A computational model for predicting nanoparticle accumulation in tumor vasculature

An Insight into Perfusion Anisotropy within Solid Murine Lung Cancer Tumors

Blood vessels are essential for maintaining tumor growth, progression, and metastasis, yet the tumor vasculature is under a constant state of remodeling. Since the tumor vasculature is an attractive therapeutic target, there is a need to predict the dynamic changes in intratumoral fluid pressure and velocity that occur across the tumor microenvironment (TME). The goal of this study was to obtain insight into perfusion anisotropy within lung tumors. To achieve this goal, we used the perfusion marker Hoechst 33342 and vascular endothelial marker CD31 to stain tumor sections from C57BL/6 mice harboring Lewis lung carcinoma tumors on their flank. Vasculature, capillary diameter, and permeability distribution were extracted at different time points along the tumor growth curve. A computational model was generated by applying a unique modeling approach based on the smeared physical fields (Kojic Transport Model, KTM). KTM predicts spatial and temporal changes in intratumoral pressure and fluid velocity within the growing tumor. Anisotropic perfusion occurs within two domains: capillary and extracellular space. Anisotropy in tumor structure causes the nonuniform distribution of pressure and fluid velocity. These results provide insights regarding local vascular distribution for optimal drug dosing and delivery to better predict distribution and duration of retention within the TME.

An in silico model of the capturing of magnetic nanoparticles in tumour spheroids in the presence of flow

One of the main challenges in improving the efficacy of conventional chemotherapeutic drugs is that they do not reach the cancer cells at sufficiently high doses while at the same time affecting healthy tissue and causing significant side effects and suffering in cancer patients. To overcome this deficiency, magnetic nanoparticles as transporter systems have emerged as a promising approach to achieve more specific tumour targeting. Drug-loaded magnetic nanoparticles can be directed to the target tissue by applying an external magnetic field. However, the magnetic forces exerted on the nanoparticles fall off rapidly with distance, making the tumour targeting challenging, even more so in the presence of flowing blood or interstitial fluid. We therefore present a computational model of the capturing of magnetic nanoparticles in a test setup: our model includes the flow around the tumour, the magnetic forces that guide the nanoparticles, and the transport within the tumour. We show how a model for the transport of magnetic nanoparticles in an external magnetic field can be integrated with a multiphase tumour model based on the theory of porous media. Our approach based on the underlying physical mechanisms can provide crucial insights into mechanisms that cannot be studied conclusively in experimental research alone. Such a computational model enables an efficient and systematic exploration of the nanoparticle design space, first in a controlled test setup and then in more complex in vivo scenarios. As an effective tool for minimising costly trial-and-error design methods, it expedites translation into clinical practice to improve therapeutic outcomes and limit adverse effects for cancer patients.

Rational nanoparticle design: Optimization using insights from experiments and mathematical models

Polymeric nanoparticles are highly tunable drug delivery systems that show promise in targeting therapeutics to specific sites within the body. Rational nanoparticle design can make use of mathematical models to organize and extend experimental data, allowing for optimization of nanoparticles for particular drug delivery applications. While rational nanoparticle design is attractive from the standpoint of improving therapy and reducing unnecessary experiments, it has yet to be fully realized. The difficulty lies in the complexity of nanoparticle structure and behavior, which is added to the complexity of the physiological mechanisms involved in nanoparticle distribution throughout the body. In this review, we discuss the most important aspects of rational design of polymeric nanoparticles. Ultimately, we conclude that many experimental datasets are required to fully model polymeric nanoparticle behavior at multiple scales. Further, we suggest ways to consider the limitations and uncertainty of experimental data in creating nanoparticle design optimization schema, which we call quantitative nanoparticle design frameworks.

