In-silico solute transport via perivascular networks in the human intracranial space

Abstract

The mechanisms of intracranial solute transport are fundamental to human brain health. However, our understanding of their interplay remains incomplete, in part due to the complexity of integrating insights across scales, between species, and from different modalities. In this work, we combine mixed-dimensional mathematical modeling, multi-modal magnetic resonance images, and high performance computing to present a computational framework for calculating the spatiotemporal spreading of a solute across the subarachnoid space, ventricular system, and brain parenchyma, including surface perivascular spaces. To illustrate applicability, we simulate a series of scenarios relating to intrathecal tracer injections, including variations in cerebrospinal fluid production, intracranial pulsatility, perivascular fluid flow and -structure. This openly available framework allows for evaluating the integrated effect of different transport mechanisms, bridging from the vascular mesoscale to the organ-level macroscale and across time scales of seconds to hours, in subject-specific geometries.

This work introduces a multiscale, integrative modeling framework for brain fluid flow and solute transport, bridging mesoscale perivascular networks with the organ-level macroscale and timescales of seconds to hours in subject-specific geometries.

Introduction

The mechanisms underlying molecular transport within the intracranial space are fundamental to human brain health and function. Neurodegenerative diseases such as Alzheimer’s, Parkinson’s, and Huntington’s disease are all associated with abnormal accumulation of protein aggregates together with alterations in transport characteristics^1–4. Moreover, sleep and, conversely, sleep deprivation play a definite yet enigmatic role in modulating solute transport^5–9. In the last decade, established theories have been challenged by new findings on molecular movement and exchange^10–14, including substantial variability between individuals and between patient cohorts^7,15–17. These observations provide distinct opportunities (and challenges) for personalized medicine, e.g., for tailored intrathecal delivery of chemotherapies¹⁸ such as methotrexate in acute lymphoblastic leukemia patients¹⁹, and for early diagnostics of impaired brain clearance^20,21. In spite of their importance, our understanding of these mechanisms is incomplete, with open challenges and significant debate – in part relating to the translation of knowledge between scales, species, experimental protocols, clinical cohorts, and individuals.

Perivascular pathways along the brain surface and within the brain parenchyma have long been hypothesized to serve a designated role in this context^10,22–28. Recently, Eide and Ringstad²⁹ and Yamamoto et al.³⁰ demonstrated that perivascular spaces (PVSs) define preferential pathways for molecular transport in humans, with delayed appearance of tracer in dementia subtypes²⁹. Perivascular flow of cerebrospinal fluid (CSF) clearly contributes to this transport, and is inherently associated with vascular pulsations^31–36. Fluid mechanics considerations point at intracranial pressure differences and shorter wavelength vascular wall pulsations as drivers of directional net flow and convection in the PVS^37–42, while longer waves, such as the pulse wave, primarily contribute to oscillatory flow and dispersion^43–48. In the bigger picture, CSF is produced by the choroid plexus^49–51, pulsates through the ventricular system, cisterns, and subarachnoid space (SAS) in association with cardiac, respiratory, and neural waves^16,52–59, and drains via the dural sinuses, meningeal lymphatics, cranial nerves, or other efflux pathways¹³. However, how these physiological factors and physical mechanisms integrate to enhance or impair human intracranial solute transport over larger spatial scales and longer time scales remains unknown. A related key question is to what extent surface PVSs are separated from the SAS by structural barriers^{23,29,60–65}, and in turn to what extent such structural compartmentalization is a prerequisite for effective perivascular transport.

In this work, we present an integrative computational framework for modeling intracranial solute transport. Focusing on the interplay between perivascular pathways, intracranial pulsatility, and CSF flow dynamics, our models predict the temporal evolution and spatial distribution of a solute concentration within image-derived representations of the human SAS and ventricular system, in networks of surface PVSs (i.e., those surrounding arteries and veins in the SAS), and in the brain parenchyma. We leverage a mixed-dimensional approach based on geometric model reduction⁶⁶, embedding one-dimensional PVS networks within geometrically resolved, three-dimensional volumes, to connect rapid mesoscale phenomena—such as perivascular pulsations occurring every few seconds—with macroscale observations of tissue-level tracer distribution over hours to days. In terms of transport dynamics, we account for heterogeneous diffusion, dispersive mixing induced by cardiac and respiratory pulsatility in the CSF spaces, convective fluid flow driven by CSF production in the CSF spaces and peristaltic pumping in the PVSs, as well as solute exchange and efflux across semipermeable membranes. A fully coupled model of CSF, ISF, and PVS flow is, however, not within the scope of the current work. We demonstrate the applicability of this computational framework via a series of model scenarios motivated by current questions relating to solute movement within the human brain environment. In particular, we simulate how the balance between CSF production and intracranial pulsatility can shape large-scale features of tracer distribution, how perivascular fluid flow induced by cardiac pulsations or low-frequency vasomotion can impact tracer arrival times within the surrounding CSF spaces and parenchyma, and how changes in structural properties, such as the diffusive permeability of the PVS interface or enlarged PVSs, can impact perivascular transport and intracranial tracer spread. This openly available technology platform⁶⁷ allows for evaluating the integrated effect of different intracranial transport mechanisms in subject-specific geometries, and provides a foundation for future in-silico studies of brain solute transport.

Results

A computational framework for intracranial solute transport

As the drivers and modes of intracranial transport are under substantial uncertainty and debate^{13,14,68–71}, our target is to introduce a computational framework that allows for integrating and evaluating different solute transport mechanisms, in particular perivascular pathways, in subject-specific geometries. To this end, we introduce the following modeling choices (Fig. 1A). Using previously published multi-modal magnetic resonance imaging (MRI) data^72–76, we construct a multiscale computational representation of the human intracranial compartments consisting of the CSF spaces and brain parenchyma as three-dimensional (3D) domains and with the PVSs surrounding major surface arteries and veins as networks of topologically one-dimensional (1D) curves embedded therein (Fig. 1B–F). We also associate the leaf nodes of the arterial PVS networks with zero-dimensional (0D) compartments representing the unresolved downstream perivascular pathways (see “Methods”).

Fig. 1. An integrative computational framework for intracranial solute transport informed by multi-modal magnetic resonance imaging (MRI).

A Illustration of physical mechanisms (Created in BioRender. Causemann, M. (2026) https://BioRender.com/k9y6s83). B Subject-specific computational geometry representation of the human brain parenchyma and cerebrospinal fluid (CSF) spaces, including the ventricular system (LV, lateral ventricles; V3& 4, third and fourth ventricles) and subarachnoid space (SAS). C The boundaries of the computational domain (LV, lateral ventricles; Pia, pia mater; AM-L and AM-U, lower and upper arachnoid mater, respectively; SSAS, spinal SAS). D rendering of the computational domain, including the perivascular space (PVS) networks. and E, F (peri)arterial and (peri)venous networks.

Relative to this geometry, we define two solute concentration fields, both varying in space and time, one in the 3D domains, one in the PVS networks, and we assume that the solute can cross between the 3D and 1D domains via semi-permeable membranes. We assume that the solute will diffuse within all compartments, with diffusivity depending on the effective properties of the relevant medium and the solute itself⁷⁷. We assume that flow in the CSF spaces will substantially affect solute transport, and we account for two main mechanisms: (i) convection via net CSF flow⁷⁸ and (ii) dispersive effects resulting from pulsatile CSF flow^54,56,79. In the surface periarterial spaces, in addition to diffusion, we account for convection via net fluid flow induced by peristaltic pumping^34,41. At the arterial PVS leaf nodes, we assume that the solute can distribute evenly into (or exit from) a local region of the surrounding 3D domain, at a rate governed by the difference between the average concentration in said region and at the leaf node and a diffusive conductance, together with the convective contribution from the periarterial net flow.

Specifically, we introduce the geometrically-reduced representation of the PVSs to bridge spatial scales, and model pulsatility via dispersion in the CSF and time-averaged flow in the PVS to bridge temporal scales. Mathematically, the solute transport model is represented by a mixed-dimensional system of coupled time-dependent partial differential equations⁶⁶, which we solve numerically with high accuracy using a mass-conserving finite element scheme. We remark that while we present a coupled framework for solute transport in the CSF spaces, brain parenchyma, and surface PVS networks, a comprehensive model of CSF and ISF flow is not within the scope of this work. In particular, we here demonstrate using separate, i.e., not coupled, flow models in the CSF spaces and PVS. The complete computational framework is implemented in the FEniCS finite element software^80,81, and all associated software is openly available⁶⁷.

