Quantitative analysis of macroscopic solute transport in the murine brain

Abstract

Background Understanding molecular transport in the brain is critical to care and prevention of neurological disease and injury. A key question is whether transport occurs primarily by diffusion, or also by convection or dispersion. Dynamic contrast-enhanced (DCE-MRI) experiments have long reported solute transport in the brain that appears to be faster than diffusion alone, but this transport rate has not been quantified to a physically relevant value that can be compared to known diffusive rates of tracers. Methods In this work, DCE-MRI experimental data is analyzed using subject-specific finite-element models to quantify transport in different anatomical regions across the whole mouse brain. The set of regional effective diffusivities ($$D_{eff}$$ D eff ), a transport parameter combining all mechanisms of transport, that best represent the experimental data are determined and compared to apparent diffusivity ($$D_{app}$$ D app ), the known rate of diffusion through brain tissue, to draw conclusions about dominant transport mechanisms in each region. Results In the perivascular regions of major arteries, $$D_{eff}$$ D eff for gadoteridol (550 Da) was over 10,000 times greater than $$D_{app}$$ D app . In the brain tissue, constituting interstitial space and the perivascular space of smaller blood vessels, $$D_{eff}$$ D eff was 10–25 times greater than $$D_{app}$$ D app . Conclusions The analysis concludes that convection is present throughout the brain. Convection is dominant in the perivascular space of major surface and branching arteries (Pe > 1000) and significant to large molecules (> 1 kDa) in the combined interstitial space and perivascular space of smaller vessels (not resolved by DCE-MRI). Importantly, this work supports perivascular convection along penetrating blood vessels.

Sensitivity analysis on a network model of glymphatic flow

“…Interface 19: 20220257 penetrating PVSs plays an important role in transport. Ray et al also find that advection plays a role in transport of gadoteridol (which has a similar diffusivity to monomeric amyloid-β [16]) in brain tissue, which includes the penetrating PVSs. We report Pe for monomeric amyloid-β, but Pe for other substances will scale linearly with the diffusivity.…”

“…The upper bound is based on the possibility that penetrating PVSs are open-as pial PVSs have been shown to be [59]-rather than porous. Ray et al conducted a quantitative analysis of murine DCE-MRI data to estimate the relative contributions of advection and diffusion, determining that the large transport rates they observed suggest that the large penetrating PVSs are open [16]. Others that have estimated penetrating PVS permeability have used values that fall in between these upper and lower bounds [22,60].…”

“…However, the 1 μm particles they used do not enter penetrating PVSs, which may indicate that the penetrating PVSs are porous, and if so, smaller particles would be required. Another exciting possibility is the approach of Ray et al [16], who used in vivo MRI to estimate effective diffusivities in different regions of the brain and from that inferred velocities and Pe. Their approach could potentially be refined to narrow the possible range of penetrating PVS permeability.…”

“…It is also important to point out that the fraction of tracer transported (as reported by Lee et al ) does not precisely reflect the fraction of fluid transport; however, if we assume that solute transport prior to delivery to the parenchyma is dominated by bulk fluid flow, the fraction of fluid delivered will approximately match the fraction of solute delivered. Solute transport is clearly dominated by advection due to unidirectional bulk flow [35,36] (as opposed to transport induced by oscillatory net zero flow and/or diffusion) in pial PVSs and probably in penetrating PVSs as well [16,37]. Of course, this bound is only valid for the conditions in Lee et al [31]: rats anaesthetized with dexmedetomidine (0.015-0.020 mg −1 kg −1 h −1 ) supplemented with 0.5-0.8% isoflurane.…”

“…Experimental measurements, including two-photon imaging [6,[8][9][10], transcranial imaging [11], magnetic resonance imaging [12][13][14][15][16] and real-time iontophoresis [17][18][19][20], provide insight regarding glymphatic flow and transport and form the basis for the glymphatic model; however, each of these measurement techniques provides only limited access to these flows, leaving gaps in our understanding and limiting our ability to prevent and treat related pathological conditions. Mathematical models provide valuable insight into the mechanisms that drive glymphatic flows and point out the most important unknown aspects.…”