Poroviscoelastic modeling of liver biomechanical response in unconfined compression

Microneedle patch capable of dual drug release for drug delivery to brain tumors

Primary brain tumors are mostly managed using surgical resection procedures. Nevertheless, in certain cases, a thin layer of tumors may remain outside of the resection process due to the possibility of permanent injury; these residual tumors expose patients to the risk of tumor recurrence. This study has introduced the use of microneedle patches implanted after surgery with a dual-release mechanism for the administration of doxorubicin. The proposed patches possess the capability to administer drugs directly to the residual tumors and initiate chemotherapy immediately following surgical procedures. Three-dimensional simulation of drug delivery to residual tumors in the brain has been performed based on a finite element method. The impact of four important parameters on drug delivery has been investigated, involving the fraction of drug released in the burst phase, the density of microneedles on the patch, the length of microneedles, and the microvascular density of the tumor. The simulation findings indicate that lowering the fraction of drug released in the initial burst phase reduces the maximum average concentration, but the sustained release that continues for a longer period, increasing the bioavailability of free drug. However, the area under curve (AUC) for different release rates remains unchanged due to the fact that an identical dose of drug is supplied in each instance. By increasing the density of microneedles on the patch, concentration accumulation is provided over an extensive region of tumor, which in turn induces more cancer cell death. A comparative analysis of various lengths reveals that longer microneedles facilitate profound penetration into the tumor layers and present better therapeutic response due to extensive area of the tumor which is exposure to chemotherapeutic drugs. Furthermore, high microvascular density, as a characteristic of the tumor microenvironment, is shown to have a significant impact on the blood microvessels drainage of drugs and consequently lower therapeutic response outcome. Our approach offers a computational framework for creating localized drug delivery systems and addressing the challenges related to residual brain tumors.

Enhancing localized chemotherapy with anti-angiogenesis and nanomedicine synergy for improved tumor penetration in well-vascularized tumors

Intratumoral delivery and localized chemotherapy have demonstrated promise in tumor treatment; however, the rapid drainage of therapeutic agents from well-vascularized tumors limits their ability to achieve maximum therapeutic efficacy. Therefore, innovative approaches are needed to enhance treatment efficacy in such tumors. This study utilizes a mathematical modeling platform to assess the efficacy of combination therapy using anti-angiogenic drugs and drug-loaded nanoparticles. Anti-angiogenic drugs are included to reduce blood microvascular density and facilitate drug retention in the extracellular space. In addition, incorporating negatively charged nanoparticles aims to enhance diffusion and distribution of therapeutic agents within well-vascularized tumors. The findings indicate that, in the case of direct injection of free drugs, using compounds with lower drainage rates and higher diffusion coefficients is beneficial for achieving broader diffusion. Otherwise, drugs tend to accumulate primarily around the injection site. For instance, the drug doxorubicin, known for its rapid drainage, requires the prior direct injection of an anti-angiogenic drug with a high diffusion rate to reduce microvascular density and facilitate broader distribution, enhancing penetration depth by 200%. Moreover, the results demonstrate that negatively charged nanoparticles effectively disperse throughout the tissue due to their high diffusion coefficient. In addition, a faster drug release rate from nanoparticles further enhance treatment efficacy, achieving the necessary concentration for complete eradication of tumor compared to slower drug release rates. This study demonstrates the potential of utilizing negatively charged nanoparticles loaded with chemotherapy drugs exhibiting high release rates for localized chemotherapy through intratumoral injection in well-vascularized tumors.

Effect of infusion direction on convection-enhanced drug delivery to anisotropic tissue

Convection-enhanced delivery (CED) can effectively overcome the blood-brain barrier by infusing drugs directly into diseased sites in the brain using a catheter, but its clinical performance still needs to be improved. This is strongly related to the highly anisotropic characteristics of brain white matter, which results in difficulties in controlling drug transport and distribution in space. In this study, the potential to improve the delivery of six drugs by adjusting the placement of the infusion catheter is examined using a mathematical model and accurate numerical simulations that account simultaneously for the interstitial fluid (ISF) flow and drug transport processes in CED. The results demonstrate the ability of this direct infusion to enhance ISF flow and therefore facilitate drug transport. However, this enhancement is highly anisotropic, subject to the orientation of local axon bundles and is limited within a small region close to the infusion site. Drugs respond in different ways to infusion direction: the results of our simulations show that while some drugs are almost insensitive to infusion direction, this strongly affects other compounds in terms of isotropy of drug distribution from the catheter. These findings can serve as a reference for planning treatments using CED.

Biomechanical Properties and Cellular Responses in Pulmonary Fibrosis

Pulmonary fibrosis is a fatal lung disease affecting approximately 5 million people worldwide, with a 5-year survival rate of less than 50%. Currently, the only available treatments are palliative care and lung transplantation, as there is no curative drug for this condition. The disease involves the excessive synthesis of the extracellular matrix (ECM) due to alveolar epithelial cell damage, leading to scarring and stiffening of the lung tissue and ultimately causing respiratory failure. Although multiple factors contribute to the disease, the exact causes remain unclear. The mechanical properties of lung tissue, including elasticity, viscoelasticity, and surface tension, are not only affected by fibrosis but also contribute to its progression. This paper reviews the alteration in these mechanical properties as pulmonary fibrosis progresses and how cells in the lung, including alveolar epithelial cells, fibroblasts, and macrophages, respond to these changes, contributing to disease exacerbation. Furthermore, it highlights the importance of developing advanced in vitro models, based on hydrogels and 3D bioprinting, which can accurately replicate the mechanical and structural properties of fibrotic lungs and are conducive to studying the effects of mechanical stimuli on cellular responses. This review aims to summarize the current understanding of the interaction between the progression of pulmonary fibrosis and the alterations in mechanical properties, which could aid in the development of novel therapeutic strategies for the disease.