In-silico tracer distribution after intrathecal injection

Before describing the CSF and perivascular flow modeling in further detail, we present a first demonstration of the computational framework. Intrathecal administration of gadolinium-based contrast agents in combination with MR imaging has emerged as a key technique to study solute distribution patterns in the human brain^{11,15,21,29,71}. We apply our framework to simulate such a contrast-enhanced MRI protocol¹⁵ by predicting the spreading of 0.5 mmol intrathecally injected Gadobutrol after its appearance at the craniocervical junction, represented by tracer inflow across the spinal SAS boundary over the first two hours (Fig. 2A). To define a baseline model, we consider a reasonably conservative set of flow patterns: the (small) net flow of CSF resulting from production in the choroid plexus with CSF efflux across the upper convexity⁷⁸, the dispersive effects of pulsatile CSF flow induced by the cardiac and respiratory cycles^54,56, and the periarterial net flow induced by cardiac pulse waves alone^34,41.

Fig. 2. In-silico predictions of tracer distribution after intrathecal injection.

A Illustration of the computational representation of an intrathecal tracer injection of Gadobutrol (Gad; Created in BioRender. Causemann, M. (2026) https://BioRender.com/f54s390). B In-silico predictions of tracer concentration after 1, 6, 12, and 24 h (opacity increasing linearly from 0 to 2 mmol/l). C Sagittal, coronal and axial views of in-silico tracer concentrations overlaid on T1-weighted magnetic resonance (MR) image after 1, 6, 12 and 24 h (low concentrations transparent, pial surface in pink, arachnoid membrane in cyan, and arteries in dark red). D Average tracer concentration in each compartment (PVS art., arterial PVS; PVS vein, venous PVS; PVS cont., unresolved continuation of the arterial PVS (0D compartments); PAR, parenchyma) over the first 24 h. E The total amount of tracer in each compartment over the first 24 h. Source data for panels D and E are provided at https://doi.org/10.5281/zenodo.14749162.

In this model, after one hour, the in-silico tracer moves upwards in the SAS frontally of the brainstem, and quickly reaches the supratentorial regions (Fig. 2B, C). Here, it spreads both posteriorly through the quadrigeminal cistern and the longitudinal fissure, and anteriorly through the outer SAS, reaching the top of the cerebral cortex after around 12 h. After 24 h, the tracer covers most of the brain surface (with the exception of some posterior regions) and has penetrated substantially into the parenchymal tissue. This pattern is reflected in the mean tracer concentrations in each compartment, where the CSF space reaches its peak of 1.33 mmol/l after 114 min, followed by the arterial PVS concentration peak (2.8 mmol/l after 3:46h) (Fig. 2D). While the mean concentrations in these compartments drop soon after peaking, the concentration in the parenchyma increases more slowly over the first 24 h, with a final value of 0.25 mmol/l. Overall, about 42% of the total amount of tracer remains in the cranium 24 h post-injection in this simulation, with the largest share in the CSF (49%), followed by the parenchyma (31%), the unresolved continuation of the arterial PVS (8%, captured via 0D downstream compartments), the venous PVS (7%) and the arterial PVS (5%) (Fig. 2E).

Modeling CSF flow and dispersion induced by pulsatility

The convective flow field and dispersion factors in the CSF spaces enter as coefficients in our computational framework for transport (u_CSF and R in (1)). To inform these, we have defined auxiliary computational flow models in the CSF spaces (see “Methods”, Fig. 1B, C and Supplementary Fig. S10). To model the convective flow field, we impose a constant CSF inflow of 400 mL/day at the lateral ventricle surfaces, representing the average daily physiological CSF production rate ⁸². This assumption yields a maximum flow velocity of 1.85 mm/s (in the aqueduct) and a mean velocity in the SAS of 2.6 μm/s (Fig. 3A, B). To estimate the dispersive effect of pulsatile CSF flow, we employ the theory of shear-augmented dispersion together with computational fluid dynamics to determine spatially varying dispersion factors R_c and R_r, enhancing the effective solute diffusivity in the CSF spaces by R = R_c + R_r. Assuming a cardiac frequency of 1 Hz, we infer that the cardiac-induced pulsatile CSF flow increases the effective diffusion by more than two orders of magnitude in the aqueduct and near the cisterna magna, but has little effect (R_c < 1) in most of the SAS (Fig. 1C, D). The dispersive effect from respiration reaches a factor of up to 320 due to the lower respiratory frequency of 0.25 Hz (Fig. 1E, F).

Fig. 3. Modeling convection and dispersion in the CSF spaces and how model variations alter computational predictions of tracer distribution patterns.

A CSF flow is induced by CSF production. B Histograms of the production-induced CSF velocities in the subarachnoid space (SAS) and third and fourth ventricle (V3 & V4) in terms of the relative frequency of the mean flow speed in each computational cell weighted by its volume. C Cardiac-induced dispersion factor R_c with histogram in (D). E Respiration-induced dispersion factor R_r with histogram in (F). In the baseline model, A represents the convective flow in the CSF spaces, while the factors R_c in (C) and R_r in E represent dispersion: D = (1  + R_c + R_r)D^Gad, where D^Gad is the free diffusion coefficient of Gadobutrol. G–J Sagittal, coronal and axial planes of tracer concentration after 12h for different model variations: baseline (G), no CSF production (H), low dispersion (I) and high dispersion (J). Source data for panels B, D and F are provided at https://doi.org/10.5281/zenodo.14749162.

Tracer distribution patterns observed after intrathecal injection differ substantially between subjects and in conditions associated with alterations in the pulsatile flow of CSF^7,15–17. Cardiac and respiratory pulsatility clearly also varies from subject to subject and between physiological states. Motivated by these observations, we illustrate tracer distribution patterns predicted by our computational framework resulting from modeling changes in CSF production or pulsatility. In particular, we introduce three variations of the baseline model: with (i) no CSF production, (ii) reduced pulsatility/decreased dispersion, and (iii) higher pulsatility/increased dispersion, respectively. We computed the reduced and increased pulsatility scenarios by halving and doubling the inflow rates associated with both cardiac and respiratory pulsations, which changed the dispersion factors by 0.25× and 4×, respectively. Note that this behavior directly reflects the nature of our CSF model: Stokes flow is linear in its inflow boundary conditions, and the diffusion enhancement factor is quadratic in the predicted pressure gradient.

Without the convective contribution from CSF production, transport is considerably delayed (Fig. 3G–H). Even after 12 h, tracer remains in the subtentorial regions around the cerebellum, the brain stem and in the surrounding CSF. Interestingly, our model instead predicts that the tracer will travel upwards through the ventricular system, reaching the third ventricle after around 12 h. On the other hand, in the model variation with reduced CSF pulsatility, we observe rapid transport towards the upper convexity of the cranium, as in the baseline model, but the tracer spreads exclusively within the anterior regions (Fig. 3I). This feature can be attributed to the CSF flow bifurcation posterior to the ambient cistern in our model (Fig. 3A): without sufficient diffusion, the tracer is unable to cross into the posterior SAS. Indeed, in the model variation with higher dispersion, the tracer moves through the quadrigeminal cistern and further upwards into the longitudinal fissure, also spreading into the cerebellum (Fig. 3J).

Modeling net flow in human surface periarterial networks

The PVSs are recognized across species as critical pathways for solute transport in and around the brain, and thus as potential targets for enhancing delivery or clearance. However, whether CSF flows more rapidly in PVSs and what the forces and mechanisms required to drive such flow are, remain as key points of debate^14,28,71. Motivated by experimental observations in animal models^10,32–34, there is now a remarkable body of literature on modeling perivascular fluid flow and transport^37–48. In particular, traveling waves of arterial wall motion, such as the pulse wave or other vasomotion^9,83–86, can induce net directional flow in the PVS^{40–42,46,87}—of magnitude and direction depending on the amplitude, frequency, and length of the waves and the characteristics of the perivascular network⁴¹. However, how these proposed mechanisms would translate from idealized geometries to human vascular networks stands as an open question.