Multiscale Modelling of Nanoparticle Distribution in a Realistic Tumour Geometry Following Local Injection

Radiosensitizers have proven to be an effective method of improving radiotherapy outcomes, with the distribution of particles being a crucial element to delivering optimal treatment outcomes due to the short range of effect of these particles. Here we present a computational model for the transport of nanoparticles within the tumour, whereby the fluid velocity and particle deposition are obtained and used as input into the convection-diffusion equation to calculate the spatio-temporal concentration of the nanoparticles. The effect of particle surface charge and injection locations on the distribution of nanoparticle concentration within the interstitial fluid and deposited onto cell surfaces is assessed. The computational results demonstrate that negatively charged particles can achieve a more uniform distribution throughout the tumour as compared to uncharged or positively charged particles, with particle volume within the fluid being 100% of tumour volume and deposited particle volume 44.5%. In addition, varying the injection location from the end to the middle of the tumour caused a reduction in particle volume of almost 20% for negatively charged particles. In conclusion, radiosensitizing particles should be negatively charged to maximise their spread and penetration within the tumour. Choosing an appropriate injection location can further improve the distribution of these particles.

Nanomedicine for Glioblastoma: Progress and Future Prospects

Glioblastoma is the most aggressive form of brain tumor, accounting for the highest mortality and morbidity rates. Current treatment for patients with glioblastoma includes maximal safe tumor resection followed by radiation therapy with concomitant temozolomide (TMZ) chemotherapy. The addition of TMZ to the conformal radiation therapy has improved the median survival time only from 12 months to 16 months in patients with glioblastoma. Despite these aggressive treatment strategies, patients' prognosis remains poor. This therapeutic failure is primarily attributed to the blood-brain barrier (BBB) that restricts the transport of TMZ from reaching the tumor site. In recent years, nanomedicine has gained considerable attention among researchers and shown promising developments in clinical applications, including the diagnosis, prognosis, and treatment of glioblastoma tumors. This review sheds light on the morphological and physiological complexity of the BBB. It also explains the development of nanomedicine strategies to enhance the permeability of drug molecules across the BBB.

Using Parallel Coordinates in Optimization of Nano-Particle Drug Delivery

Nanoparticle drug delivery better targets neoplastic lesions than free drugs and thus has emerged as a safer form of cancer therapy. Nanoparticle design variables are important determinants of efficacy as they influence the drug biodistribution and pharmacokinetics. Previously, we determined optimal designs through mechanistic modeling and optimization. However, the numerical nature of the tumor model and numerous candidate nanoparticle designs hinder hypothesis generation and treatment personalization. In this paper, we utilize the parallel coordinates technique to visualize high-dimensional optimal solutions and extract correlations between nanoparticle design and treatment outcomes. We found that at optimality, two major design variables are dependent, and thus the optimization problem can be reduced. In addition, we obtained an analytical relationship between optimal nanoparticle sizes and optimal distribution, which could facilitate the utilization of tumors models in preclinical studies. Our approach has simplified the results of the previously integrated modeling and optimization framework developed for nanotherapy and enhanced the interpretation and utilization of findings. Integrated mathematical frameworks are increasing in the medical field, and our method can be applied outside nanotherapy to facilitate the clinical translation of computational methods.

Active Targeting Significantly Outperforms Nanoparticle Size in Facilitating Tumor-Specific Uptake in Orthotopic Pancreatic Cancer

Nanoparticles are widely studied as theranostic vehicles for cancer; however, clinical translation has been limited due to poor tumor specificity. Features that maximize tumor uptake remain controversial, particularly when using clinically relevant models. We report a systematic study that assesses two major features for the impact on tumor specificity, i.e., active vs passive targeting and nanoparticle size, to evaluate relative influences in vivo. Active targeting via the V7 peptide is superior to passive targeting for uptake by pancreatic tumors, irrespective of nanoparticle size, observed through in vivo imaging. Size has a secondary effect on uptake for actively targeted nanoparticles in which 26 nm nanoparticles outperform larger 45 and 73 nm nanoparticles. Nanoparticle size had no significant effect on uptake for passively targeted nanoparticles. Results highlight the superiority of active targeting over nanoparticle size for tumor uptake. These findings suggest a framework for optimizing similar nonaggregate nanoparticles for theranostic treatment of recalcitrant cancers.

