A Model for Interstitial Drainage Through a Sliding Lymphatic Valve.

This study investigates fluid flow and elastic deformation in tissues that are drained by the primary lymphatic system. A model is formulated based on the Rossi hypothesis that states that the primary lymphatic valves, which are formed by overlapping endothelial cells around the circumferential lining of lymphatic capillaries, open in response to swelling of the surrounding tissue. Tissue deformation and interstitial fluid flow through the tissue are treated using the Biot equations of poroelasticity and, the fluid flux (into the interstitium) across the walls of the blood capillaries, is assumed to be linearly related to the pressure difference across the walls via a constant of proportionality (the vascular permeability). The resulting model is solved in a periodic domain containing one blood capillary and one lymphatic capillary starting from a configuration in which the tissue is undeformed. On imposition of a constant pressure difference between blood and lymphatic capillaries, the solutions are found to settle to a steady state. Given that the magnitude of pressure fluctuations in the lymphatic system is much smaller than this pressure difference between blood and lymph, it is postulated that the resulting steady-state solution gives a good representation of the state of the tissue under physiological conditions. The effects of changes to the Young's modulus of the tissue, the blood-lymphatic pressure difference, vascular permeability and valve dimensions on the steady state are investigated and discussed in terms of their effects on oedema in the context of age- and pregnancy-related changes to the body.

Modelling in vivo action potential propagation along a giant axon.

A partial differential equation model for the three-dimensional current flow in an excitable, unmyelinated axon is considered. Where the axon radius is significantly below a critical value R(crit) (that depends upon intra- and extra-cellular conductivity and ion channel conductance) the resistance of the intracellular space is significantly higher than that of the extracellular space, such that the potential outside the axon is uniformly small whilst the intracellular potential is approximated by the transmembrane potential. In turn, since the current flow is predominantly axial, it can be shown that the transmembrane potential is approximated by a solution to the one-dimensional cable equation. It is noted that the radius of the squid giant axon, investigated by (Hodgkin and Huxley 1952e), lies close to R(crit). This motivates us to apply the three-dimensional model to the squid giant axon and compare the results thus found to those obtained using the cable equation. In the context of the in vitro experiments conducted in (Hodgkin and Huxley 1952e) we find only a small difference between the wave profiles determined using these two different approaches and little difference between the speeds of action potential propagation predicted. This suggests that the cable equation approximation is accurate in this scenario. However when applied to the it in vivo setting, in which the conductivity of the surrounding tissue is considerably lower than that of the axoplasm, there are marked differences in both wave profile and speed of action potential propagation calculated using the two approaches. In particular, the cable equation significantly over predicts the increase in the velocity of propagation as axon radius increases. The consequences of these results are discussed in terms of the evolutionary costs associated with increasing the speed of action potential propagation by increasing axon radius.

A model for fluid drainage by the lymphatic system.

This study investigates the fluid flow through tissues where lymphatic drainage occurs. Lymphatic drainage requires the use of two valve systems, primary and secondary. Primary valves are located in the initial lymphatics. Overlapping endothelial cells around the circumferential lining of lymphatic capillaries are presumed to act as a unidirectional valve system. Secondary valves are located in the lumen of the collecting lymphatics and act as another unidirectional valve system; these are well studied in contrast to primary valves. We propose a model for the drainage of fluid by the lymphatic system that includes the primary valve system. The analysis in this work incorporates the mechanics of the primary lymphatic valves as well as the fluid flow through the interstitium and that through the walls of the blood capillaries. The model predicts a piecewise linear relation between the drainage flux and the pressure difference between the blood and lymphatic capillaries. The model describes a permeable membrane around a blood capillary, an elastic primary lymphatic valve and the interstitium lying between the two.

Ionic Accumulation as a Diagnostic Tool in Perovskite Solar Cells: Characterizing Band Alignment with Rapid Voltage Pulses.

