Mathematical model of oxygen, nutrient, and drug transport in tuberculosis granulomas.

Physiological abnormalities in pulmonary granulomas-pathological hallmarks of tuberculosis (TB)-compromise the transport of oxygen, nutrients, and drugs. In prior studies, we demonstrated mathematically and experimentally that hypoxia and necrosis emerge in the granuloma microenvironment (GME) as a direct result of limited oxygen availability. Building on our initial model of avascular oxygen diffusion, here we explore additional aspects of oxygen transport, including the roles of granuloma vasculature, transcapillary transport, plasma dilution, and interstitial convection, followed by cellular metabolism. Approximate analytical solutions are provided for oxygen and glucose concentration, interstitial fluid velocity, interstitial fluid pressure, and the thickness of the convective zone. These predictions are in agreement with prior experimental results from rabbit TB granulomas and from rat carcinoma models, which share similar transport limitations. Additional drug delivery predictions for anti-TB-agents (rifampicin and clofazimine) strikingly match recent spatially-resolved experimental results from a mouse model of TB. Finally, an approach to improve molecular transport in granulomas by modulating interstitial hydraulic conductivity is tested in silico.

Combining microenvironment normalization strategies to improve cancer immunotherapy.

Advances in immunotherapy have revolutionized the treatment of multiple cancers. Unfortunately, tumors usually have impaired blood perfusion, which limits the delivery of therapeutics and cytotoxic immune cells to tumors and also results in hypoxia-a hallmark of the abnormal tumor microenvironment (TME)-that causes immunosuppression. We proposed that normalization of TME using antiangiogenic drugs and/or mechanotherapeutics can overcome these challenges. Recently, immunotherapy with checkpoint blockers was shown to effectively induce vascular normalization in some types of cancer. Although these therapeutic approaches have been used in combination in preclinical and clinical studies, their combined effects on TME are not fully understood. To identify strategies for improved immunotherapy, we have developed a mathematical framework that incorporates complex interactions among various types of cancer cells, immune cells, stroma, angiogenic molecules, and the vasculature. Model predictions were compared with the data from five previously reported experimental studies. We found that low doses of antiangiogenic treatment improve immunotherapy when the two treatments are administered sequentially, but that high doses are less efficacious because of excessive vessel pruning and hypoxia. Stroma normalization can further increase the efficacy of immunotherapy, and the benefit is additive when combined with vascular normalization. We conclude that vessel functionality dictates the efficacy of immunotherapy, and thus increased tumor perfusion should be investigated as a predictive biomarker of response to immunotherapy.

Experimental and computational analyses reveal dynamics of tumor vessel cooption and optimal treatment strategies.

Cooption of the host vasculature is a strategy that some cancers use to sustain tumor progression without-or before-angiogenesis or in response to antiangiogenic therapy. Facilitated by certain growth factors, cooption can mediate tumor infiltration and confer resistance to antiangiogenic drugs. Unfortunately, this mode of tumor progression is difficult to target because the underlying mechanisms are not fully understood. Here, we analyzed the dynamics of vessel cooption during tumor progression and in response to antiangiogenic treatment in gliomas and brain metastases. We followed tumor evolution during escape from antiangiogenic treatment as cancer cells coopted, and apparently mechanically compressed, host vessels. To gain deeper understanding, we developed a mathematical model, which incorporated compression of coopted vessels, resulting in hypoxia and formation of new vessels by angiogenesis. Even if antiangiogenic therapy can block such secondary angiogenesis, the tumor can sustain itself by coopting existing vessels. Hence, tumor progression can only be stopped by combination therapies that judiciously block both angiogenesis and cooption. Furthermore, the model suggests that sequential blockade is likely to be more beneficial than simultaneous blockade.

Role of vascular normalization in benefit from metronomic chemotherapy.