GANDA: A deep generative adversarial network conditionally generates intratumoral nanoparticles distribution pixels-to-pixels

Intratumoral nanoparticles (NPs) distribution is critical for the success of nanomedicine in imaging and treatment, but computational models to describe the NPs distribution remain unavailable due to the complex tumor-nano interactions. Here, we develop a Generative Adversarial Network for Distribution Analysis (GANDA) to describe and conditionally generates the intratumoral quantum dots (QDs) distribution after i.v. injection. This deep generative model is trained automatically by 27,775 patches of tumor vessels and cell nuclei decomposed from whole-slide images of 4 T1 breast cancer sections. The GANDA model can conditionally generate images of intratumoral QDs distribution under the constraint of given tumor vessels and cell nuclei channels with the same spatial resolution (pixels-to-pixels), minimal loss (mean squared error, MSE = 1.871) and excellent reliability (intraclass correlation, ICC = 0.94). Quantitative analysis of QDs extravasation distance (ICC = 0.95) and subarea distribution (ICC = 0.99) is allowed on the generated images without knowing the real QDs distribution. We believe this deep generative model may provide opportunities to investigate how influencing factors affect NPs distribution in individual tumors and guide nanomedicine optimization for molecular imaging and personalized treatment.

A mathematical model for the quantification of a patient's sensitivity to checkpoint inhibitors and long-term tumour burden

A large proportion of patients with cancer are unresponsive to treatment with immune checkpoint blockade and other immunotherapies. Here, we report a mathematical model of the time course of tumour responses to immune checkpoint inhibitors. The model takes into account intrinsic tumour growth rates, the rates of immune activation and of tumour-immune cell interactions, and the efficacy of immune-mediated tumour killing. For 124 patients, four cancer types and two immunotherapy agents, the model reliably described the immune responses and final tumour burden across all different cancers and drug combinations examined. In validation cohorts from four clinical trials of checkpoint inhibitors (with a total of 177 patients), the model accurately stratified the patients according to reduced or increased long-term tumour burden. We also provide model-derived quantitative measures of treatment sensitivity for specific drug-cancer combinations. The model can be used to predict responses to therapy and to quantify specific drug-cancer sensitivities in individual patients.

Imaging-based characterization of convective tissue properties

Convective transport is an important phenomenon for nanomedicine delivery. We present an imaging-based approach to recover tissue properties that are significant in the accumulation of nanoparticles delivered via systemic methods. The classical pharmacokinetic analysis develops governing equations for the particle transport from a first principle mass balance. Fundamentally, the governing equations for compartmental mass balance represent a spatially invariant mass transport between compartments and do not capture spatially variant convection phenomena. Further, the parameters recovered from this approach do not necessarily have direct meaning with respect to the governing equations for convective transport. In our approach, a framework is presented for directly measuring permeability in the sense of Darcy flow through porous tissue. Measurements from our approach are compared to an extended Tofts model as a control. We demonstrate that a pixel-wise iterative clustering algorithm may be applied to reduce the parameter space of the measurements. We show that measurements obtained from our approach are correlated with measurements obtained from the extended Tofts model control. These correlations demonstrate that the proposed approach contains similar information to an established compartmental model and may be useful in providing an alternative theoretical framework for parameterizing mathematical models for treatment planning and diagnostic studies involving nanomedicine where convection dominated effects are important.

A Dual Nanoparticle Delivery Strategy for Enhancing Drug Distribution in Cancerous Tissue

Nanoparticle-mediated drug delivery may be a promising alternative to traditional chemotherapy of high systemic toxicity. Tumor tissue architecture poses a challenge to delivery of nanoparticles. Small and spherical nanoparticles have poor adherence to the tumor vasculature, while larger and more eccentric ones create high heterogeneity in tissue-to-drug exposure. In previous work, we quantified these tradeoffs using numerical optimization. In this study, we demonstrate that simultaneous delivery of multiple nanoparticle designs can enhance drug distribution in the cancerous tissue without compromising nanoparticle tumoral accumulation. We formulate and solve optimization problems to find the optimal constituent of the heterogeneous injection in terms of nanoparticle design diversity that increases drug distribution by 14%.