Our periarterial network extends from the internal carotid arteries and basilar artery through up to 18 bifurcations to reach upstream network ends located within the SAS or up to 6 mm inside the parenchyma and includes major surface arteries of radius 0.5–1.4 mm (Fig. 4A). Due to imaging limitations, the network primarily covers the supratentorial regions, with the lowest network point located approximately 4 cm above the craniocervical junction. Applying a semi-analytic model of the net flow induced by peristalsis in this periarterial network⁴¹ (Fig. 4B), we estimate that the cardiac pulse wave alone, traveling at a frequency of 1 Hz with a wavelength of 2.0 m and a 1% wall displacement⁸⁸, will induce mainly antegrade perivascular flow with an average net velocity of 1.05 μm/s while reaching up to 7.51 μm/s near larger, ventral vessels such as the MCA (Fig. 4C, D), and a total flow through the periarterial network of 12.8 mL/day. The same theory predicts that strong ultraslow vasomotions, if traveling antegrade at 0.1 Hz with a wavelength of 0.02 m and a 10% displacement⁸⁶, will induce both retrograde and antegrade net perivascular flow with an average velocity of 12.87 μm/s and maximum velocity 60.05 μm/s, and a total flow of 213.7 mL/day (Fig. 4E, F).

Fig. 4. Modeling of pulsation-induced net flow in human surface periarterial networks.

A Surface arterial network colored by arterial radius with vessel locations labeled (BA basilar artery; ICA internal carotid artery; MCA middle cerebral artery; PCA posterior cerebral artery; ACA anterior cerebral artery; PER pericallosal artery). B Illustration of the concept of peristaltic pumping (Created in BioRender. Causemann, M. (2026) https://BioRender.com/p80b169). C Estimated net periarterial flow induced by pulse wave peristaltic pumping alone. D Histogram of estimated cardiac-driven net PVS flow induced by pulse wave peristaltic pumping; Histograms show the relative frequencies of local periarterial velocities. Positive values indicate antegrade perivascular flow, while negative values indicate retrograde PVS flow. E Estimated net periarterial flow induced by vasomotion/slow wave peristaltic pumping alone. F Histogram of estimated net periarterial flow induced by vasomotion peristaltic pumping. Source data for panels D and F are provided at https://doi.org/10.5281/zenodo.14749162.

A natural next question is how such variations in the net periarterial flow would affect tracer distribution patterns. To illustrate, we introduce a model variation with higher net flow in the PVS by adding the contribution from strong ultraslow vasomotion to that from the cardiac pulse wave, and compare with the baseline model. Tracers first reached the basal artery after 52 min in the baseline model and 58 min in the high-flow model (Fig. 5A), as quantified by their first-time arrival (FTA), defined as the time at which the concentration first exceeds 0.1 mmol/l. At all upstream locations along the middle cerebral arteries (MCAs) and anterior cerebral artery (ACA), we found substantially reduced FTAs with higher perivascular flow (Fig. 5B), up to 2:36 h earlier in the left M2 segment of the MCA. PVS concentrations peaked before the surrounding tissue (0:38 h and 1:06 h time lag at the MCA, and 0:46 h and 1:22 h at MCA2) with high PVS flow, while these peaks occurred nearly simultaneously at the left MCA and with a smaller delay at the right MCA in the baseline model. The earlier appearance and the delay in time-to-peak between the PVS and surrounding tissue clearly indicate the directionality of tracer movement in our model—it first arrives in the PVS and subsequently spreads into the tissue and SAS (Fig. 5C, D), and especially so with higher perivascular flow. These observations also hold on an aggregated level: computing the total amount of tracer in the PVS as a function of the distance to the arterial network roots, we find accelerated tracer transport with higher perivascular flow, especially at earlier time points (2–9 h) (Fig. 5E). Moreover, differences in tracer transport along the PVS translate to altered distribution patterns on the whole-organ scale. For instance, after 4–6 h, the faster-moving tracer in the PVS is clearly visible in the space adjacent to the PVS of the ACA, MCA, and other arteries (Fig. 5G). In contrast, there are no clear signs of early appearance of tracer surrounding the PVS in the baseline model (Fig. 5F).

Fig. 5. How variations in net periarterial flow affect tracer distribution pattern predictions.

A Comparison of mean tracer concentration in the PVS and over the outer PVS surface at key locations of the arterial tree, for the baseline (lower) and high PVS flow (upper) models, with labels: peak (time-to-peak, h), Δt (time difference between peaks, h), and FTA (first-time tracer arrival, h). B First-time arrival for the main trunks of the periarterial network over the distance from the closest network root node (BA, basilar artery; ICA-R/ICA-L, right/left internal carotid artery) for the baseline, the high PVS flow and the high PVS dispersion models. C, D 2D slices showing zoom-in on the region surrounding the middle cerebral artery (MCA-R and MCA2-R) for the baseline (upper) and high PVS flow (lower) models. Innermost circle indicates the artery (blue), the surrounding annulus is the PVS (color represents concentration value), the surroundings are parenchyma and/or CSF spaces, separated by the pia (blue: towards the parenchyma, pink: towards the CSF)). E Total amount of tracer in the periarterial spaces as a function of the distance to the nearest network root over time for the baseline (left) and the high PVS flow (right) models. F–H Sagittal (upper) and coronal (lower) views of the simulated tracer concentrations overlaid on the T1-weighted magnetic resonance (MR) image after 4 and 6 h for the baseline (F), high PVS flow (G) and high PVS dispersion (H) models (concentration opacity linearly increasing with concentration value, pial surface outlined in pink, arachnoid membrane in cyan, and arteries in dark red). An interactive visualization of the baseline and the high PVS flow model can be found here and here. Source data for panels A, B and E are provided at https://doi.org/10.5281/zenodo.14749162.

A related question is whether the early appearance of tracer in the PVS could be the result of increased dispersion rather than net flow in the PVS ^43,44,47,85. Interestingly, in our model, even increasing the dispersion factor by 100× in the PVS induced only minor changes in the global spreading rate compared to the baseline (Fig. 5F, H).

The diffusive permeability of the PVS-CSF interfaces

Human and rodent observations indicate that tracers concentrate in perivascular spaces surrounding the subarachnoid and pial vasculature^{23,29,33,34,61,89}. However, it remains unclear whether such distribution patterns necessitate a structural barrier, such as a membrane with limited permeability, or if the patterns could result from enhanced flow or mixing in these areas alone. We illustrate how these types of questions could be studied within our modeling framework by modifying the diffusive permeability of the interface between the PVSs and the surrounding CSF. In particular, we demonstrate two model variations representing a highly permeable PVS-CSF interface and a less permeable interface, respectively (Fig. 6). For the low permeability model, we set the diffusive permeability to 3.8 ⋅ 10⁻⁷ m/s, consistent with previous estimates for the endfoot sheath surrounding penetrating arterioles⁹⁰, which we consider to be a lower bound for the surface PVS-CSF permeability. For the high permeability model, we increase this diffusive permeability by a factor of 100. For both scenarios, we apply the high PVS flow model as described in the previous section.

Fig. 6. Exploring structure: varying the diffusive permeability of the PVS-CSF interfaces and its impact on tracer distribution predictions.

A In our model, the PVS-CSF membrane permeability regulates the exchange of solutes between the PVS and surrounding CSF spaces (Created in BioRender. Causemann, M. (2026) https://BioRender.com/e22i894). B The arterial network with highlighted regions of interest. C 2D slices showing zoom-in to the region surrounding the basal artery after 1, 2, 3, and 4 h for a low (above) and high (below) PVS-CSF permeability model. Innermost circle indicates the artery (blue), the surrounding annulus is the PVS (color represents concentration value), the surroundings are parenchyma and/or CSF spaces, separated by the pia (blue: towards the parenchyma, pink: towards the CSF). The cutting planes are normal to the blood vessels. D As in C for regions surrounding (from upper to lower) the anterior cerebral artery (ACA-A3, ACA-A2) and middle cerebral artery (MCA-R and MCA-L) segments. E Comparison of mean tracer concentration in the PVS (dashed) and over the outer PVS surface (dotted) for the basilar artery (BA), MCA-R, MCA-L, ACA-2, and ACA3 segments over time for the high (purple) and low permeability (yellow) models. F Effect of varying the PVS-CSF permeability on first-time-of-arrival (FTA), time difference (Δt) between concentration peaks in the PVS and surrounding tissue, time of PVS peak concentration, PVS peak concentration and difference in peak concentration between PVS and surrounding tissue. Source data for panels E and F are provided at https://doi.org/10.5281/zenodo.14749162.