Charge-Switchable nanoparticles to enhance tumor penetration and accumulation

Nanoparticle-based drug delivery systems hold potential in chemotherapy, but their limited accumulation in tumor tissues hinders effective drug concentration for combating tumor growth. Hence, altering the physicochemical properties of nanoparticles, particularly their surface charge, can enhance their performance. This study utilized a computational model to explore a nanoparticle drug delivery system capable of dynamically adjusting its surface charge. In the model, nanoparticles in the bloodstream were assigned a neutral or positive charge, which, upon reaching the tumor microenvironment, switched to a neutral or negative charge, and releasing chemotherapy drugs into the extracellular space. Results revealed that circulating nanoparticles with a positive surface charge, despite having a shorter circulation and high clearance rate compared to their neutral counterparts, could accumulate significantly in the tissue due to their high transvascular rate. After extravasation, neutralized surface-charged nanoparticles tended to accumulate only near blood microvessels due to their low diffusion rate, resulting in substantial released drug drainage back into the bloodstream. On the other hand, nanoparticles with a negative surface charge in the tumor's extracellular space, due to the reduction of nano-bio interactions, were able to penetrate deeper into the tumor, and increasing drug bioavailability by reducing the volume of drained drugs. Furthermore, the analysis suggested that burst drug release yields a higher drug concentration than sustained drug release, however their creation of bioavailability dependent on nanoparticle accumulation in the tissue. The study's findings demonstrate the potential of this delivery system and offer valuable insights for future research in this area.

Spatiotemporal modeling of radiopharmaceutical transport in solid tumors: Application to 177Lu-PSMA therapy of prostate cancer

BACKGROUND AND OBJECTIVE

177Lu-labeled prostate-specific membrane antigen (PSMA) radiopharmaceutical therapy (RPT) represents a pivotal advancement in addressing prostate cancer. However, existing therapies, while promising, remain incompletely understood and optimized. Computational models offer potential insights into RPTs, aiding in clinical drug delivery enhancement. In this study, we investigate the impact of various physiological parameters on the delivery of 177Lu-PSMA-617 RPT using the convection-diffusion-reaction (CDR) model.

METHODS

Our investigation encompasses tumor geometry and surrounding tissue, characterized by well-defined boundaries and initial conditions. Utilizing the finite element method, we solve governing equations across a range of parameters: dissociation constant KD (1, 0.1, 0.01 [nM]), internalization rate (0.01-0.0001 [min-1]), diverse tumor shapes, and variable necrotic zone sizes. This model can provide an accurate analysis of radiopharmaceutical delivery from the injection site to the tumor cell, including drug transport in the vascular, interstitial, and intracellular spaces, and considering important parameters (e.g., drug extravasation from microvessels or to lymphatic vessels, the extracellular matrix, receptors, and intracellular space).

RESULTS

Our findings reveal significant enhancements in tumor-absorbed doses as KD decreases. This outcome can be attributed to the higher affinity of radiopharmaceuticals for PSMA receptors as KD diminishes, facilitating a more efficient binding and retention of the therapeutic agent within the tumor microenvironment. Additionally, tumor-absorbed doses for KD ∼ 1 [nM] show an upward trend with higher internalization rates. This observation can be rationalized by considering that a greater internalization rate would result in a higher proportion of radiopharmaceuticals being taken up by tumor cells after binding to receptors on the cell surface. Notably, tumor shape and necrotic zone size exhibit limited influence on tumor absorbed dose.

CONCLUSIONS

The present study employs the CDR model to explore the role of physiological parameters in shaping 177Lu-PSMA-617 RPT delivery. These findings provide insights for improving prostate cancer therapy by understanding radiopharmaceutical transport dynamics. This computational approach contributes to advancing our understanding of radiopharmaceutical delivery mechanisms and has implications for enhancing treatment efficacy.

Programmable intratumoral drug delivery to breast cancer using wireless bioelectronic device with electrochemical actuation

OBJECTIVE

Breast cancer is a global health concern that demands attention. In our contribution to addressing this disease, our study focuses on investigating a wireless micro-device for intratumoral drug delivery, utilizing electrochemical actuation. Microdevices have emerged as a promising approach in this field due to their ability to enable controlled injections in various applications.

METHODS

Our study is conducted within a computational framework, employing models that simulate the behavior of the microdevice and drug discharge based on the principles of the ideal gas law. Furthermore, the distribution of the drug within the tissue is simulated, considering both diffusion and convection mechanisms. To predict the therapeutic response, a pharmacodynamic model is utilized, considering the chemotherapeutic effects and cell proliferation.

RESULTS

The findings demonstrate that an effective current of 3 mA, along with an initial gas volume equal to the drug volume in the microdevice, optimizes drug delivery. Microdevices with multiple injection capabilities exhibit enhanced therapeutic efficacy, effectively suppressing cell proliferation. Additionally, tumors with lower microvascular density experience higher drug concentrations in the extracellular space, resulting in significant cell death in hypoxic regions.

CONCLUSIONS

Achieving an efficient therapeutic response involves considering both the characteristics of the tumor microenvironment and the frequency of injections within a specific time frame.

Localized radiotherapy of solid tumors using radiopharmaceutical loaded implantable system: insights from a mathematical model

Introduction

Computational models yield valuable insights into biological interactions not fully elucidated by experimental approaches. This study investigates an innovative spatiotemporal model for simulating the controlled release and dispersion of radiopharmaceutical therapy (RPT) using 177Lu-PSMA, a prostate-specific membrane antigen (PSMA) targeted radiopharmaceutical, within solid tumors via a dual-release implantable delivery system. Local delivery of anticancer agents presents a strategic approach to mitigate adverse effects while optimizing therapeutic outcomes.

Methods

This study evaluates various factors impacting RPT efficacy, including hypoxia region extension, binding affinity, and initial drug dosage, employing a novel 3-dimensional computational model. Analysis gauges the influence of these factors on radiopharmaceutical agent concentration within the tumor microenvironment. Furthermore, spatial and temporal radiopharmaceutical distribution within both the tumor and surrounding tissue is explored.

Results

Analysis indicates a significantly higher total concentration area under the curve within the tumor region compared to surrounding normal tissue. Moreover, drug distribution exhibits notably superior efficacy compared to the radiation source. Additionally, low microvascular density in extended hypoxia regions enhances drug availability, facilitating improved binding to PSMA receptors and enhancing therapeutic effectiveness. Reductions in the dissociation constant (KD) lead to heightened binding affinity and increased internalized drug concentration. Evaluation of initial radioactivities (7.1×107, 7.1×108, and 7.1×109 [Bq]) indicates that an activity of 7.1×108 [Bq] offers a favorable balance between tumor cell elimination and minimal impact on normal tissues.