Metronomic dosing of chemotherapy-defined as frequent administration at lower doses-has been shown to be more efficacious than maximum tolerated dose treatment in preclinical studies, and is currently being tested in the clinic. Although multiple mechanisms of benefit from metronomic chemotherapy have been proposed, how these mechanisms are related to one another and which one is dominant for a given tumor-drug combination is not known. To this end, we have developed a mathematical model that incorporates various proposed mechanisms, and report here that improved function of tumor vessels is a key determinant of benefit from metronomic chemotherapy. In our analysis, we used multiple dosage schedules and incorporated interactions among cancer cells, stem-like cancer cells, immune cells, and the tumor vasculature. We found that metronomic chemotherapy induces functional normalization of tumor blood vessels, resulting in improved tumor perfusion. Improved perfusion alleviates hypoxia, which reprograms the immunosuppressive tumor microenvironment toward immunostimulation and improves drug delivery and therapeutic outcomes. Indeed, in our model, improved vessel function enhanced the delivery of oxygen and drugs, increased the number of effector immune cells, and decreased the number of regulatory T cells, which in turn killed a larger number of cancer cells, including cancer stem-like cells. Vessel function was further improved owing to decompression of intratumoral vessels as a result of increased killing of cancer cells, setting up a positive feedback loop. Our model enables evaluation of the relative importance of these mechanisms, and suggests guidelines for the optimal use of metronomic therapy.

Mechanobiological oscillators control lymph flow.

The ability of cells to sense and respond to physical forces has been recognized for decades, but researchers are only beginning to appreciate the fundamental importance of mechanical signals in biology. At the larger scale, there has been increased interest in the collective organization of cells and their ability to produce complex, "emergent" behaviors. Often, these complex behaviors result in tissue-level control mechanisms that manifest as biological oscillators, such as observed in fireflies, heartbeats, and circadian rhythms. In many cases, these complex, collective behaviors are controlled--at least in part--by physical forces imposed on the tissue or created by the cells. Here, we use mathematical simulations to show that two complementary mechanobiological oscillators are sufficient to control fluid transport in the lymphatic system: Ca(2+)-mediated contractions can be triggered by vessel stretch, whereas nitric oxide produced in response to the resulting fluid shear stress causes the lymphatic vessel to relax locally. Our model predicts that the Ca(2+) and NO levels alternate spatiotemporally, establishing complementary feedback loops, and that the resulting phasic contractions drive lymph flow. We show that this mechanism is self-regulating and robust over a range of fluid pressure environments, allowing the lymphatic vessels to provide pumping when needed but remain open when flow can be driven by tissue pressure or gravity. Our simulations accurately reproduce the responses to pressure challenges and signaling pathway manipulations observed experimentally, providing an integrated conceptual framework for lymphatic function.

Lymph node effective vascular permeability and chemotherapy uptake.

OBJECTIVE: Lymph node metastases are a poor prognostic factor. Additionally, responses of lymph node metastasis to therapy can be different from the primary tumor. Investigating the physiologic lymph node blood vasculature might give insight into the ability of systemic drugs to penetrate the lymph node, and thus into the differential effect of therapy between lymph node metastasis and primary tumors. Here, we measured effective vascular permeability of lymph node blood vessels and attempted to increase chemotherapy penetration by increasing effective vascular permeability. METHODS: We developed a novel three-dimensional method to measure effective vascular permeability in murine lymph nodes in vivo. VEGF-A was systemically administered to increase effective vascular permeability. Validated high-performance liquid chromatography protocols were used to measure chemotherapeutic drug concentrations in untreated and VEGF-A-treated lymph nodes, liver, spleen, brain, and blood. RESULTS: VEGF-A-treated lymph node blood vessel effective vascular permeability (mean 3.83 × 10-7  cm/s) was significantly higher than untreated lymph nodes (mean 9.87 × 10-8  cm/s). No difference was found in lymph node drug accumulation in untreated versus VEGF-A-treated mice. CONCLUSIONS: Lymph node effective vascular permeability can be increased (~fourfold) by VEGF-A. However, no significant increase in chemotherapy uptake was measured by pretreatment with VEGF-A.

