Recanalization is the mainstay of ischemic stroke treatment. However, even with timely clot removal, many stroke patients recover poorly. Leptomeningeal collaterals (LMCs) are pial anastomotic vessels with yet-unknown functions. We applied laser speckle imaging, ultrafast ultrasound, and two-photon microscopy in a thrombin-based mouse model of stroke and fibrinolytic treatment to show that LMCs maintain cerebral autoregulation and allow for gradual reperfusion, resulting in small infarcts. In mice with poor LMCs, distal arterial segments collapse, and deleterious hyperemia causes hemorrhage and mortality after recanalization. In silico analyses confirm the relevance of LMCs for preserving perfusion in the ischemic region. Accordingly, in stroke patients with poor collaterals undergoing thrombectomy, rapid reperfusion resulted in hemorrhagic transformation and unfavorable recovery. Thus, we identify LMCs as key components regulating reperfusion and preventing futile recanalization after stroke. Future therapeutic interventions should aim to enhance collateral function, allowing for beneficial reperfusion after stroke.

Mathematical modelling allows to predict the state of a physical system based on a set of parameters. The corresponding inverse problem, i.e., when parameter values are inferred based on constraints imposed on the system state, is commonly ill-posed. Here, we consider consistent underdetermined problems, where infinitely many combinations of possible parameter values achieve a state that accurately matches all constraints. For such problems a unique regularization strategy can be used, where the ambiguity of the solution space is reduced by sequentially incorporating additional constraints. As this regularization approach always yields a consistent problem by construction, we now show that the Gauss-Newton method is the prime choice to achieve fast convergence. Moreover, using the adjoint method allows to efficiently compute the required Jacobian matrix, which makes the overall solution approach ideally suited for large test cases with many constraints and unknown parameters. We present results for several illustrative examples related to network flow, for which we visualize the solution manifolds of the regularized inverse problem. This provides an intuitive explanation of the hierarchical approach to reduce the ambiguity of the solution. Furthermore, we confirm that combining our regularization strategy with a Gauss-Newton method results in an order of magnitude lower computational cost compared to a gradient descent algorithm. This highlights the potential of our regularization strategy in combination with the Gauss-Newton method, which likely is beneficial for many comparable inverse problems, especially with large parameter spaces.

Leptomeningeal collaterals (LMCs) connect the main cerebral arteries and provide alternative pathways for blood flow during ischaemic stroke. This is beneficial for reducing infarct size and reperfusion success after treatment. However, a better understanding of how LMCs affect blood flow distribution is indispensable to improve therapeutic strategies. Here, we present a novel in silico approach that incorporates case-specific in vivo data into a computational model to simulate blood flow in large semi-realistic microvascular networks from two different mouse strains, characterised by having many and almost no LMCs between middle and anterior cerebral artery (MCA, ACA) territories. This framework is unique because our simulations are directly aligned with in vivo data. Moreover, it allows us to analyse perfusion characteristics quantitatively across all vessel types and for networks with no, few and many LMCs. We show that the occlusion of the MCA directly caused a redistribution of blood that was characterised by increased flow in LMCs. Interestingly, the improved perfusion of MCA-sided microvessels after dilating LMCs came at the cost of a reduced blood supply in other brain areas. This effect was enhanced in regions close to the watershed line and when the number of LMCs was increased. Additional dilations of surface and penetrating arteries after stroke improved perfusion across the entire vasculature and partially recovered flow in the obstructed region, especially in networks with many LMCs, which further underlines the role of LMCs during stroke.