Despite record-breaking devices, interfaces in perovskite solar cells are still poorly understood, inhibiting further progress. Their mixed ionic-electronic nature results in compositional variations at the interfaces, depending on the history of externally applied biases. This makes it difficult to measure the band energy alignment of charge extraction layers accurately. As a result, the field often resorts to a trial-and-error process to optimize these interfaces. Current approaches are typically carried out in a vacuum and on incomplete cells, hence values may not reflect those found in working devices. To address this, a pulsed measurement technique characterizing the electrostatic potential energy drop across the perovskite layer in a functioning device is developed. This method reconstructs the current-voltage (JV) curve for a range of stabilization biases, holding the ion distribution "static" during subsequent rapid voltage pulses. Two different regimes are observed: at low biases, the reconstructed JV curve is "s-shaped", whereas, at high biases, typical diode-shaped curves are returned. Using drift-diffusion simulations, it is demonstrated that the intersection of the two regimes reflects the band offsets at the interfaces. This approach effectively allows measurements of interfacial energy level alignment in a complete device under illumination and without the need for expensive vacuum equipment.

Illumination Intensity Dependence of the Recombination Mechanism in Mixed Perovskite Solar Cells.

Recombination mechanisms in solar cells are frequently assessed through the determination of ideality factors. In this work we report an abrupt change of the value of the "apparent" ideality factor (nAP ) in high-efficiency FA0.71 MA0.29 PbI2.9 Br0.1 based mesoscopic perovskite solar cells as a function of light intensity. This change is manifested as a transition from a regime characterized by nAP ∼1.8-2.5 at low light intensities (<10 mWcm-2 ) to one characterized by nAP ∼1. This transition is equally observed in the recombination resistance extracted from open-circuit impedance measurements. We use drift-diffusion simulations with explicit consideration of ion migration to determine the origin of this transition. We find that a change ofrecombination mechanism concurrent with a modification of the concentration of ionic vacancies is the most likely explanation of the observed behaviour. In the drift-diffusion simulations we show that the apparent ideality factor is in fact affected by the ion vacancy concentration so it is not the optimal parameter to assess the dominant recombination mechanism. We argue that a procedure based on a recently derived "electronic" ideality factor obtained from the high frequency feature of the impedance spectrum is better suited to determine the recombination route that dictates the photovoltage.

On a biophysical and mathematical model of Pgp-mediated multidrug resistance: understanding the "space-time" dimension of MDR.

Multidrug resistance (MDR) is explained by drug transporters with a drug-handling activity. Despite much work, MDR remains multifaceted, and several conditions are required to generate drug resistance. The drug pumping was conceptually described using a kinetic, i.e., temporal, approach. The re-emergence of physical biology has allowed us to take into account new parameters focusing on the notion of space. This, in turn, has given us important clues regarding the process whereby drug and transporter interact. We will demonstrate that the likelihood of drug-transporter meeting (i.e., the affinity) and thus interaction are also driven by the mechanical interaction between drug molecular weight (MW) and the membrane mechanical properties. This should allow us to mechanically control drug delivery.

Vasomotion Drives Periarterial Drainage of Aß from the Brain.

In this issue of Neuron, van Veluw et al. (2020) show that elimination of solutes from the brain along arterial walls is driven by low-frequency arteriolar oscillations and suggest that age-related reduction of this vasomotion may contribute to impaired clearance of Aß.

Identification of recombination losses and charge collection efficiency in a perovskite solar cell by comparing impedance response to a drift-diffusion model.

Interpreting the impedance response of perovskite solar cells (PSCs) is significantly more challenging than for most other photovoltaics. This is for a variety of reasons, of which the most significant are the mixed ionic-electronic conduction properties of metal halide perovskites and the difficulty in fabricating stable, and reproducible, devices. Experimental studies, conducted on a variety of PSCs, produce a variety of impedance spectra shapes. However, they all possess common features, the most noteworthy of which is that they have at least two features, at high and low frequency, with different characteristic responses to temperature, illumination and electrical bias. The impedance response has commonly been analyzed in terms of sophisticated equivalent circuits that can be hard to relate to the underlying physics and which complicates the extraction of efficiency-determining parameters. In this paper we show that, by a combination of experiment and drift-diffusion (DD) modelling of the ion and charge carrier transport and recombination within the cell, the main features of common impedance spectra are well reproduced by the DD simulation. Based on this comparison, we show that the high frequency response contains all the key information relating to the steady-state performance of a PSC, i.e. it is a signature of the recombination mechanisms and provides a measure of charge collection efficiency. Moreover, steady-state performance is significantly affected by the distribution of mobile ionic charge within the perovskite layer. Comparison between the electrical properties of different devices should therefore be made using high frequency impedance measurements performed in the steady-state voltage regime in which the cell is expected to operate.