Synchronization and Random Triggering of Lymphatic Vessel Contractions.

The lymphatic system is responsible for transporting interstitial fluid back to the bloodstream, but unlike the cardiovascular system, lacks a centralized pump-the heart-to drive flow. Instead, each collecting lymphatic vessel can individually contract and dilate producing unidirectional flow enforced by intraluminal check valves. Due to the large number and spatial distribution of such pumps, high-level coordination would be unwieldy. This leads to the question of how each segment of lymphatic vessel responds to local signals that can contribute to the coordination of pumping on a network basis. Beginning with elementary fluid mechanics and known cellular behaviors, we show that two complementary oscillators emerge from i) mechanical stretch with calcium ion transport and ii) fluid shear stress induced nitric oxide production (NO). Using numerical simulation and linear stability analysis we show that the newly identified shear-NO oscillator shares similarities with the well-known Van der Pol oscillator, but has unique characteristics. Depending on the operating conditions, the shear-NO process may i) be inherently stable, ii) oscillate spontaneously in response to random disturbances or iii) synchronize with weak periodic stimuli. When the complementary shear-driven and stretch-driven oscillators interact, either may dominate, producing a rich family of behaviors similar to those observed in vivo.

Angiopoietin-4 increases permeability of blood vessels and promotes lymphatic dilation.

The angiopoietin (Ang) ligands are potential therapeutic targets for lymphatic related diseases, which include lymphedema and cancer. Ang-1 and Ang-2 functions are established, but those of Ang-4 are poorly understood. We used intravital fluorescence microscopy to characterize Ang-4 actions on T241 murine fibrosarcoma-associated vessels in mice. The diameters of lymphatic vessels draining Ang-4- or VEGF-C (positive control)-expressing tumors increased to 123 and 135 µm, respectively, and parental, mock-transduced (negative controls) and tumors expressing Ang-1 or Ang-2 remained at baseline (∼60 µm). Ang-4 decreased human dermal lymphatic endothelial cell (LEC) monolayer permeability by 27% while increasing human dermal blood endothelial cell (BEC) monolayer permeability by 200%. In vivo, Ang-4 stimulated a 4.5-fold increase in tumor-associated blood vessel permeability compared with control when measured using intravital quantitative multiphoton microscopy. Ang-4 activated receptor signaling in both LECs and BECs, evidenced by tyrosine kinase with Ig and endothelial growth factor homology domains-2 (TIE2) receptor, protein kinase B, and Erk1,2 phosphorylation detectable by immunoblotting. These data suggest that Ang-4 actions are mediated through cell-type-specific networks and that lymphatic vessel dilation occurs secondarily to increased vascular leakage. Ang-4 also promoted survival of LECs. Thus, blocking Ang-4 may prune the draining lymphatic vasculature and decrease interstitial fluid pressure (IFP) by reducing vascular permeability.

Scaling rules for diffusive drug delivery in tumor and normal tissues.

Delivery of blood-borne molecules and nanoparticles from the vasculature to cells in the tissue differs dramatically between tumor and normal tissues due to differences in their vascular architectures. Here we show that two simple measures of vascular geometry--δ(max) and λ--readily obtained from vascular images, capture these differences and link vascular structure to delivery in both tissue types. The longest time needed to bring materials to their destination scales with the square of δ(max), the maximum distance in the tissue from the nearest blood vessel, whereas λ, a measure of the shape of the spaces between vessels, determines the rate of delivery for shorter times. Our results are useful for evaluating how new therapeutic agents that inhibit or stimulate vascular growth alter the functional efficiency of the vasculature and more broadly for analysis of diffusion in irregularly shaped domains.

Fluid dynamics and leukocyte transit in the lymphatic system.

