Numerical simulations of the microvascular fluid balance with a non-linear model of the lymphatic system

The role of initial lymphatics in the absorption of monoclonal antibodies after subcutaneous injection

The subcutaneous injection is the most common method of administration of monoclonal antibodies (mAbs) due to the patient's comfort and cost-effectiveness. However, the available knowledge about the transport and absorption of this type of biotherapeutics after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A poro-hyperelastic model of the tissue is exploited to find the biomechanical response of the tissue together with a transport model based on an advection-diffusion equation in large-deformation poro-hyperelastic Media. The process of mAbs transport to the lymphatic system has two major parts. First is the initial phase, where mAbs are dispersed in the tissue due to momentum exerted by injection. This stage lasts for only a few minutes after the injection. Then there is the second stage, which can take tens of hours, and as a result, mAb molecules are transported from the subcutaneous layer towards initial lymphatics in the dermis to enter the lymphatic system. In this study, we investigate both stages. The process of plume formation, interstitial pressure, and velocity development is explored. Then, the effect of the injection delivery parameters, injection site, and sensitivity of long-term lymphatic uptake due to variability in permeability, diffusivity, viscosity, and binding of mAbs are investigated. Finally, we study two different injection scenarios with variable injection volume and drug concentration inside the syringe and evaluate them based on the rate of lymphatic uptake. We use our results to find an equivalent lymphatic uptake coefficient similar to the coefficient widely used in pharmacokinetic (PK) models to study the absorption of mAbs. Ultimately, we validate our computational model against available experiments in the literature.

Dynamic multispectral NIR/SWIR for in vivo lymphovascular architectural and functional quantification

Significance

Although the lymphatic system is the second largest circulatory system in the body, there are limited techniques available for characterizing lymphatic vessel function. We report shortwave-infrared (SWIR) imaging for minimally invasive in vivo quantification of lymphatic circulation with superior contrast and resolution compared with near-infrared first window imaging.

Aim

We aim to study the lymphatic structure and function in vivo via SWIR fluorescence imaging.

Approach

We evaluated subsurface lymphatic circulation in healthy, adult immunocompromised salt-sensitive Sprague-Dawley rats using two fluorescence imaging modalities: near-infrared first window (NIR-I, 700 to 900 nm) and SWIR (900 to 1800 nm) imaging. We also compared two fluorescent imaging probes: indocyanine green (ICG) and silver sulfide quantum dots (QDs) as SWIR lymphatic contrast agents following intradermal footpad delivery in these rats.

Results

SWIR imaging exhibits reduced scattering and autofluorescence background relative to NIR-I imaging. SWIR imaging with ICG provides 1.7 times better resolution and sensitivity than NIR-I, and SWIR imaging with QDs provides nearly two times better resolution and sensitivity with enhanced vessel distinguishability. SWIR images thus provide a more accurate estimation of in vivo vessel size than conventional NIR-I images.

Conclusions

SWIR imaging of silver sulfide QDs into the intradermal footpad injection provides superior image resolution compared with conventional imaging techniques using NIR-I imaging with ICG dye.

Modeling hypoxia-induced radiation resistance and the impact of radiation sources

Hypoxia contributes significantly to resistance in radiotherapy. Our research rigorously examines the influence of microvascular morphology on radiotherapy outcome, specifically focusing on how microvasculature shapes hypoxia within the microenvironment and affects resistance to a standard treatment regimen (30×2GyRBE). Our computational modeling extends to the effects of different radiation sources. For photons and protons, our analysis establishes a clear correlation between hypoxic volume distribution and treatment effectiveness, with vascular density and regularity playing a crucial role in treatment success. On the contrary, carbon ions exhibit distinct effectiveness, even in areas of intense hypoxia and poor vascularization. This finding points to the potential of carbon-based hadron therapy in overcoming hypoxia-induced resistance to RT. Considering that the spatial scale analyzed in this study is closely aligned with that of imaging data voxels, we also address the implications of these findings in a clinical context envisioning the possibility of detecting subvoxel hypoxia.