Modeling of Nanotherapy Response as a Function of the Tumor Microenvironment: Focus on Liver Metastasis

The tumor microenvironment (TME) presents a challenging barrier for effective nanotherapy-mediated drug delivery to solid tumors. In particular for tumors less vascularized than the surrounding normal tissue, as in liver metastases, the structure of the organ itself conjures with cancer-specific behavior to impair drug transport and uptake by cancer cells. Cells and elements in the TME of hypovascularized tumors play a key role in the process of delivery and retention of anti-cancer therapeutics by nanocarriers. This brief review describes the drug transport challenges and how they are being addressed with advanced in vitro 3D tissue models as well as with in silico mathematical modeling. This modeling complements network-oriented techniques, which seek to interpret intra-cellular relevant pathways and signal transduction within cells and with their surrounding microenvironment. With a concerted effort integrating experimental observations with computational analyses spanning from the molecular- to the tissue-scale, the goal of effective nanotherapy customized to patient tumor-specific conditions may be finally realized.

Drug delivery: Experiments, mathematical modelling and machine learning

We address the problem of determining from laboratory experiments the data necessary for a proper modeling of drug delivery and efficacy in anticancer therapy. There is an inherent difficulty in extracting the necessary parameters, because the experiments often yield an insufficient quantity of information. To overcome this difficulty, we propose to combine real experiments, numerical simulation, and Machine Learning (ML) based on Artificial Neural Networks (ANN), aiming at a reliable identification of the physical model factors, e.g. the killing action of the drug. To this purpose, we exploit the employed mathematical-numerical model for tumor growth and drug delivery, together with the ANN - ML procedure, to integrate the results of the experimental tests and feed back the model itself, thus obtaining a reliable predictive tool. The procedure represents a hybrid data-driven, physics-informed approach to machine learning. The physical and mathematical model employed for the numerical simulations is without extracellular matrix (ECM) and healthy cells because of the experimental conditions we reproduce.

Multi-objective optimization of tumor response to drug release from vasculature-bound nanoparticles

The pharmacokinetics of nanoparticle-borne drugs targeting tumors depends critically on nanoparticle design. Empirical approaches to evaluate such designs in order to maximize treatment efficacy are time- and cost-intensive. We have recently proposed the use of computational modeling of nanoparticle-mediated drug delivery targeting tumor vasculature coupled with numerical optimization to pursue optimal nanoparticle targeting and tumor uptake. Here, we build upon these studies to evaluate the effect of tumor size on optimal nanoparticle design by considering a cohort of heterogeneously-sized tumor lesions, as would be clinically expected. The results indicate that smaller nanoparticles yield higher tumor targeting and lesion regression for larger-sized tumors. We then augment the nanoparticle design optimization problem by considering drug diffusivity, which yields a two-fold tumor size decrease compared to optimizing nanoparticles without this consideration. We quantify the tradeoff between tumor targeting and size decrease using bi-objective optimization, and generate five Pareto-optimal nanoparticle designs. The results provide a spectrum of treatment outcomes - considering tumor targeting vs. antitumor effect - with the goal to enable therapy customization based on clinical need. This approach could be extended to other nanoparticle-based cancer therapies, and support the development of personalized nanomedicine in the longer term.

Mathematical prediction of clinical outcomes in advanced cancer patients treated with checkpoint inhibitor immunotherapy

We present a mechanistic mathematical model of immune checkpoint inhibitor therapy to address the oncological need for early, broadly applicable readouts (biomarkers) of patient response to immunotherapy. The model is built upon the complex biological and physical interactions between the immune system and cancer, and is informed using only standard-of-care CT. We have retrospectively applied the model to 245 patients from multiple clinical trials treated with anti-CTLA-4 or anti-PD-1/PD-L1 antibodies. We found that model parameters distinctly identified patients with common (n = 18) and rare (n = 10) malignancy types who benefited and did not benefit from these monotherapies with accuracy as high as 88% at first restaging (median 53 days). Further, the parameters successfully differentiated pseudo-progression from true progression, providing previously unidentified insights into the unique biophysical characteristics of pseudo-progression. Our mathematical model offers a clinically relevant tool for personalized oncology and for engineering immunotherapy regimens.