At the basal artery (BA), tracer appears within one hour in the surrounding CSF in both models (Fig. 6C, E). With a more permeable PVS-CSF interface, tracer quickly crosses from the CSF into the PVS, resulting in similar peak concentrations of 25 mmol/l in the PVS and at its outer surface, while values up to 50 mmol/l are attained in the vicinity. In contrast, the low permeability model exhibits substantially lower perivascular tracer concentrations, with a maximum concentration of 10 mmol/l after approximately two hours. For the middle cerebral arteries (MCA-R and MCA-L), tracer appears first in the PVS in both models (Fig. 6D, E), though with higher concentrations in the high permeability model (up to 22 mmol/l). We also observe that the higher permeability allows the tracer to leak out of the PVS and spread within the Sylvian fissure to a greater extent. With a small delay, more tracer appears via the CSF pathway (Fig. 6D). At the anterior cerebral artery (ACA-A2), the first tracer arrival in the PVS occurs after 3 h, with a peak at 5 h. The concentration peak in the PVS is tailed by a higher peak in the CSF (Fig. 6E), indicating tracer arrival through a second pathway; i.e., directly through the CSF-filled space outside of the PVS. Similar patterns are observed for ACA-A3. In summary, neither the time of first arrival nor the time-to-peak is substantially affected by the PVS-CSF diffusive permeability at any of the periarterial segments considered (BA, MCAs, ACAs) (Fig. 6F). However, the concentration difference between the PVS and its surrounding CSF quickly decreases with higher diffusive permeability, as does the time lag between the concentration peaks in these domains.

The width of the PVS

Idiopathic normal pressure hydrocephalus (iNPH), a dementia subtype, is associated with enlarged PVS in the SAS and impaired periarterial and parenchymal tracer transport²⁹. More generally, enlarged PVSs are associated with a range of pathophysiological conditions and cognitive decline⁹¹. A natural question is thus whether enlarged PVSs alone lead to delayed perivascular and intracranial tracer spread. Again to illustrate how these types of questions could be addressed within our modeling framework, we consider a final model variation in which we examine the predicted effect of perivascular dilation on perivascular flow velocities and tracer distribution patterns (Fig. 7A). We again compute cardiac and vasomotion-induced net perivascular flow velocities, but now in a periarterial geometry with an increased outer radius ($R_2^{\mathrm{d}ilated}=3R_1$) compared to the previous ($R_2^{\mathrm{control}}=2R_1$), which corresponds to a 2.67 × increase in PVS cross-section area.

Fig. 7. Exploring structure: varying the width of the PVS and its impact on tracer distribution predictions.

A Modeling dilated PVS in the subarachnoid space (SAS) by extending the outer PVS boundaries (Created in BioRender. Causemann, M. (2026) https://BioRender.com/s78k932). B Mean and max PVS flow velocities with normal/control and dilated PVS. C, D 3D rendering of vasomotion-induced PVS flow in the normal (C) and dilated (D) periarterial networks. E 2D slices showing zoom-in to the region surrounding the middle cerebral artery (MCA-R) after 1, 2, 3, and 4 h with normal (lower) and dilated (upper) PVS. Innermost circle indicates the artery (blue), the surrounding annulus is the PVS (color represents concentration value), the surroundings are parenchyma and/or CSF spaces, separated by the pia (blue: towards the parenchyma, pink: towards the CSF). The cutting plane is normal to the blood vessel. F First-time arrival for different branches of the arterial tree for the baseline model (with pressure-driven and cardiac-induced net PVS flow) and the high PVS flow model (also including vasomotion-induced net PVS flow) for normal and dilated PVS. G Total tracer content in the CSF, parenchyma and arterial and venous PVS at 1,3,6,12 and 24 h for the four models from (F). H Mean concentration in the CSF, parenchyma and arterial and venous PVS over time for the four models from (F). Source data for panels F, G and H are provided at https://doi.org/10.5281/zenodo.14749162.

With dilated PVSs, the peristaltic pumping becomes considerably less effective: the cardiac and vasomotion-induced net CSF flow velocities drop from a mean of 1.05 μm/s to 0.19 μm/s and from 12.87 μm/s to 2.30 μm/s, respectively (Fig. 7B–D). In turn, this alters the tracer spread within the dilated PVS. Notably, we observe later tracer arrival in all MCA segments, with up to 2:04 h later arrival in the MCA2s for the high PVS flow scenario (Fig. 7E, F). For the model without vasomotion-induced flow, the effect is less pronounced in the MCA but clearly persists and is evident in the MCA2s (Fig. 7F). Finally, we note that the larger volume of the dilated PVS results in a greater total accumulation of tracer in the PVS from 3–24 h and reduced amounts of tracer in the parenchyma at 6 and 12 h, while the mean PVS concentration is initially lower, but later exceeds the baseline model (Fig. 7G, H).

Discussion

We have presented an in-silico modeling framework for solute transport in human intracranial spaces, informed by multi-modal structural MRI and integrating transport mechanisms across spatial and temporal scales. To demonstrate its features and applicability, we have presented a series of simulation scenarios relating to the intracranial distribution of a gadolinium-based contrast agent after intrathecal injection, exploring the influence of CSF space and (peri)vascular morphology as well as physiological factors such as cardiac, respiratory, and low-frequency pulsatility. In our simulations, the balance between CSF production and intracranial pulsatility significantly affects tracer distribution patterns at the macroscale, with e.g., ventricular tracer reflux after intrathecal injection in the absence of CSF production, and preference towards anterior brain regions with reduced pulsatility. In terms of perivascular pathways, even moderate net flow on the order of 0.1–1.0 μm/s in the surface PVSs results in earlier appearance of tracer around major cerebral arteries in our model scenarios. This effect is more pronounced—with up to a three-hour difference in time of arrival—with mean PVS flow rates of approximately 10 μm/s. Our models of CSF flow in perivascular networks, based on a full physical compartmentalization of the PVS in combination with first principles and asymptotic analysis, predict net flow of such magnitudes and both antegrade and retrograde flow within the periarterial network. In our simulations, the PVSs thus function as highways facilitating rapid transport, even in the absence of tight structural barriers to solute exchange. Note, however, that our PVS flow models are not coupled to flow in the SAS or within the brain parenchyma, a limitation of this work that is further discussed below.

While tracer spread within the brain and surrounding CSF spaces has been extensively studied in animal models, especially in murine models, there are fewer reports of intracranial tracer distribution in human subjects over 0–24 h after intrathecal injection. Direct validation of our transport model predictions is therefore not possible with the current data availability. Instead, we mainly compare our in-silico tracer predictions with the series of papers by Eide and colleagues^6,11,15,29 and Watts et al.⁹². Ringstad et al.¹⁵ report of tracer distribution in a centripetal pattern, primarily in regions near large cerebral surface arteries, peaking in the CSF spaces between 6 and 9 h, with parenchymal tracer content still increasing after 24 h, but with large individual differences. Watts et al.⁹² report of a similar distribution pattern and a concentration peak in the SAS of ≈0.5 mmol/l (relative to a total amount of 1.0 mmol) occurring after 10 to 15 h. Our in-silico tracer distribution patterns agree with these observations, though with an earlier rather than later peak in the CSF spaces (2 h after first tracer appearance at the craniocervical junction). In particular, we note that the variation in predicted distribution patterns associated with reduced CSF production or reduced intracranial pulsatility is compatible with the substantial individual variation observed clinically. Further, our simulated peak concentrations of 1.33 mmol/l in the CSF and 0.25 mmol/l in the parenchyma align closely with the peaks of 0.5 mmol/l and 0.1 mmol/l reported by Watts et al.⁹², once the twofold difference in injected tracer volume is taken into account.

