Apparent Exchange Rate in Multi-compartment Anisotropic Tissue
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1
CR Development AB, -, Sweden
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2
Aarhus University, Department of Physics and Astronomy, Denmark
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3
Aarhus University, CFIN/MINDLab, Department of Clinical Medicine, Denmark
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4
Copenhagen University Hospital, Danish Research Centre for Magnetic Resonance, Denmark
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5
Lund University, Lund University Bioimaging Centre , Sweden
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6
Lund University, Physical Chemistry, Sweden
Introduction: Apparent Exchange Rate (AXR) of water between micro-environments with different apparent diffusivities can be quantified by filter exchange imaging (FEXI). FEXI is a double diffusion encoding (DDE) experiment consisting two diffusion weighting blocks (filter and detection) separated by a variable mixing time (tm) [1,2]. In anisotropic tissue, AXR may depend on the diffusion encoding direction [3]. Understanding how diffusion anisotropy affects the AXR is fundamental in experimental design and interpretation of results. We present illustrative examples of anisotropic conditions that affect AXR. Our initial investigations indicate that AXR is expected to be orientationaly dependent even in simple anisotropic systems with a single exchange rate if there are more than two orientationally dispersed compartments.
In FEXI, the equilibrium apparent diffusivity, D, is perturbed by the low pass diffusion filter, characterized by diffusion weighting bf. To quantify AXR, the perturbed diffusivity, D’, is measured as a function of tm. By considering the orientational dependence of D’, the original definition of AXR [1] can be applied to anisotropic systems. The AXR is given as the initial variation in D’(tm). The time course of D’(tm) is calculated considering the evolution of signals from multiple compartments with different diffusivities, according to the first order exchange kinetics [4,5]. In the limit of small perturbation
D − D′ → 0 at bf → 0 and for tm → 0, an analytical expression can be obtained for AXR. This expression reflects the fact that AXR entangles the effect of exchange and the apparent compartment diffusivities, which may depend on dispersion restriction size and/or orientation dispersion of anisotropic
compartments.
For simplicity in seeking qualitative understanding, we consider three anisotropic compartments, two intracellular and one extracellular. Spins in the two intracellular compartments can exchange between each other only via the extracellular compartment. We set both intracellular exchange rate constants
(inverse of lifetime) to be identical. We also consider a similar case with several anisotropic intracellular compartments dispersed according to the Watson probability distribution. This simple setup suffices to reveal a complex orientational dependence of AXR.
For systems with only two compartments, i.e. one intracellular compartment, AXR is independent of direction, regardless of anisotropy of any of the compartments. When more than two anisotropic compartments are included, the AXR depends on direction even in simple systems with a single
exchange rate (intracellular lifetime), provided that intracellular compartments are orientationally dispersed. This effect can be understood by noting that AXR is reduced along the main axis of intracellular compartments. The AXR is dominated by exchange from those compartments that are mostly
affected by the filter. The degree of AXR anisotropy cannot be inferred from the diffusion tensor model alone. We expect that when sufficiently simple assumptions about the systems configuration are possible, e.g. using a parametric orientation distribution function of cylinders in exchange with the
extracellular compartment, it is possible to determine the underling exchange rate constants based on FEXI data acquired in several directions.
In conclusion, we have found that the AXR is anisotropic even in simple systems. This is of importance in the interpretation of the AXR, but could also be
useful for detailed analysis of fiber-specific characteristics.
References: [1] Lasič, S et al. 2011, Magn Reson Med: 66. [2] Nilsson, M et al. 2013, Magn Reson Med: 69. [3] Sønderby CK, et al. 2014, Magn Reson Med: 72, [4] Zimmerman, JR et al., 1957, J Phys Chem, 61, [5] Allan, EA et al., 1972, Pure Appl Chem: 32(1)
Keywords:
Diffusion,
MRI,
dMRI,
multidimensional,
diffusion encoding
Conference:
New dimensions in diffusion encoding, Fjälkinge, Sweden, 11 Jan - 14 Jan, 2016.
Presentation Type:
Oral presentation
Topic:
New Dimensions in Diffusion Encoding
Citation:
Lasič
S,
Jespersen
SN,
Lundell
H,
Nilsson
M,
Dyrby
TB and
Topgaard
D
(2016). Apparent Exchange Rate in Multi-compartment Anisotropic Tissue.
Front. Phys.
Conference Abstract:
New dimensions in diffusion encoding.
doi: 10.3389/conf.FPHY.2016.01.00026
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Received:
07 Jul 2016;
Published Online:
07 Jul 2016.
*
Correspondence:
Prof. Daniel Topgaard, Lund University, Physical Chemistry, Lund, 221 00, Sweden, daniel.topgaard@fkem1.lu.se