Cerebrovascular Smooth Muscle Cells as the Drivers of Intramural Periarterial Drainage of the Brain.

The human brain is the organ with the highest metabolic activity but it lacks a traditional lymphatic system responsible for clearing waste products. We have demonstrated that the basement membranes of cerebral capillaries and arteries represent the lymphatic pathways of the brain along which intramural periarterial drainage (IPAD) of soluble metabolites occurs. Failure of IPAD could explain the vascular deposition of the amyloid-beta protein as cerebral amyloid angiopathy (CAA), which is a key pathological feature of Alzheimer's disease. The underlying mechanisms of IPAD, including its motive force, have not been clarified, delaying successful therapies for CAA. Although arterial pulsations from the heart were initially considered to be the motive force for IPAD, they are not strong enough for efficient IPAD. This study aims to unravel the driving force for IPAD, by shifting the perspective of a heart-driven clearance of soluble metabolites from the brain to an intrinsic mechanism of cerebral arteries (e.g., vasomotion-driven IPAD). We test the hypothesis that the cerebrovascular smooth muscle cells, whose cycles of contraction and relaxation generate vasomotion, are the drivers of IPAD. A novel multiscale model of arteries, in which we treat the basement membrane as a fluid-filled poroelastic medium deformed by the contractile cerebrovascular smooth muscle cells, is used to test the hypothesis. The vasomotion-induced intramural flow rates suggest that vasomotion-driven IPAD is the only mechanism postulated to date capable of explaining the available experimental observations. The cerebrovascular smooth muscle cells could represent valuable drug targets for prevention and early interventions in CAA.

Experimental and theoretical modelling of blind-ended vessels within a developing angiogenic plexus.

Angiogenic sprouts at the leading edge of an expanding vascular plexus are recognised as major regulators of the structure of the developing network. Early in sprout development, a vascular lumen is often evident which communicates with the parent vessel while the distal tip is blind-ended. Here we describe the temporal evolution of blind-ended vessels (BEVs) in a small wound made in the panniculus carnosus muscle of a mouse viewed in a dorsal skin-fold window-chamber model with intra-vital microscopy during the most active period of angiogenesis (days 5-8 after injury). Although these structures have been mentioned anecdotally in previous studies, we observed BEVs to be frequent, albeit transient, features of plexus formation. Plasma leakage into the surrounding extracellular matrix occurring from these immature conduits could play an important role in preparing hypoxic tissue for vascular invasion. Although sprout growth is likely to be regulated by its flow environment, the parameters regulating flow into and through BEVs have not been characterised in situ. Longitudinal data from individual animals show that the number of BEVs filled with plasma alone peaks at day 7, when they can exceed 150 microm in length. Additionally, BEVs greater than 40 microm in length are more likely to be filled with stationary erythrocytes than with plasma alone. Using a mathematical model, we show how the flux of 150 kD fluorinated (FITC-) dextran through an individual plasma-filled BEV is related to its geometry being determined primarily by its surface area; by fitting theoretical intensity values to experimental data we assess the permeability of the vessel to FITC-dextran. Plasma skimming provides a mechanistic explanation for the observation that BEVs with larger surface area are more likely to recruit erythrocytes.

Arterial Pulsations cannot Drive Intramural Periarterial Drainage: Significance for Aß Drainage.