To what extent does intracranial tracer transport rely on perivascular transport mechanisms beyond cardiac peristalsis? Dispersion due to cardiac and respiratory pulsations has been hypothesized to enhance transport in the perivascular spaces as well as in the CSF spaces. However, recent estimates indicate that the effect of dispersion in the PVS does not exceed a factor of 2 compared to diffusion alone ^43,44,47,85. Moreover, the effective diffusion is typically reduced in conduits with semi-permeable compared to non-permeable walls, see e.g. the analyses^93,94 and references therein. In our model, not even a 100-fold increase in the PVS dispersion coefficient accelerates transport substantially (Fig. 5H). We also compared our simulation results to tracer arrival times reported by Eide and Ringstad²⁹, who observed a delay of just 15.3 min between the M1 and M2 segments of the MCA. First, we note that the spaces studied by Eide and Ringstad²⁹, labeled therein as the PVSAS, are naturally compared to the parts of our surface PVS networks embedded within the SAS. Our baseline model, accounting for CSF production and cardiac-driven periarterial flow, predicted a physiologically unrealistic delay of more than 90 min. In contrast, our high PVS flow scenario, which incorporates the effects of low-frequency vasomotion, yielded a delay of 26 min (left) and 28 min (right), values more consistent with the clinical reports²⁹. Furthermore, after adjusting for the 13 min travel time from injection to the craniocervical junction²⁹, the high PVS flow model’s FTAs (82–102 min for M1) align well with the upper end of the reported clinical range (37.8 ± 47.0), particularly when considering potentially delayed transport due to the limited caudal extent of our PVS network.

The existence, magnitude, and directionality of flow in surface and parenchymal PVSs have been the subject of active debate for decades^{10,14,22,25,31–35,37–42,45,48,83,95}. In mice, Mestre et al.³⁴ observe CSF flow in surface perivascular regions surrounding branches of the MCA with average flow speeds of 18.7 μm/s and net flow in the antegrade direction, but also regions with retrograde flow. Similarly, Bedussi et al.³³ report of oscillatory flow, with an average (net) CSF velocity of 17 ± 2 μm/s in the antegrade direction. Using physics-informed neural networks, Boster et al.³⁵ estimate PVS velocities of 12.75 ± 6.25 μm/s. Less is known about the magnitude and directionality of CSF flow in surface PVSs in humans, though CSF flowmetry techniques that can measure slower flows, e.g., on the order of hundreds of μm/s in the SAS, are beginning to emerge⁹⁶, as are reports of flow surrounding surface periarterial spaces⁹⁷. Our estimates of time-averaged net flow in the periarterial networks, induced by cardiac pulsations and ultraslow vasomotion, feature spatially varying net flow rates with both antegrade and retrograde flow segments. In terms of magnitude, the contribution from cardiac wall motion is low to moderate (on average 1.05 μm/s), but intriguingly, our estimates of the contribution from vasomotion (12.87 μm/s) are comparable to the experimental reports. We do note that this estimate is based on the theoretical presence of rhythmic waves of vasomotion at a frequency of 0.1 Hz, a wavelength of 20 mm, an inner wall displacement of up to 10% in the antegrade direction, and an outer PVS membrane not permeable to fluid exchange, all values currently associated with major uncertainty^83,84,86,98. In particular, Broggini et al.⁸⁶ report of near-0.1 Hz vasomotion waves traveling both antegrade and retrograde along pial arterioles in mice, while Munting et al.⁸⁴ report of vessel diameter changes at similar frequencies mainly (but not entirely) in the retrograde direction. To the best of our knowledge, less is known about vasomotion wave characteristics in the human cerebral vasculature, though Gokina et al.⁹⁸ report of spontaneous vasomotion also in human pial arteries ex-vivo.

To what extent are the surface PVS separated from the surrounding SAS? Originally, Weller and coauthors^23,60,89 identified thin sheaths of pial cells surrounding human surface arteries (but not veins). On the other hand, Bakker and coauthors report that the SAS, the cisterns, and spaces surrounding major arteries and veins form a continuous CSF space⁶¹. Thorne and colleagues studied the architectures of rat perivascular spaces in detail, emphasizing the presence of openings (stomata) on the interface between the vasculature and the CSF within the SAS^27,62. Further, Mestre et al.⁶³ study the properties of pial perivascular spaces in mice, and report of pial cells forming sheaths for larger surface arteries and partially cover smaller surface arteries, with higher coverage in ventral SAS regions. In our simulations, the PVSs act as rapid transport pathways even with only a partial barrier to diffusion between the PVS and surrounding CSF, though under the assumption that the PVSs are fully physically compartmentalized with regard to flow. Indeed, we emphasize that we report on the isolated effect of variations in diffusive permeability on solute transport, separated from any effects on fluid flow in the PVS. Clearly, one would expect the properties of such a barrier to also affect PVS flow⁹⁹.

Lifestyle factors such as sleep^{5,6,8,9,85,100,101}, exercise^102,103, and alcohol intake¹⁰⁴ affect molecular transport and clearance of the brain. In particular, pial arteries display higher-amplitude low-frequency vasomotion during NREM and intermediate sleep states, while REM sleep is associated with reduced PVS width⁸⁵. Peristaltic pumping is more effective under both of these configurations, resulting in higher estimated net PVS flow velocities⁴¹. Even-higher PVS velocities would amplify the PVS flow effects simulated here, with earlier arrival times along the PVSs, clear distribution into adjacent spaces, and accelerated tracer spread overall. Moreover, sleep is linked with low-frequency oscillations in human CSF flow⁵⁵. The high dispersion scenario considered here can be viewed as representative of additional pulsatility induced by, e.g., neural waves^55,58 or other respiration patterns, depending on activity level.

In terms of limitations, we emphasize that while we here present a coupled modeling framework for solute transport in the CSF spaces, parenchyma, and surface PVS networks, we do not present a comprehensive, coupled model of fluid flow in the same compartments. Moreover, each of the separate fluid flow models comes with its own set of assumptions. Regarding the lack of coupling, we first note that our computational model for net flow in the surface periarterial networks is fully decoupled from (i.e., does not inform and is not informed by) the model for flow in the CSF spaces induced by CSF production. Moreover, these estimates of net flow in the PVS are based on the simplifying assumptions that human surface PVS follow the major surface vessels, are CSF-filled but otherwise open regions of width proportional to the vessel radius, have fixed outer boundaries that are not permeable to fluid exchange, and experience uniform traveling waves of vascular wall motion with specific characteristics. Thus, in particular, we represent a total flow of 12.8–213.7 mL/day in the periarterial network without explicitly modeling how this volume enters or exits the network and otherwise interacts with its surroundings. Our choice—to consider decoupled flow models—is based on the current lack of consensus on the underlying physiology, the mathematical and computational complexity associated with coupled mixed-dimensional fluid flow models, especially the auxiliary modeling choices to be made regarding interaction at the network end nodes, and our lack of more complete vascular network data.

Another important and related limitation relates to our approach of representing the dispersive effect of pulsatile CSF flow through an effective diffusion factor. This is a simplification that does not capture the full complexity of transient fluid dynamics, such as non-uniform wall motion and ependymal cilia within the ventricular system¹⁰⁵, dynamic CSF flow at the craniocervical junction, or the effect of microanatomical features such as subarachnoid trabeculae on flow resistance and dispersion in the SAS. In addition, we combine cardiac and respiratory dispersion enhancement factors in an additive manner. While there are theoretical considerations indicating that contributions from different frequencies are indeed additive¹⁰⁶ we note that such derivations rely on several simplifying assumptions, and therefore consider our dispersion estimates as heuristic. Overall, this approach has not been validated against direct spatio-temporal numerical simulations of solute transport in the CSF spaces in the presence of pulsatile fluid flow nor against clinical flow measurements; these points should be considered in future work. We do note that high-resolution MRI measurements by Hirschler et al.³⁶ reveal that CSF mobility in regions with high pulsatility is approximately tenfold greater than the self-diffusion of water, an enhancement factor consistent with the values used in our model. As a result of these limitations in the CSF flow modeling and the lack of direct validation data, the simulation scenarios presented here should be viewed as demonstrations of the applicability of the modeling framework rather than validated computational models.

Furthermore, we have considered a basic transport model within the parenchyma, modeling extracellular diffusion alone and no bulk interstitial fluid flow. Previously, by inferring transport parameters within the human brain from contrast-enhanced MRI data, we have found that solute transport within the parenchyma is well-represented by ≈3× enhanced diffusion augmented by local efflux, e.g., across the blood-brain barrier, or by diffusion-convection with a complex pattern of spatially-varying interstitial fluid flow on the order of 1–10 μm/min¹⁰⁰. We will incorporate such transport mechanisms within the parenchyma in future work.