Discussion

These findings underscore the potential of localized radiopharmaceutical delivery strategies and emphasize the crucial role of released drugs relative to the radiation source (implant) in effective tumor treatment. Decreasing the proximity of the drug to the microvascular network and enhancing its distribution within the tumor promote a more effective therapeutic outcome. The study furnishes valuable insights for future experimental investigations and clinical trials, aiming to refine medication protocols and minimize reliance on in vivo testing.

Improving tumor treatment through intratumoral injection of drug-loaded magnetic nanoparticles and low-intensity ultrasound

The intratumoral injection of therapeutic agents responsive to external stimuli has gained considerable interest in treating accessible tumors due to its biocompatibility and capacity to reduce side effects. For the first time, a novel approach is explored to investigate the feasibility of utilizing low-intensity ultrasound in combination with intratumoral injection of drug-loaded magnetic nanoparticles (MNPs) to thermal necrosis and chemotherapy with the objective of maximizing tumor damage while avoiding harm to surrounding healthy tissue. In this study, a mathematical framework is proposed based on a multi-compartment model to evaluate the effects of ultrasound transducer's specifications, MNPs size and distribution, and drug release in response to the tumor microenvironment characteristics. The results indicate that while a higher injection rate may increase interstitial fluid pressure, it also simultaneously enhances the concentration of the therapeutic agent. Moreover, by increasing the power and frequency of the transducer, the acoustic pressure and intensity can be enhanced. This, in turn, increases the impact on accumulated MNPs, resulting in a rise in temperature and localized heat generation. Results have demonstrated that smaller MNPs have a lower capacity to generate heat compared to larger MNPs, primarily due to the impact of sound waves on them. It is worth noting that smaller MNPs have been observed to have enhanced diffusion, allowing them to effectively spread within the tumor. However, their smaller size also leads to rapid elimination from the extracellular space into the bloodstream. To summarize, this study demonstrated that the local injection of MNPs carrying drugs not only enables localized chemotherapy but also enhances the effectiveness of low-intensity ultrasound in inducing tissue thermal necrosis. The findings of this study can serve as a valuable and reliable resource for future research in this field and contribute to the development of personalized medicine.

Distinguishing poroelasticity and viscoelasticity of brain tissue with time scale

Brain tissue is considered to be biphasic, with approximately 80% liquid and 20% solid matrix, thus exhibiting viscoelasticity due to rearrangement of the solid matrix and poroelasticity due to fluid migration within the solid matrix. However, how to distinguish poroelastic and viscoelastic effects in brain tissue remains challenging. In this study, we proposed a method of unconfined compression-isometric hold to measure the force versus time relaxation curves of porcine brain tissue samples with systematically varied sample lengths. Upon scaling the measured relaxation force and relaxation time with different length-dependent physical quantities, we successfully distinguished the poroelasticity and viscoelasticity of the brain tissue. We demonstrated that during isometric hold, viscoelastic relaxation dominated the mechanical behavior of brain tissue in the short-time regime, while poroelastic relaxation dominated in the long-time regime. Furthermore, compared with poroelastic relaxation, viscoelastic relaxation was found to play a more dominant role in the mechanical response of porcine brain tissue. We then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue. Because of the draining of pore fluid, the Young's moduli in poroelastic relaxation were lower than those in viscoelastic relaxation; brain tissue changed from incompressible during viscoelastic relaxation to compressible during poroelastic relaxation, resulting in reduced Poisson ratios. This study provides new insights into the physical mechanisms underlying the roles of viscoelasticity and poroelasticity in brain tissue. STATEMENT OF SIGNIFICANCE: Although the poroviscoelastic model had been proposed to characterize brain tissue mechanical behavior, it is difficult to distinguish the poroelastic and viscoelastic behaviors of brain tissue. The study distinguished viscoelasticity and poroelasticity of brain tissue with time scales and then evaluated the differences between poroelastic and viscoelastic effects for both porcine and human brain tissue, which helps to accurate selection of constitutive models suitable for application in certain situations (e.g., pore-dominant and viscoelastic-dominant deformation).

Convection-Enhanced Delivery of Antiangiogenic Drugs and Liposomal Cytotoxic Drugs to Heterogeneous Brain Tumor for Combination Therapy

Simple Summary

Although developed anticancer drugs have shown desirable effects in preclinical trials, the clinical efficacy of chemotherapy against brain cancer remains disappointing. One of the important obstacles is the highly heterogeneous environment in tumors. This study aims to evaluate the performance of an emerging treatment using antiangiogenic and cytotoxic drugs. Our mathematical modelling confirms the advantage of this combination therapy in homogenizing the intratumoral environment for better drug delivery outcomes. In addition, the effects of local microvasculature and cell density on this therapy are also discussed. The results would contribute to the development of more effective treatments for brain cancer.

Abstract

Although convection-enhanced delivery can successfully bypass the blood-brain barrier, its clinical performance remains disappointing. This is primarily attributed to the heterogeneous intratumoral environment, particularly the tumor microvasculature. This study investigates the combined convection-enhanced delivery of antiangiogenic drugs and liposomal cytotoxic drugs in a heterogeneous brain tumor environment using a transport-based mathematical model. The patient-specific 3D brain tumor geometry and the tumor’s heterogeneous tissue properties, including microvascular density, porosity and cell density, are extracted from dynamic contrast-enhanced magnetic resonance imaging data. Results show that antiangiogenic drugs can effectively reduce the tumor microvascular density. This change in tissue structure would inhibit the fluid loss from the blood to prevent drug concentration from dilution, and also reduce the drug loss by blood drainage. The comparisons between different dosing regimens demonstrate that the co-infusion of liposomal cytotoxic drugs and antiangiogenic drugs has the advantages of homogenizing drug distribution, increasing drug accumulation, and enlarging the volume where tumor cells can be effectively killed. The delivery outcomes are susceptible to the location of the infusion site. This combination treatment can be improved by infusing drugs at higher microvascular density sites. In contrast, infusion at a site with high cell density would lower the treatment effectiveness of the whole brain tumor. Results obtained from this study can deepen the understanding of this combination therapy and provide a reference for treatment design and optimization that can further improve survival and patient quality of life.