Computational fluid dynamic modeling of the lymphatic system: a review of existing models and future directions

Historically, research into the lymphatic system has been overlooked due to both a lack of knowledge and limited recognition of its importance. In the last decade however, lymphatic research has gained substantial momentum and has included the development of a variety of computational models to aid understanding of this complex system. This article reviews existing computational fluid dynamic models of the lymphatics covering each structural component including the initial lymphatics, pre-collecting and collecting vessels, and lymph nodes. This is followed by a summary of limitations and gaps in existing computational models and reasons that development in this field has been hindered to date. Over the next decade, efforts to further characterize lymphatic anatomy and physiology are anticipated to provide key data to further inform and validate lymphatic fluid dynamic models. Development of more comprehensive multiscale- and multi-physics computational models has the potential to significantly enhance the understanding of lymphatic function in both health and disease.

Sensitivity analysis of a multi-physics model for the vascular microenvironment

The vascular microenvironment is the scale at which microvascular transport, interstitial tissue properties and cell metabolism interact. The vascular microenvironment has been widely studied by means of quantitative approaches, including multi-physics mathematical models as it is a central system for the pathophysiology of many diseases, such as cancer. The microvascular architecture is a key factor for fluid balance and mass transfer in the vascular microenvironment, together with the physical parameters characterizing the vascular wall and the interstitial tissue. The scientific literature of this field has witnessed a long debate about which factor of this multifaceted system is the most relevant. The purpose of this work is to combine the interpretative power of an advanced multi-physics model of the vascular microenvironment with state of the art and robust sensitivity analysis methods, in order to determine the factors that most significantly impact quantities of interest, related in particular to cancer treatment. We are particularly interested in comparing the factors related to the microvascular architecture with the ones affecting the physics of microvascular transport. Ultimately, this work will provide further insight into how the vascular microenvironment affects cancer therapies, such as chemotherapy, radiotherapy or immunotherapy.

Lymphatic microcirculation profile in the progression of hypertension in spontaneously hypertensive rats

OBJECTIVE

The contractile behavior of collecting lymphatic vessels occurs in essential hypertension in response to homeostasis, suggesting a possible role for microcirculation. We aimed to clarify the nature of the lymphatic microcirculation profile in spontaneously hypertensive rats (SHRs) and normotensive controls.

METHODS

The vasomotion of collecting lymphatic vessels in eight- and thirteen-week-old SHRs and age-matched Wistar-Kyoto rats (WKYs, n = 4 per group) was visualized by intravital video and VasTrack. The lymphatic vasomotion profile (frequency and amplitude) and contractile parameters (contraction fraction and total contractility activity index) were compared. Plasma nitrite/nitrate levels were assessed by the Griess reaction, and plasma endothelin-1 was measured by enzyme-linked immunosorbent assay.

RESULTS

WKYs and SHRs differed in the vasomotion of collecting lymphatic vessels. Both eight- and thirteen-week-old WKYs revealed a high-amplitude pumping pattern, whereas a low-amplitude pattern was observed in SHRs. Moreover, compared with age-matched WKYs, SHRs exhibited deteriorated output and reflux capability and lost the ability to regulate collecting lymphatic vasomotion. Additionally, the chemistry complements the microcirculatory lymphatic profile as demonstrated by an increase in plasma nitrite, nitrate, and endothelin-1 in SHRs. ET-1 inhibitor meliorated the lymphatic contractile capability in SHRs partially through regulating frequency of lymphatic vasomotion.

CONCLUSIONS

We used an intravital lymphatic imaging system to observe that SHRs exhibit an impaired collecting lymphatic vasomotion profile and deteriorated contractility and reflux.

Transport and lymphatic uptake of monoclonal antibodies after subcutaneous injection

The subcutaneous injection has emerged to become a feasible self-administration practice for biotherapeutics due to the patient comfort and cost-effectiveness. However, the available knowledge about transport and absorption of these agents after subcutaneous injection is limited. Here, a mathematical framework to study the subcutaneous drug delivery of mAbs from injection to lymphatic uptake is presented. A three-dimensional poroelastic model is exploited to find the biomechanical response of the tissue by taking into account tissue deformation during the injection. The results show that including tissue deformability noticeably changes tissue poromechanical response due to the significant dependence of interstitial pressure on the tissue deformation. Moreover, the importance of the amount of lymph fluid at the injection site and the injection rate on the drug uptake to lymphatic capillaries is highlighted. Finally, variability of lymphatic uptake due to uncertainty in parameters including tissue poromechanical and lymphatic absorption parameters is evaluated. It is found that interstitial pressure due to injection is the major contributing factor in short-term lymphatic absorption, while the amount of lymph fluid at the site of injection determines the long-term absorption of the drug. Finally, it is shown that the lymphatic uptake results are consistent with experimental data available in the literature.