Similarly, while our model incorporates the perivenous network for anatomical completeness, we intentionally kept its physics simplified. Unlike the arterial network, we do not model any active fluid flow mechanisms, and perivenous transport is thus purely driven by diffusion. This lack of active venous flow modeling, combined with our simplified model of the parenchyma, is the main reason we restrict our simulation to the first 24 h. While our current framework captures the early influx and distribution phases, accurately simulating later-stage brain clearance (e.g., 48 to 72 h post-injection) would require more detailed parenchymal and venous clearance mechanisms. Furthermore, direct validation of the in-silico perivenous signal against clinical measures is currently difficult; as recently noted by Eide and Ringstad²⁹, veins at the human brain surface are generally harder to depict on MRI than arteries, and perivenous tracer was identified in very few instances in their clinical cohort.

Due to the limited extent of our vascular networks, we lack representation of the cortical and subcortical vasculature. Concretely, we account for no vessels below the original MRI resolution limits, and thus only a part of the cerebral surface vasculature and effectively not the cortical vessels. In addition, and again due to a lack of resolution, there is uncertainty associated with the location of the vessel segments relative to the CSF spaces and parenchyma, with some vessels surrounded by both domains and some vessels completely entering the parenchyma before returning to the SAS. Higher resolution MRI data (T1w and e.g., time-of-flight, QSM or other modalities) in more subjects would immediately allow for more detailed studies of this aspect. Finally, we also note that we simulate the intracranial distribution of a tracer concentration appearing at the craniocervical junction rather than as an intrathecal injection. We thus neglect absorption of both CSF and tracer in the spinal compartment, and therefore overestimate the amount of tracer entering the intracranial spaces; however, due to the linearity of the mathematical model, it is valid to directly interpret the in-silico concentrations relative to the total amount of tracer.

In conclusion, this computational framework allows for transferring and integrating insights from experimental and clinical studies and theoretical analysis to a virtual human setting. The complete simulation pipeline is openly available, including interactive visualization of simulation results for all model variations⁶⁷. Advancing this platform to a fully coupled flow framework requires a stable discretization of a 3D-1D Stokes-Darcy flow model that integrates vascular pulsations into a net flow field, alongside resolving open biophysical questions regarding PVS-tissue and PVS-SAS fluid exchange, and the boundary treatment of the artificially truncated network ends. Future studies will focus on direct model validation, including comparisons between in-silico predictions and contrast-enhanced MRI for a number of subjects across several patient cohorts. Moreover, the rapid development of new CSF flow and mobility imaging techniques^36,96,97 offers striking opportunities – both for model validation or for directly informing the model parameters. Looking ahead, this framework establishes a foundation for in-silico studies of solute movement within the human brain environment.

Methods

This section gives a condensed summary of the in-silico modeling framework. For a complete description of the mathematical models and simulation scenarios, we refer to the Supplementary Methods.

Intracranial spaces: ventricular system, SAS, and parenchyma

From T1-weighted MR images of a 26-year-old, healthy male volunteer⁷², we first automatically segment the brain parenchyma and CSF spaces, including the ventricular system and SAS, using Synthseg^107,108 (Fig. 1A–B). We next manually adjust the segmentation to accurately represent the connections and barriers between CSF spaces (aqueduct, median aperture, tentorium cerebelli), smooth, and finally extract surface representations of the outer (arachnoid) boundary, the pial membrane and other interfaces. Conforming to these surface and interface representations, we generate a tetrahedral mesh Ω representing the complete intracranial volume as the union of the parenchyma Ω_PAR and CSF spaces Ω_CSF, using fTetWild¹⁰⁹ (Fig. 3A–B). The resulting computational mesh consists of 233,592 vertices and 1 290,131 mesh cells, which vary between 0.22 mm and 8.9 mm in mesh cell diameter. The parenchyma has a total volume of 1318 ml, whereas the ventricles and the outer SAS contribute 32 ml and 329 ml, respectively, to a total CSF volume of 361 ml, in agreement with recent estimates¹¹⁰.

Periarterial and perivenous spaces

To represent surface networks of periarterial and perivenous spaces, we use Kiminaro¹¹¹ to separately skeletonize time-of-flight angiography (ToF) and quantitative susceptibility mapping (QSM) images from the same human subject⁷². This technique yields networks of one-dimensional curves, each curve Λⁱ indicating the centerline of a blood vessel segment and labeled with its lumen radius $R_1^i$ (Fig. 4A). We also assign an outer radius $R_2^i>R_1^i$ to each segment i, form the annular cylinder ensheathing Λⁱ and define the union of these as the PVS. The periarterial network graph consists of 12,708 edges connected at 12,562 inner nodes and with 147 end nodes, and the associated domain is denoted by Λ_a. We identify three of the end nodes – corresponding to the two internal carotid arteries (ICAs) and the basilar artery (BA) – as root nodes, and designate the other ends as leaf nodes. The resulting perivenous network graph consists of 24 829 edges connected at 23 881 inner nodes and with 949 end nodes, and the associated domain is denoted by Λ_v. Finally, we label the outer surface of the PVSs associated with Λ_a and Λ_v, by Γ_a and Γ_v, respectively.

Steady flow in the CSF spaces induced by CSF production

We model CSF as an incompressible Newtonian fluid at low Reynolds and Womersley numbers via the Stokes equations with viscosity μ (see Table 1 for parameter values). To account for steady flow induced by CSF production, we compute the CSF velocity field u_CSF and associated pressure field p_CSF in the SAS and ventricular system Ω_CSF that result from a steady CSF production at a rate of u_in = 400 mL/day across the lateral ventricle walls (Fig. 1). We allow for CSF efflux across the upper, outer (arachnoid) boundary with efflux resistance R_CSF,0. In model variations with no CSF production, we set u_CSF = 0, p_CSF = 0.

Table 1.

Model parameters

Parameter	Symbol	Value	Unit	Reference
Extracellular space volume fraction	ϕECS	0.2	–	124
Free diffusion coefficient, Gadobutrol	DGad	3.8 ⋅ 10−4	mm2/s	125
Parenchymal diffusion coefficient, Gadobutrol	$D_{\mathrm{PAR}}^{\mathrm{Gad}}$	1.2 ⋅ 10−4	mm2/s	78
Diffusive permeability coefficient, endfoot sheath	ξEF	3.8 ⋅ 10−7	m/s	90
Diffusive permeability coefficient, PVS–CSF	ξPV S	3.8 ⋅ 10−7	m/s	90
Diffusive permeability coefficient, pia	βpia	2.6 ⋅ 10−8	m/s	126
Solute efflux rate	βexit	8.0 ⋅ 10−7	m/s	*
Total amount of injected tracer	mtot	0.5	mmol	29
Solute influx, time-to-peak	$T_{\max }$	1	h	*
CSF production rate	uin	0.4	l / day	127
CSF viscosity	μ	0.7	mPa ⋅ s	128
CSF outflow resistance	RCSF,0	104	Pa ⋅ s/m	*
Dispersion factor, CSF spaces	R	†	–	*

†/* denotes computed/estimated within this work. The diffusion coefficient D^Gad represents the diffusion coefficient of Gadobutrol in CSF (water), and $D_{\mathrm{PAR}}^{\mathrm{Gad}}$ its effective diffusion coefficient in human cortical tissue, both at body temperature^77,78,125. We use the astrocytic endfeet diffusive permeability ξ_EF estimated by Koch et al.⁹⁰, and we set ξ_{PV S} = ξ_EF as a baseline.

Dispersion in the CSF spaces induced by pulsatile CSF flow

The pulsatile flow of CSF in the SAS and ventricular system substantially enhances molecular diffusion through dispersion^{43,44,47,79,112,113}. To account for such dispersive effects, while bridging from the pulsatile flow time scale of seconds to a solute transport time scale of hours, we estimate spatially-varying, cardiac- and respiratory dispersion factors (R_c and R_r) in Ω_CSF (Fig. 1). Combining the cardiac and respiratory effects, we set R = R_c + R_r in Ω_CSF. To compute R_c and R_r, we rely on a simplified model that combines computational estimates of peak CSF pressure gradients (Fig. 1) with theoretical estimates for shear-augmented (Taylor) dispersion ^44,112,113. We present the method in brief here, and refer to the Supplementary Methods, S1.3 Estimating dispersion factors from pulsatile CSF flow, for a comprehensive description.