Spatiotemporal multi-scale modeling of radiopharmaceutical distributions in vascularized solid tumors

We present comprehensive mathematical modeling of radiopharmaceutical spatiotemporal distributions within vascularized solid tumors. The novelty of the presented model is at mathematical level. From the mathematical viewpoint, we provide a general modeling framework for the process of radiopharmaceutical distribution in the tumor microenvironment to enable an analysis of the effect of various tumor-related parameters on the distribution of different radiopharmaceuticals. We argue that partial differential equations (PDEs), beyond conventional methods, including ODE-based kinetic compartment modeling, can be used to evaluate radiopharmaceutical distribution in both time and space. In addition, we consider the spatially-variable dynamic structure of tumor microvascular networks to simulate blood flow distribution. To examine the robustness of the model, the effects of microvessel density (MVD) and tumor size, as two important factors in tumor prognosis, on the radiopharmaceutical distribution within the tumor are investigated over time (in the present work, we focus on the radiopharmaceutical [¹⁸F]FDG, yet the framework is broadly applicable to radiopharmaceuticals). Results demonstrate that the maximum total uptake of [¹⁸F]FDG at all time frames occurs in the tumor area due to the high capillary permeability and lack of a functional lymphatic system. As the MVD of networks increases, the mean total uptake in the tumor is also enhanced, where the rate of diffusion from vessel to tissue has the highest contribution and the rate of convection transport has the lowest contribution. The results of this study can be used to better investigate various phenomena and bridge a gap among cancer biology, mathematical oncology, medical physics, and radiology.

Role of Tissue Hydraulic Permeability in Convection-Enhanced Delivery of Nanoparticle-Encapsulated Chemotherapy Drugs to Brain Tumour

PURPOSE

Tissue hydraulic permeability of brain tumours can vary considerably depending on the tissue microstructure, compositions in interstitium and tumour cells. Its effects on drug transport and accumulation remain poorly understood.

METHODS

Mathematical modelling is applied to predict the drug delivery outcomes in tumours with different tissue permeability upon convection-enhanced delivery. The modelling is based on a 3-D realistic tumour model that is extracted from patient magnetic resonance images.

RESULTS

Modelling results show that infusing drugs into a permeable tumour can facilitate a more favourable hydraulic environment for drug transport. The infused drugs will exhibit a relatively uniform distribution and cover a larger tumour volume for effective cell killing. Cross-comparisons show the delivery outcomes are more sensitive to the changes in tissue hydraulic permeability and blood pressure than the fluid flow from the brain ventricle. Quantitative analyses demonstrate that increasing the fluid gain from both the blood and brain ventricle can further improve the interstitial fluid flow, and thereby enhance the delivery outcomes. Furthermore, similar responses to the changes in tissue hydraulic permeability can be found for different types of drugs.

CONCLUSIONS

Tissue hydraulic permeability as an intrinsic property can influence drug accumulation and distribution. Results from this study can deepen the understanding of the interplays between drug and tissues that are involved in the drug delivery processes in chemotherapy.

Effects of hypoxia and nanocarrier size on pH-responsive nano-delivery system to solid tumors

One of the special features of solid tumors is the acidity of the tumor microenvironment, which is mainly due to the presence of hypoxic regions. Therefore, pH-responsive drug delivery systems have recently been highly welcomed. In the present study, a comprehensive mathematical model is presented based on extravascular drug release paradigm. Accordingly, drug delivery system using pH-responsive nanocarriers is taken into account to examine the impacts of hypoxic regions as well as the size of nanocarriers for cancerous cell-death. The extent of hypoxic regions is controlled by vascular density. This means that regions with very low vascular density represent regions of hypoxia. Using this mathematical model, it is possible to simulate the extracellular and intracellular concentrations of drug by considering the association/disassociation of the free drug to the cell-surface receptors and cellular uptake. Results show that nanocarriers with smaller sizes are more effective due to higher accumulation in the tumor tissue interstitium. The small size of the nanocarriers also allows them to penetrate deeper, so they can expose a larger portion of the tumor to the drug. Additionally, the presence of hypoxic regions in tumor reduces the fraction of killed cancer cells due to reduced penetration depth. The proposed model can be considered for optimizing and developing pH-sensitive delivery systems to reduce both cost and time of the process.

In-vivoviscoelastic properties estimation in subcutaneous adipose tissue by integration of poroviscoelastic-mass transport model (pve-MTM) into wearable electrical impedance tomography (w-EIT)

In-vivoviscoelastic properties have been estimated in human subcutaneous adipose tissue (SAT) by integration of poroviscoelastic-mass transport model (pve-MTM) into wearable electrical impedance tomography (w-EIT) under the influence of external compressive pressure-P.Thepve-MTM predicts the ion concentration distributioncmod(t)by coupling the poroviscoelastic and mass transport model to describe the hydrodynamics, rheology, and transport phenomena inside SAT. Thew-EIT measures the time-difference conductivity distribution∆γ(t)in SAT resulted from the ion transport. Based on the integration, the two viscoelastic properties which are viscoelastic shear modulus of SATGvand relaxation time of SATτvare estimated by applying an iterative curve-fitting between the normalized average ion concentration distributioncˆmod(t)predicted frompve-MTM and the experimental normalized average ion concentration distributioncˆexp(t)derived fromw-EIT. Thein-vivoexperiments were conducted by applying external compressive pressure-Pon human calf boundary to induce interstitial fluid flow and ion movement in SAT. As a result, the value ofGvwas range from 4.9-6.3 kPa and the value ofτvwas range from 27.50-38.5 s with the value of average goodness-of-fit curve fittingR² > 0.76. These values ofGvandτvwere compared to the human and animal tissue from the literature in order to verify this method. The results frompve-MTM provide evidence thatGvandτvplay a role in the predicted value ofcˆmod.