Estimating modeling parameters based on a prescribed optimization target requires to solve an inverse problem, which is commonly ill-posed. Consequently, either infinitely many or no solutions may exist, depending on whether the system is under- or overdetermined, and whether it is consistent or inconsistent. This paper focuses on scenarios where the solution is ambiguous and infinitely many combinations of possible parameter values can accurately achieve the optimization target. Selecting the most suitable solution requires incorporating additional constraints into the model, which is achieved by regularizing the inverse problem. However, common regularization approaches require the specification of a priori unknown regularization hyperparameters that are difficult and tedious to obtain, and can have a large impact on the result. Here, a novel strategy to reduce the ambiguity of such inverse problems is presented, ensuring that the primary optimization target is always reached accurately. To further reduce the solution space, additional constraints are included, until the optimal modeling parameters are found. Importantly, the required regularization parameters have a direct physical meaning and can be derived sequentially, starting from an initial guess that can be obtained conveniently by solving the system without regularization. By considering several illustrative examples, the applicability of the method is demonstrated, and its potential for various comparable inverse problems is highlighted.

A dense network of blood vessels distributes blood to different regions of the brain. To meet the temporarily and spatially varying energy demand resulting from changes in neuronal activity, the vasculature is able to locally up-regulate the blood supply. However, to which extent diameter changes of different vessel types contribute to the up-regulation, as well as the spatial and temporal characteristics of their changes, are currently unknown. Here, we present a new simulation method, which solves an inverse problem to calculate diameter changes of individual blood vessels needed to achieve predefined blood flow distributions in microvascular networks. This allows us to systematically compare the impact of different vessel types in various regulation scenarios. Moreover, the method offers the advantage that it handles the stochastic nature of blood flow originating from tracking the movement of individual red blood cells. Since the inverse problem is formulated for time-averaged pressures and flow rates, a deterministic approach for calculating the diameter changes is used, which allows us to apply the method for large realistic microvascular networks with high-dimensional parameter spaces. Our results obtained in both artificial and realistic microvascular networks reveal that diameter changes at the level of capillaries enable a very localized regulation of blood flow. In scenarios where only larger vessels, i.e., arterioles, are allowed to adapt, the flow increase cannot be confined to a specific activated region and flow changes spread into neighboring regions. Furthermore, relatively small dilations and constrictions of all vessel types can lead to substantial changes of capillary blood flow distributions. This suggests that small scale regulation is necessary to obtain a localized increase in blood flow.

The acute rise in interstitial K+ that accompanies neural activity couples the energy demand of neurons to the metabolism of astrocytes. The effects of elevated K+ on astrocytes include activation of aerobic glycolysis, inhibition of mitochondrial respiration and the release of lactate. Using a genetically encoded FRET glucose sensor and a novel protocol based on 3-O-methylglucose trans-acceleration and numerical simulation of glucose dynamics, we report that extracellular K+ is also a potent and reversible modulator of the astrocytic glucose transporter GLUT1. In cultured mouse astrocytes, the stimulatory effect developed within seconds, engaged both the influx and efflux modes of the transporter, and was detected even at 1 mM incremental K+ . The modulation of GLUT1 explains how astrocytes are able to maintain their glucose pool in the face of strong glycolysis stimulation. We propose that the stimulation of GLUT1 by K+ supports the production of lactate by astrocytes and the timely delivery of glucose to active neurons.

Pore-scale simulations of multiphase flow in porous media are useful in understanding the relations between macroscopic variables relevant in many applications. It is critical that simulation domains are large enough to be considered representative elementary volumes for the relevant macroscopic quantities such as relative permeability, macroscopic capillary pressure and average saturation. However, multiphase pore-scale solvers, such as dynamic flow solvers for pore network models, are typically computationally expensive due to the required solution of a global pressure problem at every time-step. In this paper, an approximate multiscale flow solver is presented, which overcomes this limitation. The solver is applicable to arbitrary unstructured pore networks and consists of three main steps. First, the global pressure problem is solved using the multiscale finite volume (MSFV) method in combination with the multiscale restricted-smoothed basis (MsRSB) prolongation operator. The computed pressure field leads to conservative fluxes across pre-defined subnetwork boundaries. Second, these conservative fluxes are used as boundary conditions to solve local problems on the subnetworks. Third, once these local problems are solved, the subnetworks are synchronized. Validation studies are presented and results obtained using the multiscale solver are compared to results obtained using an existing dynamic network flow solver.