Alzheimer's Disease (AD) is the most common form of dementia and to date there is no cure or efficient prophylaxis. The cognitive decline correlates with the accumulation of amyloid-ß (Aß) in the walls of capillaries and arteries. Our group has demonstrated that interstitial fluid and Aß are eliminated from the brain along the basement membranes of capillaries and arteries, the intramural periarterial drainage (IPAD) pathway. With advancing age and arteriosclerosis, the stiffness of arterial walls, this pathway fails in its function and Aß accumulates in the walls of arteries. In this study we tested the hypothesis that arterial pulsations drive IPAD and that a valve mechanism ensures the net drainage in a direction opposite to that of the blood flow. This hypothesis was tested using a mathematical model of the drainage mechanism. We demonstrate firstly that arterial pulsations are not strong enough to produce drainage velocities comparable to experimental observations. Secondly, we demonstrate that a valve mechanism such as directional permeability of the IPAD pathway is necessary to achieve a net reverse flow. The mathematical simulation results are confirmed by assessing the pattern of IPAD in mice using pulse modulators, showing no significant alteration of IPAD. Our results indicate that forces other than the cardiac pulsations are responsible for efficient IPAD.

Improving the Long-Term Stability of Perovskite Solar Cells with a Porous Al2O3 Buffer Layer.

Hybrid perovskites represent a new paradigm for photovoltaics, which have the potential to overcome the performance limits of current technologies and achieve low cost and high versatility. However, an efficiency drop is often observed within the first few hundred hours of device operation, which could become an important issue. Here, we demonstrate that the electrode's metal migrating through the hole transporting material (HTM) layer and eventually contacting the perovskite is in part responsible for this early device degradation. We show that depositing the HTM within an insulating mesoporous "buffer layer" comprised of Al2O3 nanoparticles prevents the metal electrode migration while allowing for precise control of the HTM thickness. This enables an improvement in the solar cell fill factor and prevents degradation of the device after 350 h of operation.

Mathematical modeling predicts synergistic antitumor effects of combining a macrophage-based, hypoxia-targeted gene therapy with chemotherapy.

Tumor hypoxia is associated with low rates of cell proliferation and poor drug delivery, limiting the efficacy of many conventional therapies such as chemotherapy. Because many macrophages accumulate in hypoxic regions of tumors, one way to target tumor cells in these regions could be to use genetically engineered macrophages that express therapeutic genes when exposed to hypoxia. Systemic delivery of such therapeutic macrophages may also be enhanced by preloading them with nanomagnets and applying a magnetic field to the tumor site. Here, we use a new mathematical model to compare the effects of conventional cyclophosphamide therapy with those induced when macrophages are used to deliver hypoxia-inducible cytochrome P450 to locally activate cyclophosphamide. Our mathematical model describes the spatiotemporal dynamics of vascular tumor growth and treats cells as distinct entities. Model simulations predict that combining conventional and macrophage-based therapies would be synergistic, producing greater antitumor effects than the additive effects of each form of therapy. We find that timing is crucial in this combined approach with efficacy being greatest when the macrophage-based, hypoxia-targeted therapy is administered shortly before or concurrently with chemotherapy. Last, we show that therapy with genetically engineered macrophages is markedly enhanced by using the magnetic approach described above, and that this enhancement depends mainly on the strength of the applied field, rather than its direction. This insight may be important in the treatment of nonsuperficial tumors, where generating a specific orientation of a magnetic field may prove difficult. In conclusion, we demonstrate that mathematical modeling can be used to design and maximize the efficacy of combined therapeutic approaches in cancer.

Intracellular flow in optic nerve axons: a mechanism for cell death in glaucoma.

PURPOSE: In glaucoma, elevated intraocular pressure causes a progressive loss of retinal ganglion cells and results in optic neuropathy. The authors propose a potential mechanism for cell death, whereby elevated intraocular pressure causes fluid to permeate axonal membranes, creating a passive intracellular fluid flow within the axons. It is hypothesized that this intracellular flow locally depletes the adenosine triphosphate (ATP) concentration, disrupting axonal transport and leading to cell death. METHODS: A mathematical model was developed that takes into account the biomechanical principles underpinning the proposed hypothesis, and was solved to determine the implications of the mechanism. RESULTS: The model suggests that the raised intraocular pressures present in glaucoma are adequate to produce significant intracellular fluid flow. In the periphery of the optic nerve head, this flow may be sufficient to disrupt the diffusion of ATP and hence interrupt active axonal transport. CONCLUSIONS: The mathematical model demonstrates that it is physically plausible that a passive intracellular fluid flow could significantly contribute to the pathophysiology of the retinal ganglion cell axon in glaucoma.