Impact of tumor-parenchyma biomechanics on liver metastatic progression: a multi-model approach

Colorectal cancer and other cancers often metastasize to the liver in later stages of the disease, contributing significantly to patient death. While the biomechanical properties of the liver parenchyma (normal liver tissue) are known to affect tumor cell behavior in primary and metastatic tumors, the role of these properties in driving or inhibiting metastatic inception remains poorly understood, as are the longer-term multicellular dynamics. This study adopts a multi-model approach to study the dynamics of tumor-parenchyma biomechanical interactions during metastatic seeding and growth. We employ a detailed poroviscoelastic model of a liver lobule to study how micrometastases disrupt flow and pressure on short time scales. Results from short-time simulations in detailed single hepatic lobules motivate constitutive relations and biological hypotheses for a minimal agent-based model of metastatic growth in centimeter-scale tissue over months-long time scales. After a parameter space investigation, we find that the balance of basic tumor-parenchyma biomechanical interactions on shorter time scales (adhesion, repulsion, and elastic tissue deformation over minutes) and longer time scales (plastic tissue relaxation over hours) can explain a broad range of behaviors of micrometastases, without the need for complex molecular-scale signaling. These interactions may arrest the growth of micrometastases in a dormant state and prevent newly arriving cancer cells from establishing successful metastatic foci. Moreover, the simulations indicate ways in which dormant tumors could "reawaken" after changes in parenchymal tissue mechanical properties, as may arise during aging or following acute liver illness or injury. We conclude that the proposed modeling approach yields insight into the role of tumor-parenchyma biomechanics in promoting liver metastatic growth, and advances the longer term goal of identifying conditions to clinically arrest and reverse the course of late-stage cancer.

Micromechanical poroelastic and viscoelastic properties of ex-vivo soft tissues

Soft biological tissues demonstrate strong time-dependent mechanical behavior, arising from their intrinsic viscoelasticity and fluid flow-induced poroelasticity. It is increasingly recognized that time-dependent mechanical properties of soft tissues influence their physiological functions and are linked to several pathological processes. Nevertheless, soft tissue time-dependent characteristics, especially their micromechanical variation with tissue composition and location, remain poorly understood. Nanoindentation is a well-established technique to measure local elastic properties but has not been fully explored to determine micro-scale time-dependent properties of soft tissues. Here, a nanoindentation-based experimental strategy is implemented to characterize the micro-scale poroelastic and viscoelastic behavior of mouse heart, kidney, and liver tissues. It is demonstrated that heart tissue exhibits substantial mechanical heterogeneity where the elastic modulus varies spatially from 1 to 30 kPa. In contrast, both kidney and liver tissues show relatively homogeneous response with elastic modulus 0.5-3 kPa. All three tissues demonstrate marked load relaxation under constant indentation, where the relaxation behavior is observed to be largely dominated by tissue viscoelasticity. Intrinsic permeability varies among different tissues, where heart tissue is found to be less permeable compared to kidney and liver tissues. Overall, the results presented herein provide key insights into the time-dependent micromechanical behavior of different tissues and can therefore contribute to studies of tissue pathology and tissue engineering applications.

Liver Bioreactor Design Issues of Fluid Flow and Zonation, Fibrosis, and Mechanics: A Computational Perspective

Tissue engineering, with the goal of repairing or replacing damaged tissue and organs, has continued to make dramatic science-based advances since its origins in the late 1980’s and early 1990’s. Such advances are always multi-disciplinary in nature, from basic biology and chemistry through physics and mathematics to various engineering and computer fields. This review will focus its attention on two topics critical for tissue engineering liver development: (a) fluid flow, zonation, and drug screening, and (b) biomechanics, tissue stiffness, and fibrosis, all within the context of 3D structures. First, a general overview of various bioreactor designs developed to investigate fluid transport and tissue biomechanics is given. This includes a mention of computational fluid dynamic methods used to optimize and validate these designs. Thereafter, the perspective provided by computer simulations of flow, reactive transport, and biomechanics responses at the scale of the liver lobule and liver tissue is outlined, in addition to how bioreactor-measured properties can be utilized in these models. Here, the fundamental issues of tortuosity and upscaling are highlighted, as well as the role of disease and fibrosis in these issues. Some idealized simulations of the effects of fibrosis on lobule drug transport and mechanics responses are provided to further illustrate these concepts. This review concludes with an outline of some practical applications of tissue engineering advances and how efficient computational upscaling techniques, such as dual continuum modeling, might be used to quantify the transition of bioreactor results to the full liver scale.

Effect of tissue permeability and drug diffusion anisotropy on convection-enhanced delivery

Although convection-enhanced delivery (CED) can successfully facilitate a bypass of the blood brain barrier, its treatment efficacy remains highly limited in clinic. This can be partially attributed to the brain anisotropic characteristics that lead to the difficulties in controlling the drug spatial distribution. Here, the responses of six different drugs to the tissue anisotropy are examined through a parametric study performed using a multiphysics model, which considers interstitial fluid flow, tissue deformation and interlinked drug transport processes in CED. The delivery outcomes are evaluated in terms of the penetration depth and delivery volume for effective therapy. Simulation results demonstrate that the effective penetration depth in a given direction can be improved with the increase of the corresponding component of anisotropic characteristics. The anisotropic tissue permeability could only reshape the drug distribution in space but has limited contribution to the total effective delivery volume. On the other hand, drugs respond in different ways to the anisotropic diffusivity. The large delivery volumes of fluorouracil, carmustine, cisplatin and doxorubicin could be achieved in relatively isotropic tissue, while paclitaxel and methotrexate are able to cover enlarged regions into anisotropic tissues. Results obtained from this study serve as a guide for the design of CED treatments.