The lymphatic system plays a vital role in maintaining fluid balance in living tissue and serves as a pathway for the transport of antigen, immune cells, and metastatic cancer cells. In this study, we investigate how the movement of cells through a contracting lymphatic vessel differs from steady flow, using a lattice Boltzmann-based computational model. Our model consists of cells carried by flow in a 2D vessel with regularly spaced, bi-leaflet valves that ensure net downstream flow as the vessel walls contract autonomously in response to calcium and nitric oxide levels regulated by stretch and shear stress levels. The orientation of the vessel with respect to gravity, which may oppose or assist fluid flow, significantly modulates cellular motion due to its effect on the contraction dynamics of the vessel, even when the cells themselves are neutrally buoyant. Additionally, our model shows that cells are carried along with the flow, but when the vessel is actively contracting, they move faster than the average fluid velocity. We also find that the fluid forces cause significant deformation of the compliant cells, especially in the vicinity of the valves. Our study highlights the importance of considering the complex, transient flows near the valves in understanding cellular motion in lymphatic vessels.

Cancer immunotherapy responses persist after lymph node resection.

Surgical removal of lymph nodes (LNs) to prevent metastatic recurrence, including sentinel lymph node biopsy (SLNB) and completion lymph node dissection (CLND), are performed in routine practice. However, it remains controversial whether removing LNs which are critical for adaptive immune responses impairs immune checkpoint blockade (ICB) efficacy. Here, our retrospective analysis demonstrated that stage III melanoma patients retain robust response to anti-PD1 inhibition after CLND. Using orthotopic murine mammary carcinoma and melanoma models, we show that responses to ICB persist in mice after TDLN resection. Mechanistically, after TDLN resection, antigen can be re-directed to distant LNs, which extends the responsiveness to ICB. Strikingly, by evaluating head and neck cancer patients treated by neoadjuvant durvalumab and irradiation, we show that distant LNs (metastases-free) remain reactive in ICB responders after tumor and disease-related LN resection, hence, persistent anti-cancer immune reactions in distant LNs. Additionally, after TDLN dissection in murine models, ICB delivered to distant LNs generated greater survival benefit, compared to systemic administration. In complete responders, anti-tumor immune memory induced by ICB was systemic rather than confined within lymphoid organs. Based on these findings, we constructed a computational model to predict free antigen trafficking in patients that will undergo LN dissection.

Transport Barriers Influence the Activation of Anti-Tumor Immunity: A Systems Biology Analysis.

Effective anti-cancer immune responses require activation of one or more naïve T cells. If the correct naïve T cell encounters its cognate antigen presented by an antigen presenting cell, then the T cell can activate and proliferate. Here, mathematical modeling is used to explore the possibility that immune activation in lymph nodes is a rate-limiting step in anti-cancer immunity and can affect response rates to immune checkpoint therapy. The model provides a mechanistic framework for optimizing cancer immunotherapy and developing testable solutions to unleash anti-tumor immune responses for more patients with cancer. The results show that antigen production rate and trafficking of naïve T cells into the lymph nodes are key parameters and that treatments designed to enhance tumor antigen production can improve immune checkpoint therapies. The model underscores the potential of radiation therapy in augmenting tumor immunogenicity and neoantigen production for improved ICB therapy, while emphasizing the need for careful consideration in cases where antigen levels are already sufficient to avoid compromising the immune response.

Regeneration of collecting lymphatic vessels following injury.

Secondary lymphedema is a debilitating condition driven by impaired regeneration of lymphatic vasculature following lymphatic injury, surgical removal of lymph nodes in cancer patients or infection. However, the extent to which collecting lymphatic vessels regenerate following injury remains unclear. Here, we employed a novel mouse model of lymphatic injury in combination with state-of-the-art lymphatic imaging to demonstrate that the implantation of an optimized fibrin gel following lymphatic vessel injury leads to the growth and reconnection of the injured lymphatic vessel network, resulting in the restoration of lymph flow to the draining node. Intriguingly, we found that fibrin implantation elevates the tissue levels of CCL5, a potent macrophage-recruiting chemokine. Notably, CCL5-KO mice displayed a reduced ability to reconnect injured vessels following fibrin gel implantation. These novel findings shed light on the mechanisms underlying lymphatic regeneration and suggest that enhancing CCL5 signaling may be a promising therapeutic strategy for enhancing lymphatic regeneration.