A Mesoscale Computational Model for Microvascular Oxygen Transfer

We address a mathematical model for oxygen transfer in the microcirculation. The model includes blood flow and hematocrit transport coupled with the interstitial flow, oxygen transport in the blood and the tissue, including capillary-tissue exchange effects. Moreover, the model is suited to handle arbitrarily complex vascular geometries. The purpose of this study is the validation of the model with respect to classical solutions and the further demonstration of its adequacy to describe the heterogeneity of oxygenation in the tissue microenvironment. Finally, we discuss the importance of these effects in the treatment of cancer using radiotherapy.

Voxelized simulation of cerebral oxygen perfusion elucidates hypoxia in aged mouse cortex

Departures of normal blood flow and metabolite distribution from the cerebral microvasculature into neuronal tissue have been implicated with age-related neurodegeneration. Mathematical models informed by spatially and temporally distributed neuroimage data are becoming instrumental for reconstructing a coherent picture of normal and pathological oxygen delivery throughout the brain. Unfortunately, current mathematical models of cerebral blood flow and oxygen exchange become excessively large in size. They further suffer from boundary effects due to incomplete or physiologically inaccurate computational domains, numerical instabilities due to enormous length scale differences, and convergence problems associated with condition number deterioration at fine mesh resolutions. Our proposed simple finite volume discretization scheme for blood and oxygen microperfusion simulations does not require expensive mesh generation leading to the critical benefit that it drastically reduces matrix size and bandwidth of the coupled oxygen transfer problem. The compact problem formulation yields rapid and stable convergence. Moreover, boundary effects can effectively be suppressed by generating very large replica of the cortical microcirculation in silico using an image-based cerebrovascular network synthesis algorithm, so that boundaries of the perfusion simulations are far removed from the regions of interest. Massive simulations over sizeable portions of the cortex with feature resolution down to the micron scale become tractable with even modest computer resources. The feasibility and accuracy of the novel method is demonstrated and validated with in vivo oxygen perfusion data in cohorts of young and aged mice. Our oxygen exchange simulations quantify steep gradients near penetrating blood vessels and point towards pathological changes that might cause neurodegeneration in aged brains. This research aims to explain mechanistic interactions between anatomical structures and how they might change in diseases or with age. Rigorous quantification of age-related changes is of significant interest because it might aide in the search for imaging biomarkers for dementia and Alzheimer’s disease.

Brain function critically depends on the maintenance of physiological blood supply and metabolism in the cortex. Disturbances to adequate perfusion have been linked to age-related neurodegeneration. However, the precise correlation between age-related hemodynamic changes and the resulting decline in oxygen delivery is not well understood and has not been quantified. Therefore, we introduce a new compact, and therefore highly scalable, computational method for predicting the physiological relationship between hemodynamics and cortical oxygen perfusion for large sections of the cortical microcirculation. We demonstrate the novel mesh generation-free (MGF), multi-scale simulation approach through realistic in vivo case studies of cortical microperfusion in the mouse brain. We further validate mechanistic correlations and a quantitative relationship between blood flow and brain oxygenation using experimental data from cohorts of young, middle aged and old mouse brains. Our computational approach overcomes size and performance limitations of previous unstructured meshing techniques to enable the prediction of oxygen tension with a spatial resolution of least two orders of magnitude higher than previously possible. Our simulation results support the hypothesis that structural changes in the microvasculature induce hypoxic pockets in the aged brain that are absent in the healthy, young mouse.