Characterization of breast tissue permeability for detection of vascular breast tumors: An in vitro study

The biological tissue could be considered as a porous matrix filled with the interstitial fluid. The tumoral tissue has a different permeability from the healthy tissue. With regard to this knowledge, the main objective of the present study is to study the tissue permeability as a diagnostic parameter for the detection of breast cancer. To this end, the healthy and the cancerous specimens of the breast tissue are taken from 17 female cases. All cancerous tumors are in the vascular phase of the growth. The samples undergo a uniaxial compression test by a robotic system while the strain rate is set to remain unchanged. Using the stress and the strain rate data, the strain-dependent permeability is determined, which is an exponential function of the strain level. The permeability function is identified by the initial permeability at the zero compressive strain and a material constant. Results show that the initial permeability of the healthy breast tissue is significantly different from the corresponding value for the cancerous tissue. For all cancerous samples, the permeability is less than the healthy tissue samples; as 40-70% reduction in the initial permeability is observed compared to the healthy breast tissue. The evaluation of the permeability between the healthy and the cancerous specimens is accompanied by the biopsy reports and observing structural images of the specimens using environmental scanning electron microscope. Based on the results, the permeability is suggested to have a diagnostic application for the detection of vascular breast tumors.

Convection enhanced delivery of anti-angiogenic and cytotoxic agents in combination therapy against brain tumour

Convection enhanced delivery is an effective alternative to routine delivery methods to overcome the blood brain barrier. However, its treatment efficacy remains disappointing in clinic owing to the rapid drug elimination in tumour tissue. In this study, multiphysics modelling is employed to investigate the combination delivery of anti-angiogenic and cytotoxic drugs from the perspective of intratumoural transport. Simulations are based on a 3-D realistic brain tumour model that is reconstructed from patient magnetic resonance images. The tumour microvasculature is targeted by bevacizumab, and six cytotoxic drugs are included, as doxorubicin, carmustine, cisplatin, fluorouracil, methotrexate and paclitaxel. The treatment efficacy is evaluated in terms of the distribution volume where the drug concentration is above the corresponding LD90. Results demonstrate that the infusion of bevacizumab can slightly improve interstitial fluid flow, but is significantly efficient in reducing the fluid loss from the blood circulatory system to inhibit the concentration dilution. As the transport of bevacizumab is dominated by convection, its spatial distribution and anti-angiogenic effectiveness present high sensitivity to the directional interstitial fluid flow. Infusing bevacizumab could enhance the delivery outcomes of all the six drugs, however, the degree of enhancement differs. The delivery of doxorubicin can be improved most, whereas, the impacts on methotrexate and paclitaxel are limited. Fluorouracil could cover the comparable distribution volume as paclitaxel in the combination therapy for effective cell killing. Results obtain in this study could be a guide for the design of this co-delivery treatment.

Computational modelling of drug delivery to solid tumour: Understanding the interplay between chemotherapeutics and biological system for optimised delivery systems

Drug delivery to solid tumour involves multiple physiological, biochemical and biophysical processes taking place across a wide range of length and time scales. The therapeutic efficacy of anticancer drugs is influenced by the complex interplays among the intrinsic properties of tumours, biophysical aspects of drug transport and cellular uptake. Mathematical and computational modelling allows for a well-controlled study on the individual and combined effects of a wide range of parameters on drug transport and therapeutic efficacy, which would not be possible or economically viable through experimental means. A wide spectrum of mathematical models has been developed for the simulation of drug transport and delivery in solid tumours, including PK/PD-based compartmental models, microscopic and macroscopic transport models, and molecular dynamics drug loading and release models. These models have been used as a tool to identify the limiting factors and for optimal design of efficient drug delivery systems. This article gives an overview of the currently available computational models for drug transport in solid tumours, together with their applications to novel drug delivery systems, such as nanoparticle-mediated drug delivery and convection-enhanced delivery.

Models and tissue mimics for brain shift simulations

Capturing the deformation of human brain during neurosurgical operations is an extremely important task to improve the accuracy or surgical procedure and minimize permanent damage in patients. This study focuses on the development of an accurate numerical model for the prediction of brain shift during surgical procedures and employs a tissue mimic recently developed to capture the complexity of the human tissue. The phantom, made of a composite hydrogel, was designed to reproduce the dynamic mechanical behaviour of the brain tissue in a range of strain rates suitable for surgical procedures. The use of a well-controlled, accessible and MRI compatible alternative to real brain tissue allows us to rule out spurious effects due to patient geometry and tissue properties variability, CSF amount uncertainties, and head orientation. The performance of different constitutive descriptions is evaluated using a brain-skull mimic, which enables 3D deformation measurements by means of MRI scans. Our combined experimental and numerical investigation demonstrates the importance of using accurate constitutive laws when approaching the modelling of this complex organic tissue and supports the proposal of a hybrid poro-hyper-viscoelastic material formulation for the simulation of brain shift.

Progress Towards Computational 3-D Multicellular Systems Biology

Tumors cannot be understood in isolation from their microenvironment. Tumor and stromal cells change phenotype based upon biochemical and biophysical inputs from their surroundings, even as they interact with and remodel the microenvironment. Cancer should be investigated as an adaptive, multicellular system in a dynamical microenvironment. Computational modeling offers the potential to detangle this complex system, but the modeling platform must ideally account for tumor heterogeneity, substrate and signaling factor biotransport, cell and tissue biophysics, tissue and vascular remodeling, microvascular and interstitial flow, and links between all these sub-systems. Such a platform should leverage high-throughput experimental data, while using open data standards for reproducibility. In this chapter, we review advances by our groups in these key areas, particularly in advanced models of tissue mechanics and interstitial flow, open source simulation software, high-throughput phenotypic screening, and multicellular data standards. In the future, we expect a transformation of computational cancer biology from individual groups modeling isolated parts of cancer, to coalitions of groups combining compatible tools to simulate the 3-D multicellular systems biology of cancer tissues.

On the characterization of the heterogeneous mechanical response of human brain tissue

The mechanical characterization of brain tissue is a complex task that scientists have tried to accomplish for over 50 years. The results in the literature often differ by orders of magnitude because of the lack of a standard testing protocol. Different testing conditions (including humidity, temperature, strain rate), the methodology adopted, and the variety of the species analysed are all potential sources of discrepancies in the measurements. In this work, we present a rigorous experimental investigation on the mechanical properties of human brain, covering both grey and white matter. The influence of testing conditions is also shown and thoroughly discussed. The material characterization performed is finally adopted to provide inputs to a mathematical formulation suitable for numerical simulations of brain deformation during surgical procedures.