A mathematical model to predict nanomedicine pharmacokinetics and tumor delivery

Towards clinical translation of cancer nanomedicine, it is important to systematically investigate the various parameters related to nanoparticle (NP) physicochemical properties, tumor characteristics, and inter-individual variability that affect the tumor delivery efficiency of therapeutic nanomaterials. Comprehensive investigation of these parameters using traditional experimental approaches is impractical due to the vast parameter space; mathematical models provide a more tractable approach to navigate through such a multidimensional space. To this end, we have developed a predictive mathematical model of whole-body NP pharmacokinetics and their tumor delivery in vivo, and have conducted local and global sensitivity analyses to identify the factors that result in low tumor delivery efficiency and high off-target accumulation of NPs. Our analyses reveal that NP degradation rate, tumor blood viscosity, NP size, tumor vascular fraction, and tumor vascular porosity are the key parameters in governing NP kinetics in the tumor interstitium. The impact of these parameters on tumor delivery efficiency of NPs is discussed, and optimal values for maximizing NP delivery are presented.

Improving nanotherapy delivery and action through image-guided systems pharmacology

Despite recent advances in the translation of therapeutic nanoparticles (TNPs) into the clinic, the field continues to face challenges in predictably and selectively delivering nanomaterials for the treatment of solid cancers. The concept of enhanced permeability and retention (EPR) has been coined as a convenient but simplistic descriptor of high TNP accumulation in some tumors. However, in practice EPR represents a number of physiological variables rather than a single one (including dysfunctional vasculature, compromised lymphatics and recruited host cells, among other aspects of the tumor microenvironment) — each of which can be highly heterogenous within a given tumor, patient and across patients. Therefore, a clear need exists to dissect the specific biophysical factors underlying the EPR effect, to formulate better TNP designs, and to identify patients with high-EPR tumors who are likely to respond to TNP. The overall pharmacology of TNP is governed by an interconnected set of spatially defined and dynamic processes that benefit from a systems-level quantitative approach, and insights into the physiology have profited from the marriage between in vivo imaging and quantitative systems pharmacology (QSP) methodologies. In this article, we review recent developments pertinent to image-guided systems pharmacology of nanomedicines in oncology. We first discuss recent developments of quantitative imaging technologies that enable analysis of nanomaterial pharmacology at multiple spatiotemporal scales, and then examine reports that have adopted these imaging technologies to guide QSP approaches. In particular, we focus on studies that have integrated multi-scale imaging with computational modeling to derive insights about the EPR effect, as well as studies that have used modeling to guide the manipulation of the EPR effect and other aspects of the tumor microenvironment for improving TNP action. We anticipate that the synergistic combination of imaging with systems-level computational methods for effective clinical translation of TNPs will only grow in relevance as technologies increase in resolution, multiplexing capability, and in the ability to examine heterogeneous behaviors at the single-cell level.

Recent progress in the research of suicide gene therapy for malignant glioma

Malignant glioma, which is characterized by diffuse infiltration into the normal brain parenchyma, is the most aggressive primary brain tumor with dismal prognosis. Over the past 40 years, the median survival has only slightly improved. Therefore, new therapeutic modalities must be developed. In the 1990s, suicide gene therapy began attracting attention for the treatment of malignant glioma. Some clinical trials used a viral vector for suicide gene transduction; however, it was found that viral vectors cannot cover the large invaded area of glioma cells. Interest in this therapy was recently revived because some types of stem cells possess a tumor-tropic migratory capacity, which can be used as cellular delivery vehicles. Immortalized, clonal neural stem cell (NSC) line has been used for patients with recurrent high-grade glioma, which showed safety and efficacy. Embryonic and induced pluripotent stem cells may be considered as sources of NSC because NSC is difficult to harvest, and ethical issues have been raised. Mesenchymal stem cells are alternative candidates for cellular vehicle and are easily harvested from the bone marrow. In addition, a new type of nonlytic, amphotropic retroviral replicating vector encoding suicide gene has shown efficacy in patients with recurrent high-grade glioma in a clinical trial. This replicating viral capacity is another possible candidate as delivery vehicle to tackle gliomas. Herein, we review the concept of suicide gene therapy, as well as recent progress in preclinical and clinical studies in this field.