On the poro-elastic models for microvascular blood flow resistance: An in vitro validation

Nowadays, adequate and accurate representation of the microvascular flow resistance constitutes one of the major challenges in computational haemodynamic studies. In this work, a theoretical, porous media framework, ultimately designed for representing downstream resistance, is presented and compared against an in vitro experimental results. The resistor consists of a poro-elastic tube, with either a constant or variable porosity profile in space. The underlying physics, characterizing the fluid flow through the porous media, is analysed by considering flow variables at different network locations. Backward reflections, originated in the reservoir of the in vitro model, are accounted for through a reflection coefficient imposed as an outflow network condition. The simulation results are in good agreement with the measurements for both the homogenous and heterogeneous porosity conditions. In addition, the comparison allows identification of the range of values representing experimental reservoir reflection coefficients. The pressure drops across the heterogeneous porous media increases with respect to the simpler configuration, whilst flow remains almost unchanged. The effect of some fluid network features, such as tube Young's modulus and fluid viscosity, on the theoretical results is also elucidated, providing a reference for the invitro and insilico simulation of different microvascular conditions.

Glucagon-like peptide 1 and glucose-dependent insulinotropic polypeptide stimulate release of substance P from TRPV1- and TRPA1-expressing sensory nerves

Glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) are released from enteroendocrine cells (EECs) in response to nutrient ingestion and lower blood glucose levels by stimulation of insulin secretion and thus are defined as incretins. GLP-1 receptor (GLP-1R) expression has been identified on enteric neurons that include intrinsic afferent neurons, extrinsic spinal, and vagal sensory afferents but has not been shown to have an incretin effect through these nerves. GLP-1 and GIP enter the mesenteric lymphatic fluid (MLF) after a meal via the interstitial fluid (IF) from local tissue secretion and/or blood capillaries. We tested if MLF could induce diet-dependent intransient increases in intracellular calcium ([Ca²⁺]_i) in cultured sensory neurons. Postprandial rat MLF, collected from the superior mesenteric lymphatic duct, induced a significant twofold higher intransient increase in [Ca²⁺]_i in primary-cultured sensory neurons than MLF from fasted rats. Inhibition of transient receptor potential vanilloid 1 (TRPV1) and TRPV1 and ankyrin 1 cation channels (TRPA1) with ruthenium red eliminated the difference. Substance P (SP) (a peptide that stimulates insulin secretion) sensor cells cocultured with sensory neurons showed both the GLP-1R agonist exendin-4 (Ex-4) and GIP induced transient increases in [Ca²⁺]_i directly coupled to SP secretion in the sensory nerves. Ex-4-induced release of SP required expression of either TRPA1 or TRPV1. These data identify unrecognized actions of GLP-1 and GIP as incretins by acting as neurolymphocrines and suggest a mechanism for sensory nerves to respond to the postprandial state through MLF.NEW & NOTEWORTHY Glucagon-like peptide-1 (GLP-1) and glucose-dependent insulinotropic polypeptide (GIP) are secreted upon eating to lower blood sugar. GLP-1 and GIP were found to induce the secretion of substance P (SP) from cultured sensory nerves. SP enhances insulin secretion. Mesenteric lymphatic fluid (MLF) also stimulates sensory neurons in a diet-dependent manner. These studies identify new actions of GLP-1 and GIP as incretins and suggest a mechanism for sensory nerves to respond to diet through MLF.

Application of Transmural Flow Across In Vitro Microvasculature Enables Direct Sampling of Interstitial Therapeutic Molecule Distribution

In vitro prediction of physiologically relevant transport of therapeutic molecules across the microcirculation represents an intriguing opportunity to predict efficacy in human populations. On-chip microvascular networks (MVNs) show physiologically relevant values of molecular permeability, yet like most systems, they lack an important contribution to transport: the ever-present fluid convection through the endothelium. Quantification of transport through the MVNs by current methods also requires confocal imaging and advanced analytical techniques, which can be a bottleneck in industry and academic laboratories. Here, it is shown that by recapitulating physiological transmural flow across the MVNs, the concentration of small and large molecule therapeutics can be directly sampled in the interstitial fluid and analyzed using standard analytical techniques. The magnitudes of transport measured in MVNs reveal trends with molecular size and type (protein versus nonprotein) that are expected in vivo, supporting the use of the MVNs platform as an in vitro tool to predict distribution of therapeutics in vivo.