Sample, testing and analysis variables affecting liver mechanical properties: A review

Given the critical role of liver mechanics in regulating cell response and directing the development of tissue fibrosis, accurately characterising its mechanical behaviour is of relevance for both diagnostic purposes as well as for tissue engineering and for the development of in-vitro models. Determining and quantifying the mechanical behaviour of soft biological tissues is, however, highly challenging due to their intrinsic labile nature. Indeed, a unique set of values of liver mechanical properties is still lacking to date; testing conditions can significantly affect sample status and hence the measured behaviour and reported results are strongly dependent on the adopted testing method and configuration as well as sample type and status. This review aims at summarising the bulk mechanical properties of liver described in the literature, discussing the possible sources of variation and their implications on the reported results. We distinguish between the intrinsic mechanical behaviour of hepatic tissue, which depends on sample variables, and the measured mechanical properties which also depend on the testing and analysis methods. Finally, the review provides guidelines on tissue preparation and testing conditions for generating reproducible data which can be meaningfully compared across laboratories.

STATEMENT OF SIGNIFICANCE

Soft tissue mechanics is widely investigated, but poorly understood. This review identifies and discusses sample and testing variables which can influence the mechanical behaviour of hepatic tissue and consequently the measured mechanical properties. To encourage the biomaterial community towards more standardized testing of soft tissues and enable comparisons between data from different laboratories, we have established new testing methods and experimental recommendations for sample preparation and testing. The review could be of wide interest to scientists involved in biomaterials research because it addresses and proposes guidelines for several issues related to the mechanical testing of soft tissues whose implications have not been considered together before.

Multiscale computational model of fluid flow and matrix deformation in decellularized liver

Currently little is known about the biomechanical environment in decellularized tissue. The goal of this research is to quantify the mechanical microenvironment in decellularized liver, for varying organ-scale perfusion conditions, using a combined experimental/computational approach. Needle-guided ultra-miniature pressure sensors were inserted into liver tissue to measure parenchymal fluid pressure ex-situ in portal vein-perfused native (n=5) and decellularized (n=7) ferret liver, for flow rates from 3-12mL/min. Pressures were also recorded at the inlet near the portal vein cannula to estimate total vascular resistance of the specimens. Experimental results were fit to a multiscale computational model to simulate perfusion conditions inside native versus decellularized livers for four experimental flow rates. The multiscale model consists of two parts: an organ-scale electrical analog model of liver hemodynamics and a tissue-scale model that predicts pore fluid pressure, pore fluid velocity, and solid matrix stress and deformation throughout the 3D hepatic lobule. Distinct models were created for native versus decellularized liver. Results show that vascular resistance decreases by 82% as a result of decellularization. The hydraulic conductivity of the decellularized liver lobule, a measure of tissue permeability, was 5.6 times that of native liver. For the four flow rates studied, mean fluid pressures in the decellularized lobule were 0.6-2.4mmHg, mean fluid velocities were 211-767μm/s, and average solid matrix principal strains were 1.7-6.1%. In the future this modeling platform can be used to guide the optimization of perfusion seeding and conditioning strategies for decellularized scaffolds in liver bioengineering.

The nano-epsilon dot method for strain rate viscoelastic characterisation of soft biomaterials by spherical nano-indentation

Nano-indentation is widely used for probing the micromechanical properties of materials. Based on the indentation of surfaces using probes with a well-defined geometry, the elastic and viscoelastic constants of materials can be determined by relating indenter geometry and measured load and displacement to parameters which represent stress and deformation. Here we describe a method to derive the viscoelastic properties of soft hydrated materials at the micro-scale using constant strain rates and stress-free initial conditions. Using a new self-consistent definition of indentation stress and strain and corresponding unique depth-independent expression for indentation strain rate, the epsilon dot method, which is suitable for bulk compression testing, is transformed to nano-indentation. We demonstrate how two materials can be tested with a displacement controlled commercial nano-indentor using the nano-espilon dot method (nano-ε̇M) to give values of instantaneous and equilibrium elastic moduli and time constants with high precision. As samples are tested in stress-free initial conditions, the nano-ε̇M could be useful for characterising the micro-mechanical behaviour of soft materials such as hydrogels and biological tissues at cell length scales.

Geometrical features assessment of liver's tumor with application of artificial neural network evolved by imperialist competitive algorithm

Geometrical features of a cancerous tumor embedded in biological soft tissue, including tumor size and depth, are a necessity in the follow-up procedure and making suitable therapeutic decisions. In this paper, a new socio-politically motivated global search strategy which is called imperialist competitive algorithm (ICA) is implemented to train a feed forward neural network (FFNN) to estimate the tumor's geometrical characteristics (FFNNICA). First, a viscoelastic model of liver tissue is constructed by using a series of in vitro uniaxial and relaxation test data. Then, 163 samples of the tissue including a tumor with different depths and diameters are generated by making use of PYTHON programming to link the ABAQUS and MATLAB together. Next, the samples are divided into 123 samples as training dataset and 40 samples as testing dataset. Training inputs of the network are mechanical parameters extracted from palpation of the tissue through a developing noninvasive technology called artificial tactile sensing (ATS). Last, to evaluate the FFNNICA performance, outputs of the network including tumor's depth and diameter are compared with desired values for both training and testing datasets. Deviations of the outputs from desired values are calculated by a regression analysis. Statistical analysis is also performed by measuring Root Mean Square Error (RMSE) and Efficiency (E). RMSE in diameter and depth estimations are 0.50 mm and 1.49, respectively, for the testing dataset. Results affirm that the proposed optimization algorithm for training neural network can be useful to characterize soft tissue tumors accurately by employing an artificial palpation approach.

Strain rate viscoelastic analysis of soft and highly hydrated biomaterials

Measuring the viscoelastic behavior of highly hydrated biological materials is challenging because of their intrinsic softness and labile nature. In these materials, it is difficult to avoid prestress and therefore to establish precise initial stress and strain conditions for lumped parameter estimation using creep or stress-relaxation (SR) tests. We describe a method ( ɛ˙M or epsilon dot method) for deriving the viscoelastic parameters of soft hydrated biomaterials which avoids prestress and can be used to rapidly test degradable samples. Standard mechanical tests are first performed compressing samples using different strain rates. The dataset obtained is then analyzed to mathematically derive the material's viscoelastic parameters. In this work a stable elastomer, polydimethylsiloxane, and a labile hydrogel, gelatin, were first tested using the ɛ˙M, in parallel SR was used to compare lumped parameter estimation. After demonstrating that the elastic parameters are equivalent and that the estimation of short-time constants is more precise using the proposed method, the viscoelastic behavior of porcine liver was investigated using this approach. The results show that the constitutive parameters of hepatic tissue can be quickly quantified without the application of any prestress and before the onset of time-dependent degradation phenomena.

