0118

Imaging the pulsatile fluid source distribution and pressure gradients in the brain using a poroelastic model and intrinsic pulsatile motions.

Matthew McGarry¹, John Weaver^1,2, and Keith Paulsen^1,2
¹Dartmouth College, Hanover, NH, United States, ²Dartmouth-Hitchcock Medical Center, Lebanon, NH, United States

Synopsis

The pulsatile tissue motions from the cardiac cycle can be imaged using retrospectively gated phase contrast MRI. Modeling brain tissue as a poroelastic material allows a distribution of pulsatile fluid sources to be computed which reproduce the measured motions by estimating the RHS vector of a finite element representation of the poroelastic system. This Fluid source imaging (FSI) represents a completely new type of image parameterization that could offer unique diagnostic signatures. The associated pressure field gradients are also the driving force for interstitial fluid movement, where disruptions are thought to cause buildup of waste products which leads to dementia.

INTRODUCTION

Fluid flow within the brain is currently thought to be critical in the genesis of dementia^1–6. Aberrations in interstitial fluid (ISF) flow reduce clearance of waste products from the brain through the glymphatic system, and the resulting buildup of waste products leads to dementia. ISF flow is also known to influence drug delivery to solid tumors dramatically⁷. Measurement methods for ISF movement are limited. The “gold standard” is intrathecal gadobutrol contrast enhanced MRI⁸ which is invasive and not commonly performed outside of neurosurgery9. Less invasive estimates of CSF flow made with phase-contrast MRI are related but lack a direct link to ISF flow and molecular clearance10. Intravascular Gd also correlates with molecular clearance¹¹, but also lacks a direct link. More complex methods using MRI to estimate the spectrum of fluid flow in the brain^12,13 have potential are challenging to implement in vivo. The difficulties in measuring fluid flow directly in the brain render any flow properties valuable to our understanding. Fluid flow is governed by pressure gradients and resistance to fluid flow, and accordingly, any information on either component is extremely useful to our understanding of fluid flow in the human brain. The ability of blood to flow is related to blood vessel size whereas the ability of ISF to flow is related to size of the interstitial space and the number of glycoproteins inhibiting flow. Nonetheless, the pressure source driving all fluid flows is likely to be similar: it is the cardiac pressure. Brain structures are not capable of sustaining a pressure gradient over a small distance; hence, the pressure that drives blood flow through capillaries is very close to the pressure that drives ISF flow. These conditions make pressure gradients measured using blood relevant to ISF flow as well.

METHODS

Brain tissue is modeled as a poroelastic continuum, with a porous elastic matrix fully saturated in an infiltrating pore fluid. The steady-state harmonic form representing repeated pulsatile flow¹⁴ is given by $$∇∙(μ(∇u ⃗+ ∇u ⃗^T ))+∇(λ ∇∙u ⃗ )-(1-β)∇P=-ω^2 (ρ-βρ_f ) u [1a]$$ $$∇∙(β∇P)+ρ_f ω^2 ∇∙((1-β) u ⃗ )=iωρ_f γ [1b]$$ $$β=ωϕ^2 ρ_f κ/(iϕ^2+κω(ρ_a +ϕ_p ρ_f ) ) [1c]$$ Here, the shear modulus, μ, Lame parameter, λ, and solid displacement field, u are properties of the porous solid phase, ρ, ρ_f and ρ_a are the bulk, fluid and apparent densities, and the coupling of the solid and fluid phases are described by hydrodynamic parameters including pore fluid pressure field, P, porosity, Φ, hydraulic conductivity, κ, and fluid source, γ. Fluid moves through the matrix in response to a pressure gradient, governed by the hydraulic conductivity, which is the proportionality constant in Darcy’s law, $$$q ⃗=κ∇P$$$. As the fluid moves, coupling terms in Eq 1 cause the elastic matrix to deform. Retrospectively gated phase contrast MRI can be used to measure three-dimensional pulsatile motion fields. Taking the first harmonic gives the bulk movement of tissue in response to the pulsatile flow field, illustrated in figure 1. Intrinsic actuation MR elastography (IA-MRE)¹⁵ uses these measurements to produce images of the poroelastic shear moduli and hydraulic conductivity, and assumes the fluid source term, γ, is zero. Fluid Source Imaging (FSI): Rather than estimating a mechanical property distribution that matches the computational model to the measured pulsatile data (as in IA-MRE), mechanical and hydrodynamic properties are prescribed, and the driving endogenous source distribution responsible for generation of the measured motion (γ in Eq 1) is computed on a spatial scale commensurate with the model discretization. FSI represents a completely new type of image parameterization likely associated with vascular density that could offer a unique diagnostic signature. The fluid source is estimated using Generalized least squares (GLS)¹⁶, which minimizes $$Ω=b^T W_b b+(u_c-u_m )^T W_δ (u_c-u_m )^T$$, subject to the constraint of u and b satisfying the finite element system, [K]{u}={b}. $$$W_b$$$ and $$$W_δ$$$ are weighting matrices which are the inverse prior covariances of b and the model-data misfit, $$$δ=(u_c-u_m )$$$, respectively, and can be used to control which terms of b to estimate – internal elements are body forces and fluid sources, γ, for the solid (Eq 1a) and fluid (Eq 1b) equations, respectively, whereas elements at boundary locations in the fluid equation represent unknown fluid boundary conditions. GLS is a linear problem with a direct solution possible through the method of unit responses, or a memory-efficient solution using conjugate gradient iteration.

RESULTS

Figure 2 shows a fluid source simulation where FSI was able to accurately recover the unknown source distribution from simulated pulsatile motion data, even with 20% simulated Gaussian noise added to the motions data. Figure 3 shows FSI results in a disease-free human brain. Figure 4 shows the gradient of the associated pressure field, which is the driving force for ISF flow.

DISCUSSION

Estimations of pressure gradient and interstitial fluid flow, along with the physical parameters defining their relationship are central to exploring the most widely accepted hypothesis on the genesis of dementia. Early identification of these conditions is crucial to effective interventions with next-generation therapeutic agents^17,18. Estimating pressure gradients and other factors driving ISF flows noninvasively could provide new and sensitive diagnostic indicators of dementia and shed new light on the early stages of disease.

Acknowledgements

R01EB018230-04

References

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Figures

Figure 1: Intrinsic brain pulsations measured with retrospectively gated phase contrast MRI. Stretch and compression in the x and y directions is evident, and bulk translation out of the image plane in the z direction. Typical imaging time is on the order of 20 minutes for 3D motions of a full brain (dependent on heart rate).

Figure 2: Simulated pulsatile motions from a 100mm cube with a 20mm spherical pulsatile source in the corner. FSI was able to accurately recover the true fluid source (lower images) even with up to 20% gaussian noise added to the simulated displacements.

Figure 3: Central slice of single-fluid FSI data from a healthy volunteer. γ and P are mostly positive at t=0 in the cardiac cycle (approximately systole), except for the ventricle region which is expected to have significant model-data mismatch. The fitted model displacements reproduce the measured data well, although the assumed constant μ and κ limit the ability to fit small scale features.

Figure 4: Pressure gradient amplitudes in the brain from fluid source imaging. The pressure gradient drives fluid flow through the brain. The same pressure drives the flow of all fluid compartments including interstitial fluid which is thought to clear metabolic waste. The result is an image of the pressure gradients in the brain over the cardiac cycle, systole on the right, and diastole on the left.

Proc. Intl. Soc. Mag. Reson. Med. 30 (2022)

0118

DOI: https://doi.org/10.58530/2022/0118