Lymphatic muscle cells are unique cells that undergo aging induced changes.

Lymphatic muscle cells (LMCs) within the wall of collecting lymphatic vessels exhibit tonic and autonomous phasic contractions, which drive active lymph transport to maintain tissue-fluid homeostasis and support immune surveillance. Damage to LMCs disrupts lymphatic function and is related to various diseases. Despite their importance, knowledge of the transcriptional signatures in LMCs and how they relate to lymphatic function in normal and disease contexts is largely missing. We have generated a comprehensive transcriptional single-cell atlas-including LMCs-of collecting lymphatic vessels in mouse dermis at various ages. We identified genes that distinguish LMCs from other types of muscle cells, characterized the phenotypical and transcriptomic changes in LMCs in aged vessels, and uncovered a pro-inflammatory microenvironment that suppresses the contractile apparatus in advanced-aged LMCs. Our findings provide a valuable resource to accelerate future research for the identification of potential drug targets on LMCs to preserve lymphatic vessel function as well as supporting studies to identify genetic causes of primary lymphedema currently with unknown molecular explanation.

The effects of gravity and compression on interstitial fluid transport in the lower limb.

Edema in the limbs can arise from pathologies such as elevated capillary pressures due to failure of venous valves, elevated capillary permeability from local inflammation, and insufficient fluid clearance by the lymphatic system. The most common treatments include elevation of the limb, compression wraps and manual lymphatic drainage therapy. To better understand these clinical situations, we have developed a comprehensive model of the solid and fluid mechanics of a lower limb that includes the effects of gravity. The local fluid balance in the interstitial space includes a source from the capillaries, a sink due to lymphatic clearance, and movement through the interstitial space due to both gravity and gradients in interstitial fluid pressure (IFP). From dimensional analysis and numerical solutions of the governing equations we have identified several parameter groups that determine the essential length and time scales involved. We find that gravity can have dramatic effects on the fluid balance in the limb with the possibility that a positive feedback loop can develop that facilitates chronic edema. This process involves localized tissue swelling which increases the hydraulic conductivity, thus allowing the movement of interstitial fluid vertically throughout the limb due to gravity and causing further swelling. The presence of a compression wrap can interrupt this feedback loop. We find that only by modeling the complex interplay between the solid and fluid mechanics can we adequately investigate edema development and treatment in a gravity dependent limb.

Normalizing tumor microenvironment with nanomedicine and metronomic therapy to improve immunotherapy.

Nanomedicine offered hope for improving the treatment of cancer but the survival benefits of the clinically approved nanomedicines are modest in many cases when compared to conventional chemotherapy. Metronomic therapy, defined as the frequent, low dose administration of chemotherapeutics - is being tested in clinical trials as an alternative to the conventional maximum tolerated dose (MTD) chemotherapy schedule. Although metronomic chemotherapy has not been clinically approved yet, it has shown better survival than MTD in many preclinical studies. When beneficial, metronomic therapy seems to be associated with normalization of the tumor microenvironment including improvements in tumor perfusion, tissue oxygenation and drug delivery as well as activation of the immune system. Recent preclinical studies suggest that nanomedicines can cause similar changes in the tumor microenvironment. Here, by employing a mathematical framework, we show that both approaches can serve as normalization strategies to enhance treatment. Furthermore, employing murine breast and fibrosarcoma tumor models as well as ultrasound shear wave elastography and contrast-enhanced ultrasound, we provide evidence that the approved nanomedicine Doxil can induce normalization in a dose-dependent manner by improving tumor perfusion as a result of tissue softening. Finally, we show that pretreatment with a normalizing dose of Doxil can improve the efficacy of immune checkpoint inhibition.