To estimate the cardiac contribution, we compute the steady state CSF pressure and flow fields at peak systolic blood inflow. Modeling the reduction in CSF space volume corresponding to peak systolic conditions, we assume a total inflow rate of 6 ml/s^57,114 in the SAS across its outer surface and 0.31 ml/s across the lateral ventricle surface⁵⁶. This scenario sets up a pressure drop of 10 Pa (0.075 mmHg) between the lateral ventricles and the spinal SAS and a maximum flow velocity of 19.8 cm/s (Supplementary Fig. S10A). For the respiratory contribution, we employ the same methodology, but with a total rate of 1 ml/s¹¹⁵ in the SAS and 0.121 ml/s¹¹⁶ in the lateral ventricles, yielding a respiratory peak flow volume of 1.121  ml/s at the craniocervical junction (Supplementary Fig. S10B). While the resulting flow velocities are only about one fourth of their cardiac-induced counterparts, the respiratory dispersive effect reaches a factor of up to 320 due to the lower respiratory frequency of 0.25 Hz.

Perivascular fluid flow induced by arterial wall motion

Using the theoretical framework introduced by Gjerde et al.⁴¹, we also compute analytic estimates for the time-average perivascular flow rate $⟨Q^{\prime }⟩$ induced by peristalsis in the arterial network Λ_a; i.e. the net flow induced by traveling waves of arterial wall motion of frequency f, amplitude ε and wave lengths λ (Fig. 4C). The corresponding contribution to the periarterial flow velocity is defined for each segment Λ_i as $⟨Q_i^{\prime }⟩/A_i$ where $A_i=\pi \left({R_2^i}^2-{R_1^i}^2\right)$ is the cross-section area of the PVS segment and $⟨Q_i^{\prime }⟩$ is the estimated mean flow rate (see Supplementary Methods, S1.4 Estimating net perivascular flow induced by peristaltic waves, for more details). Two wall motion patterns are considered: cardiac pulsations with f = 1.0 Hz, λ = 2 m and ε = 1% yielding ${\widehat{u}}_a^c$ (Fig. 4D), and very low-frequency vasomotion with f = 0.1 Hz, λ = 0.02 m, and ε = 10% yielding ${\widehat{u}}_a^v$ (Fig. 4E). No flow induced by peristalsis is considered for the perivenous network, and we thus set ${\widehat{u}}_v=0$ in Λ_v in all simulations. Consequently, solute transport within the perivenous spaces is driven solely by diffusion and passive exchange with the surrounding tissue. For the periarterial network, we account for cardiac peristalsis in the baseline model, and set $\widehat{u}$ as ${\widehat{u}}_a={\widehat{u}}_a^c$ in Λ_a. We remark that none of these models account for fluid exchange across the lateral outer interface of the PVSs (over Γ_a, Γ_v), while fluid entry and exit are allowed at the end nodes of the PVS networks. However, note that we do not account for any coupling between the fluid flow entering/exiting the PVS networks and flow in the CSF spaces/parenchyma.

Solute transport equations

We represent the evolution and distribution of a solute in the CSF spaces Ω_CSF, brain parenchyma Ω_PAR, and periarterial and perivenous networks Λ_a ∪ Λ_v via a mixed-dimensional transport model⁶⁶ over a timescale of minutes to hours (Figs. 1A–B and 3A–C). The current model accounts for solute exchange between the CSF spaces, brain parenchyma, and the PVSs, diffusion within all compartments, dispersion and convection in the CSF spaces, and convection within the PVS. Specifically, for t > 0, we solve for a concentration field c(x, t) in the 3D intracranial compartments (for x ∈ Ω_CSF ∪ Ω_PAR), a cross section-averaged concentration field $\widehat{c}\left(s,t\right)$ in the perivascular networks (for s ∈ Λ_a, Λ_v), and a set of scalar concentrations $c_k^0\left(t\right)$ for the 0D compartments at the arterial leaf nodes, satisfying the following equations:

$${\partial }_{t}c-\nabla \cdot D\left(1+R\right)\nabla c+\nabla \cdot \left({\mathbf{u}}_{\mathrm{CSF}}c\right)+\xi \left(\overline{c}-\widehat{c}\right){\delta }_{\mathrm{\Gamma }}=S_{\mathrm{0D}\leftrightarrow \text{3D}}\mathrm{in}{\mathrm{\Omega }}_{\mathrm{CSF}},$$ 1a

$${\partial }_t\left(\varphi c\right)-\nabla \cdot D^{*}\nabla \left(\varphi c\right)+\nabla \cdot \left({\mathbf{u}}_{\mathrm{PAR}}c\right)+\xi \left(\overline{c}-\widehat{c}\right){\delta }_{\mathrm{\Gamma }}=S_{0\mathrm{D}\leftrightarrow 3\mathrm{D}}\mathrm{in}{\mathrm{\Omega }}_{\mathrm{PAR}},$$ 1b

$${\partial }_t\left(A\widehat{c}\right)-{\partial }_s\left(\widehat{D}A{\partial }_s\left(\widehat{c}\right)\right)+{\partial }_s\left(A\widehat{u}\widehat{c}\right)+\xi P\left(\widehat{c}-\overline{c}\right)=0\mathrm{in}{\mathrm{\Lambda }}_a,{\mathrm{\Lambda }}_v.$$ 1c

$$V_k{\partial }_t{c}_k^0-{\left(A\widehat{u}n\right)}_k^{+}\widehat{c}-{\left(A\widehat{u}n\right)}_k^{-}{c}_k^0-{\alpha }_k\left(\widehat{c}-c_k^0\right)-{\beta }_k\left({\overline{c}}_{B_k}-c_k^0\right)=0\forall y_k\in {\mathcal{N}}_{\mathrm{leaf}}.$$ 1d

In (1a), D is the (free) diffusion coefficient of the solute, R is the dispersion coefficient in the CSF spaces, u_CSF is the steady CSF velocity, ξ is a diffusive permeability allowing for solute transfer/exchange across the interfaces Γ_a, Γ_v between the periarterial and perivenous networks and their surroundings, the overlined $\overline{c}$ denotes the average of c over cross-sections of Γ_a, Γ_v, δ_Γ is a Dirac term concentrated on Γ_a, Γ_v, and S_0D↔3D is a localized mass transfer term coupling the 3D domains to unresolved downstream perivascular continuations. In (1d), these continuations are modeled as 0D compartments at the arterial leaf nodes ${\mathcal{N}}_{\mathrm{leaf}}$, where V_k is the effective downstream volume, n ∈ {−1, 1} is an orientation indicator pointing outward at the network ends, ${\left(A\widehat{u}n\right)}_k^{\pm }$ denotes the outward/inward advective fluid flux, α_k and β_k are the 1D-0D and 0D-3D diffusive conductances respectively, and ${\overline{c}}_{B_k}$ is the locally averaged 3D concentration. Additionally, in (1b), ϕ = ϕ_ECS is the brain extracellular volume fraction, D^* is the effective diffusion coefficient in the parenchyma, and u_PAR is an interstitial fluid velocity. In this study, we set u_PAR = 0. In (1c), $A=\pi \left(R_2^2-R_1^2\right)$ is the area and P = 2πR₂ is the perimeter of the PVS cross-sections, $\widehat{D}$ is the effective diffusion coefficient in the PVSs, and $\widehat{u}$ is the fluid velocity (in the axial direction) in the PVS defined for the periarterial and perivenous spaces separately ($\widehat{u}{\mid }_{{\mathrm{\Lambda }}_a}={\widehat{u}}_a$, $\widehat{u}{\mid }_{{\mathrm{\Lambda }}_v}={\widehat{u}}_v$). Further, we model the membrane between the parenchyma and the CSF spaces as a semi-permeable membrane with diffusive permeability coefficient β_pia, allowing for a jump in c there. The initial concentrations in Ω and networks Λ_a, Λ_v are all set to zero.

Solute efflux from the intracranial space and perivascular network ends

We model solute efflux into the meningeal lymphatics or other pathways, across the upper, outer (arachnoid) boundary (Figs. 1A and 3C), proportional to the concentration in the SAS with a rate constant β_exit. At all other perivascular network end nodes not coupled to the 0D compartments (i.e., the arterial root nodes and all perivenous end nodes), we prescribe a no-flux boundary condition.