Porohyperviscoelastic model simultaneously predicts parenchymal fluid pressure and reaction force in perfused liver

Porohyperviscoelastic (PHVE) modeling gives a simplified continuum approximation of pore fluid behavior within the parenchyma of liver tissue. This modeling approach is particularly applicable to tissue engineering of artificial livers, where the inherent complexity of the engineered scaffolds prevents the use of computational fluid dynamics. The objectives of this study were to simultaneously predict the experimental parenchymal fluid pressure (PFP) and compression response in a PHVE liver model. The model PFP matched the experimental measurements (318 Pa) to within 1.5%. Linear regression of both phases of compression, ramp, and hold, demonstrated a strong correlation between the model and the experimental reaction force (p<0.5). The ability of this PVE model to accurately predict both fluid and solid behavior is important due to the highly vascularized nature of liver tissue and the mechanosensitivity of liver cells to solid matrix and fluid flow properties.

A viscoelastic constitutive model can accurately represent entire creep indentation tests of human patella cartilage

Cartilage material properties provide important insights into joint health, and cartilage material models are used in whole-joint finite element models. Although the biphasic model representing experimental creep indentation tests is commonly used to characterize cartilage, cartilage short-term response to loading is generally not characterized using the biphasic model. The purpose of this study was to determine the short-term and equilibrium material properties of human patella cartilage using a viscoelastic model representation of creep indentation tests. We performed 24 experimental creep indentation tests from 14 human patellar specimens ranging in age from 20 to 90 years (median age 61 years). We used a finite element model to reproduce the experimental tests and determined cartilage material properties from viscoelastic and biphasic representations of cartilage. The viscoelastic model consistently provided excellent representation of the short-term and equilibrium creep displacements. We determined initial elastic modulus, equilibrium elastic modulus, and equilibrium Poisson's ratio using the viscoelastic model. The viscoelastic model can represent the short-term and equilibrium response of cartilage and may easily be implemented in whole-joint finite element models.

Scale-dependent mechanical properties of native and decellularized liver tissue

Decellularization, a technique used in liver regenerative medicine, is the removal of all the cellular components from a tissue or organ, leaving behind an intact structure of extracellular matrix. The biomechanical properties of this novel scaffold material are currently unknown and are important due to the mechanosensitivity of liver cells. Characterizing this material is important for bioengineering liver tissue from this decellularized scaffold as well as creating new 3-dimensional mimetic structures of liver extracellular matrix. This study set out to characterize the biomechanical properties of perfused liver tissue in its native and decellularized states on both a macro- and nano-scale. Poroviscoelastic finite element models were then used to extract the fluid and solid mechanical properties from the experimental data. Tissue-level spherical indentation-relaxation tests were performed on 5 native livers and 8 decellularized livers at two indentation rates and at multiple perfusion rates. Cellular-level spherical nanoindentation was performed on 2 native livers and 1 decellularized liver. Tissue-level results found native liver tissue to possess a long-term Young's modulus of 10.5 kPa and decellularized tissue a modulus of 1.18 kPa. Cellular-level testing found native tissue to have a long-term Young's modulus of 4.40 kPa and decellularized tissue to have a modulus of 0.91 kPa. These results are important for regenerative medicine and tissue engineering where cellular response is dependent on the mechanical properties of the engineered scaffold.

Perfusion Characteristics of the Human Hepatic Microcirculation Based on Three-Dimensional Reconstructions and Computational Fluid Dynamic Analysis

The perfusion of the liver microcirculation is often analyzed in terms of idealized functional units (hexagonal liver lobules) based on a porous medium approach. More elaborate research is essential to assess the validity of this approach and to provide a more adequate and quantitative characterization of the liver microcirculation. To this end, we modeled the perfusion of the liver microcirculation using an image-based three-dimensional (3D) reconstruction of human liver sinusoids and computational fluid dynamics techniques. After vascular corrosion casting, a microvascular sample (±0.134 mm3) representing three liver lobules, was dissected from a human liver vascular replica and scanned using a high resolution (2.6 μm) micro-CT scanner. Following image processing, a cube (0.15 × 0.15 × 0.15 mm3) representing a sample of intertwined and interconnected sinusoids, was isolated from the 3D reconstructed dataset to define the fluid domain. Three models were studied to simulate flow along three orthogonal directions (i.e., parallel to the central vein and in the radial and circumferential directions of the lobule). Inflow and outflow guidances were added to facilitate solution convergence, and good quality volume meshes were obtained using approximately 9 × 106 tetrahedral cells. Subsequently, three computational fluid dynamics models were generated and solved assuming Newtonian liquid properties (viscosity 3.5 mPa s). Post-processing allowed to visualize and quantify the microvascular flow characteristics, to calculate the permeability tensor and corresponding principal permeability axes, as well as the 3D porosity. The computational fluid dynamics simulations provided data on pressure differences, preferential flow pathways and wall shear stresses. Notably, the pressure difference resulting from the flow simulation parallel to the central vein (0–100 Pa) was clearly smaller than the difference from the radial (0–170 Pa) and circumferential (0–180 Pa) flow directions. This resulted in a higher permeability along the central vein direction (kd,33 = 3.64 × 10−14 m2) in comparison with the radial (kd,11 = 1.56 × 10−14 m2) and circumferential (kd,22 = 1.75 × 10−14 m2) permeabilities which were approximately equal. The mean 3D porosity was 14.3. Our data indicate that the human hepatic microcirculation is characterized by a higher permeability along the central vein direction, and an about two times lower permeability along the radial and circumferential directions of a lobule. Since the permeability coefficients depend on the flow direction, (porous medium) liver microcirculation models should take into account sinusoidal anisotropy.