Computational simulations of the effects of gravity on lymphatic transport.

Physical forces, including mechanical stretch, fluid pressure, and shear forces alter lymphatic vessel contractions and lymph flow. Gravitational forces can affect these forces, resulting in altered lymphatic transport, but the mechanisms involved have not been studied in detail. Here, we combine a lattice Boltzmann-based fluid dynamics computational model with known lymphatic mechanobiological mechanisms to investigate the movement of fluid through a lymphatic vessel under the effects of gravity that may either oppose or assist flow. Regularly spaced, mechanical bi-leaflet valves in the vessel enforce net positive flow as the vessel walls contract autonomously in response to calcium and nitric oxide (NO) levels regulated by vessel stretch and shear stress levels. We find that large gravitational forces opposing flow can stall the contractions, leading to no net flow, but transient mechanical perturbations can re-establish pumping. In the case of gravity strongly assisting flow, the contractions also cease due to high shear stress and NO production, which dilates the vessel to allow gravity-driven flow. In the intermediate range of oppositional gravity forces, the vessel actively contracts to offset nominal gravity levels or to modestly assist the favorable hydrostatic pressure gradients.

The effects of valve leaflet mechanics on lymphatic pumping assessed using numerical simulations.

The lymphatic system contains intraluminal leaflet valves that function to bias lymph flow back towards the heart. These valves are present in the collecting lymphatic vessels, which generally have lymphatic muscle cells and can spontaneously pump fluid. Recent studies have shown that the valves are open at rest, can allow some backflow, and are a source of nitric oxide (NO). To investigate how these valves function as a mechanical valve and source of vasoactive species to optimize throughput, we developed a mathematical model that explicitly includes Ca2+ -modulated contractions, NO production and valve structures. The 2D lattice Boltzmann model includes an initial lymphatic vessel and a collecting lymphangion embedded in a porous tissue. The lymphangion segment has mechanically-active vessel walls and is flanked by deformable valves. Vessel wall motion is passively affected by fluid pressure, while active contractions are driven by intracellular Ca2+ fluxes. The model reproduces NO and Ca2+ dynamics, valve motion and fluid drainage from tissue. We find that valve structural properties have dramatic effects on performance, and that valves with a stiffer base and flexible tips produce more stable cycling. In agreement with experimental observations, the valves are a major source of NO. Once initiated, the contractions are spontaneous and self-sustained, and the system exhibits interesting non-linear dynamics. For example, increased fluid pressure in the tissue or decreased lymph pressure at the outlet of the system produces high shear stress and high levels of NO, which inhibits contractions. On the other hand, a high outlet pressure opposes the flow, increasing the luminal pressure and the radius of the vessel, which results in strong contractions in response to mechanical stretch of the wall. We also find that the location of contraction initiation is affected by the extent of backflow through the valves.

Solid stress in brain tumours causes neuronal loss and neurological dysfunction and can be reversed by lithium.

The compression of brain tissue by a tumour mass is believed to be a major cause of the clinical symptoms seen in patients with brain cancer. However, the biological consequences of these physical stresses on brain tissue are unknown. Here, via imaging studies in patients and by using mouse models of human brain tumours, we show that a subgroup of primary and metastatic brain tumours, classified as nodular on the basis of their growth pattern, exert solid stress on the surrounding brain tissue, causing a decrease in local vascular perfusion as well as neuronal death and impaired function. We demonstrate a causal link between solid stress and neurological dysfunction by applying and removing cerebral compression, which respectively mimic the mechanics of tumour growth and of surgical resection. We also show that, in mice, treatment with lithium reduces solid-stress-induced neuronal death and improves motor coordination. Our findings indicate that brain-tumour-generated solid stress impairs neurological function in patients, and that lithium as a therapeutic intervention could counter these effects.