Intracranial influx after intrathecal injection

To represent solute influx into the intracranial compartments following intrathecal injection, without modeling the spinal compartment explicitly, we prescribe a time-dependent influx over the interface towards the spinal CSF compartment with the condition

$$\left(D\nabla c-{\mathbf{u}}_{\mathrm{CSF}}c\right)\cdot \mathbf{n}=g_{\mathrm{influx}},\mathrm{on}{\mathrm{\Gamma }}_{\mathrm{SSAS}}.$$

Here we set

$$g_{\mathrm{influx}}\left(t\right)=\frac{m_{\mathrm{tot}}}{T_{\max }^2\mid {\mathrm{\Gamma }}_{\mathrm{SSAS}}\mid }\max \left(0,T_{\max }-\mid t-T_{\max }\mid \right),$$ 2

which expresses a hat-shaped influx function with a peak at $T_{\max }$ and a total tracer injection of m_tot (Table 1). We here consider a fixed $T_{\max }=1.0$ h in (2), and do not consider the effect of, e.g., reduced pulsatility on spinal transit time.

Model and material parameters

Model and material parameters are summarized in Table 1, and Table 2 gives an overview of the different in-silico scenarios. The effective diffusion coefficient is set equal to that of Gadobutrol in water in the PVS networks $\widehat{D}=D\equiv D^{\mathrm{Gad}}$; is weighted by the dispersion factor R in the CSF spaces: (1 + R)D; and modulated by the porosity and tortuosity (λ = 1.78) in the parenchyma $D^{*}=D_{\mathrm{PAR}}^{\mathrm{Gad}}$. We set ξ depending on whether the PVS segment is fully embedded within the CSF spaces (ξ = ξ_{PV S}) or parenchyma (ξ = ξ_EF), or neither (see also Supplementary Methods).

Table 2.

Overview of model variations, with color highlighting changes from the baseline model

No.	Model description	uCSF	$\widehat{u}{\mid }_{{\mathrm{\Lambda }}_a}$	$\widehat{u}{\mid }_{{\mathrm{\Lambda }}_v}$	R	ξPV S	R2
0	Baseline	uCSF	${\widehat{u}}_a^c$	0	Rc + Rr	ξEF	2R1
1	No CSF production	0	${\widehat{u}}_a^c$	0	Rc + Rr	ξEF	2R1
2	Reduced CSF pulsatility	uCSF	${\widehat{u}}_a^c$	0	$R_c^{\mathrm{red}}+R_r^{\mathrm{red}}$	ξEF	2R1
3	Increased CSF pulsatility	uCSF	${\widehat{u}}_a^c$	0	$R_c^{\mathrm{inc}}+R_r^{\mathrm{inc}}$	ξEF	2R1
4	Higher PVS flow	uCSF	${\widehat{u}}_a^c+{\widehat{u}}_a^v$	0	Rc + Rr	ξEF	2R1
5	Higher PVS exchange	uCSF	${\widehat{u}}_a^c+{\widehat{u}}_a^v$	0	Rc + Rr	100 ξEF	2R1
6	Dilated PVS in the SAS	uCSF	${\tilde{u}}_a^c+{\tilde{u}}_a^v$	0	Rc + Rr	ξEF	3R1

u_CSF is the CSF velocity field induced by CSF production in Ω_CSF. Moreover, ${\widehat{u}}_a^c$ and ${\widehat{u}}_a^v$ are the periarterial velocities induced by arterial pulse wave wall motion and slow vasomotion, respectively. R_c + R_r is the combined cardiac and respiratory dispersion factor in the CSF spaces, with model variations $R_{r/c}^{\mathrm{red}}$ and $R_{r/c}^{\mathrm{inc}}$ corresponding to reduced pulsatility and increased pulsatility, respectively. Each PVS cross-section is modeled as a concentric annulus with inner radius R₁ and outer radius R₂ > R₁. Finally, ${\tilde{u}}_a^c$ and ${\tilde{u}}_a^v$ are as ${\widehat{u}}_a^c$ and ${\widehat{u}}_a^v$, respectively, but with a dilated PVS (R₂ = 3R₁).

Numerical approximation, implementation, and verification

We give a concise summary of the numerical approach here (see Supplementary Methods for a comprehensive description). To solve (1) numerically, we use the interior penalty discontinuous Galerkin (DG) method with weighted averages and upwinding for the convection term in the 3D domains¹¹⁷—to ensure numerical stability and minimize the artificial presence of negative concentration values. For the 1D domain, we use continuous finite element spaces defined over each of the networks and stabilized with numerical diffusion when $\widehat{u}$ is non–zero. Note that the 3D–1D coupling in (1) leads to a 3D solution c with low regularity properties. Thus, one can only expect lower-order error convergence near Λ_a and Λ_v, see the refs. ^118,119 for the numerical analysis of DG and continuous Galerkin schemes, respectively. However, away from these 1D networks, an almost optimal approximation is expected^120,121. To numerically solve the Stokes equations to compute the CSF flow velocity and pressure in the ventricular system and SAS, we use finite element spaces that preserve the incompressibility condition on the discrete level¹²². This requirement is important for numerical stability when subsequently solving (1)¹²³. The spaces we used for the velocity are continuous along the normal direction; continuity of the tangential component is enforced via interior penalty approaches¹²². Optimal approximation properties are expected for this scheme. These numerical methods were implemented using the FEniCS finite element framework⁸⁰, and the 3D-1D coupling is handled by the extension FEniCS_ii⁸¹. The correctness and accuracy of the numerical solutions were verified by a series of numerical verification experiments (see Supplementary Methods, S1.6 Numerical verification).

The majority of the simulation time was spent on the Stokes flow and transport model simulations. Each Stokes flow simulation utilizes a hybrid parallel approach with 16 MPI processes and 4 threads each, requiring approximately 300 GB of RAM and completing in 23 min. The transport model is limited to serial execution by FEniCS_ii, but employs 16 threads for the linear system factorization, taking 22 min and consuming about 50 GB of memory on an AMD EPYC 9684X machine.

Comparison with literature results

As the primary means of model validation, we compare the in-silico predictions of tracer distribution against contrast-enhanced MRI studies (Discussion). In addition, we compare auxiliary model quantities (CSF flow rates and pressure differences, dispersion factor estimates, and the shapes and sizes of PVSs) with the current literature (see Supplementary Discussion).

Reporting summary

Further information on research design is available in the Nature Portfolio Reporting Summary linked to this article.

Author contributions

M.C., M.K, R.M., and M.E.R. conceived and designed the project. M.C., M.K, R.M., and M.E.R. contributed to software development. M.C., M.K., and R.M. conducted the experiments. M.C. analyzed the results and prepared the figures. M.C., M.K., R.M., and M.E.R wrote the manuscript. All authors edited and reviewed the manuscript.

Peer review

Peer review information

Nature Communications thanks the anonymous reviewer(s) for their contribution to the peer review of this work. A peer review file is available.

Funding

M.C., R.M., and M.E.R. acknowledge support from the Research Council of Norway via grant #324239 (EMIx). M.E.R. acknowledges support from Stiftelsen Kristian Gerhard Jebsen via the K. G. Jebsen Center for Brain Fluid Research and from the Research Council of Norway via grant #360005 (DigiCells). M.K. acknowledges support from the RCN grant #303362. M.C. acknowledges support from the European Research Council under grant #101141807 (aCleanBrain). Simulations were performed on the Experimental Infrastructure for Exploration of Exascale Computing (eX3), which is financially supported by the RCN under contract 270053.

Data availability

Numerical simulation results generated as part of this study have been deposited on Zenodo with the identifier https://doi.org/10.5281/zenodo.14749162. This archive includes surface triangulations used for geometry representation, computational meshes (3D meshes and 1D networks), segmentations, sample simulation outputs from the baseline and high PVS flow models, animations, and relevant source data files for the figures and tables.

Code availability

The software developed to generate and analyze the numerical results of this study has been deposited on Zenodo with the identifier https://doi.org/10.5281/zenodo.14749162. In addition to simulation and analysis software, this archive also includes surface triangulations used for geometry representation, computational meshes (3D meshes and 1D networks), segmentations, sample simulation outputs from the baseline and high PVS flow models, animations, and relevant source data files for the figures and tables.

Competing interests

The authors declare no competing interests.

Supplementary information

The online version contains supplementary material available at https://doi.org/10.1038/s41467-026-77174-z.