide chelates in normal brain: contrast due to magnetic susceptibility effects. Magn Reson Med 1988; 6: 164–74.

2 Meier P, Zierler KL. On the theory of the indicator-dilution method for measurement of blood flow and volume. J Appl Physiol 1954; 6: 731–44.

3 Østergaard L, Weisskoff RM, Chesler DA, Gyldensted C, Rosen BR. High resolution measurement of cerebral blood flow using intravascular tracer bolus passages. Part I: Mathematical approach and statistical analysis. Magn Reson Med 1996; 36: 715–25.

4 Zierler KL. Theoretical basis of indicator-dilution methods for measuring flow and volume. Circ Res 1962; 10: 393–407.

5 Gobbel GT, Fike JR. A deconvolution method for evaluating indicator-dilution curves. Phys Med Biol 1994; 39: 1833–54.

6 Zierler KL. Equations for measuring blood flow by external monitoring of radioisotopes. Circ Res 1965; 16: 309–21.

7 Axel L. Cerebral blood flow determination by rapid-sequence computed tomography: theoretical analysis. Radiology 1980; 137: 679–86.

8 Mehndiratta A, Calamante F, MacIntosh BJ, Crane DE, Payne SJ, Chappell MA. Modeling the residue function in DSC-MRI simulations: Analytical approximation to in vivo data. Magn Reson Med 2014; 72: 1486–91.

9 Jacquez J. Compartmental analysis in biology and medicine: kinetics of distribution of tracer-labeled materials. Elsevier: Amsterdam, 1972http://www.worldcat.org/title/compartmental-analysis-in-biology-and-medicine-kinetics-of-distribution-of-tracer-labeled-materials/oclc/605657126 (accessed 2 Nov2011).

10 Jerosch-Herold M. Quantification of myocardial perfusion by cardiovascular magnetic resonance. J Cardiovasc Magn Reson Off J Soc Cardiovasc Magn Reson 2010; 12: 57.

11 Mouridsen K, Friston K, Hjort N, Gyldensted L, Østergaard L, Kiebel S. Bayesian estimation of cerebral perfusion using a physiological model of microvasculature. Neuroimage 2006; 33: 570–9.

12 Rempp KA, Brix G, Wenz F, Becker CR, Gückel F, Lorenz WJ. Quantification of regional cerebral blood flow and volume with dynamic susceptibility contrast-enhanced MR imaging. Radiology 1994; 193: 637–41.

13 Wu O, Østergaard L, Weisskoff RM, Benner T, Rosen BR, Sorensen AG. Tracer arrival timing-insensitive technique for estimating flow in MR perfusion-weighted imaging using singular value decomposition with a block-circulant deconvolution matrix. Magn Reson Med 2003; 50: 164–74.

14 Calamante F, Gadian DG, Connelly A. Quantification of bolus-tracking MRI: Improved characterization of the tissue residue function using Tikhonov regularization. Magn Reson Med 2003; 50: 1237–47.

15 Vonken EP, Beekman FJ, Bakker CJ, Viergever MA. Maximum likelihood estimation of cerebral blood flow in dynamic susceptibility contrast MRI. Magn Reson Med 1999; 41: 343–50.

16 Andersen IK, Szymkowiak A, Rasmussen CE, Hanson LG, Marstrand JR, Larsson HBW et al. Perfusion quantification using Gaussian process deconvolution. Magn Reson Med 2002; 48: 351–61.

17 Zanderigo F, Bertoldo A, Pillonetto G, Cobelli Ast C. Nonlinear stochastic regularization to characterize tissue residue function in bolus-tracking MRI: assessment and comparison with SVD, block-circulant SVD, and Tikhonov. IEEE Trans Biomed Eng 2009; 56: 1287–97.

18 Mehndiratta A, Macintosh BJ, Crane DE, Payne SJ, Chappell MA. A control point interpolation method for the non-parametric quantification of cerebral haemodynamics from dynamic susceptibility contrast MRI. Neuroimage 2013; 64: 560–570.

19 Mehndiratta A. Quantitative measurements of cerebral hemodynamics using magnetic resonance imaging. 2014.https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.604531.

20 Calamante F, Gadian DG, Connelly A. Delay and dispersion effects in dynamic susceptibility contrast MRI: Simulations using singular value decomposition. Magn Reson Med 2000; 44: 466–473.

21 Calamante F, Gadian DG, Connelly A. Quantification of perfusion using bolus tracking magnetic resonance imaging in stroke: Assumptions, limitations, and potential implications for clinical use. Stroke 2002; 33: 1146–1151.

22 Calamante F. Artifacts and pitfalls in perfusion MR imaging. In: Gillard J, Waldman A, Barker P (eds). Clinical MR Neuroimaging: diffusion, perfusion and spectroscopy. Cambridge University Press, 2005, pp 141–160.

23 Iida H, Kanno I, Miura S, Murakami M, Takahashi K, Uemura K. Error analysis of a quantitative cerebral blood flow measurement using H2(15)O autoradiography and positron emission tomography, with respect to the dispersion of the input function. J Cereb blood flow Metab Off J Int Soc Cereb Blood Flow Metab 1986; 6: 536–45.

24 Calamante F, Willats L, Gadian DG, Connelly A. Bolus delay and dispersion in perfusion MRI: implications for tissue predictor models in stroke. Magn Reson Med Off J Soc Magn Reson Med / Soc Magn Reson Med 2006; 55: 1180–5.

25 Schmidt R, Graafen D, Weber S, Schreiber LM. Computational fluid dynamics simulations of contrast agent bolus dispersion in a coronary bifurcation: impact on MRI-based quantification of myocardial perfusion. Comput Math Methods Med 2013; 2013: 513187.

26 Mehndiratta A, Calamante F, MacIntosh BJ, Crane DE, Payne SJ, Chappell MA. Modeling and Correction of Bolus Dispersion Effects in Dynamic Susceptibility Contrast MRI. Magn Reson Med 2014. doi:10.1002/mrm.25077.

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