Pharmacokinetic/Pharmacodynamics Modeling of Drug-Loaded PLGA Nanoparticles Targeting Heterogeneously Vascularized Tumor Tissue

PURPOSE

Nanoparticle-mediated drug delivery and efficacy for cancer applications depends on systemic as well as local microenvironment characteristics. Here, a novel coupling of a nanoparticle (NP) kinetic model with a drug pharmacokinetic/pharmacodynamics model evaluates efficacy of cisplatin-loaded poly lactic-co-glycolic acid (PLGA) NPs in heterogeneously vascularized tumor tissue.

METHODS

Tumor lesions are modeled with various levels of vascular heterogeneity, as would be encountered with different types of tumors. The magnitude of the extracellular to cytosolic NP transport is varied to assess tumor-dependent cellular uptake. NP aggregation is simulated to evaluate its effects on drug distribution and tumor response.

RESULTS

Cisplatin-loaded PLGA NPs are most effective in decreasing tumor size in the case of high vascular-induced heterogeneity, a high NP cytosolic transfer coefficient, and no NP aggregation. Depending on the level of tissue heterogeneity, NP cytosolic transfer and drug half-life, NP aggregation yielding only extracellular drug release could be more effective than unaggregated NPs uptaken by cells and releasing drug both extra- and intra-cellularly.

CONCLUSIONS

Model-based customization of PLGA NP and drug design parameters, including cellular uptake and aggregation, tailored to patient tumor tissue characteristics such as proportion of viable tissue and vascular heterogeneity, could help optimize the NP-mediated tumor drug response.

Biological intratumoral therapy for the high-grade glioma part II: vector- and cell-based therapies and radioimmunotherapy

Management of high-grade gliomas (HGGs) remains a complex challenge with an overall poor prognosis despite aggressive multimodal treatment. New translational research has focused on maximizing tumor cell eradication through improved tumor cell targeting while minimizing collateral systemic side effects. In particular, biological intratumoral therapies have been the focus of novel translational research efforts due to their inherent potential to be both dynamically adaptive and target specific. This two part review will provide an overview of biological intratumoral therapies that have been evaluated in human clinical trials in HGGs, and summarize key advances and remaining challenges in the development of these therapies as a potential new paradigm in the management of HGGs. Part II discusses vector-based therapies, cell-based therapies and radioimmunotherapy.

Nanoparticle Optimization for Enhanced Targeted Anticancer Drug Delivery

Nanoparticle (NP)-based drug delivery is a promising method to increase the therapeutic index of anticancer agents with low median toxic dose. The delivery efficiency, corresponding to the fraction of the injected NPs that adhere to the tumor site, depends on NP size a and aspect ratio AR. Values for these variables are currently chosen empirically, which may not result in optimal targeted drug delivery. This study applies rigorous optimization to the design of NPs. A preliminary investigation revealed that delivery efficiency increases monotonically with a and AR. However, maximizing a and AR results in nonuniform drug distribution, which impairs tumor regression. Therefore, a multiobjective optimization (MO) problem is formulated to quantify the trade-off between NPs accumulation and distribution. The MO is solved using the derivative-free mesh adaptive direct search algorithm. Theoretically, the Pareto-optimal set consists of an infinite number of mathematically equivalent solutions to the MO problem. However, interesting design solutions can be identified subjectively, e.g., the ellipsoid with a major axis of 720 nm and an aspect ratio of 7.45, as the solution closest to the utopia point. The MO problem formulation is then extended to optimize NP biochemical properties: ligand-receptor binding affinity and ligand density. Optimizing physical and chemical properties simultaneously results in optimal designs with reduced NP sizes and thus enhanced cellular uptake. The presented study provides an insight into NP structures that have potential for producing desirable drug delivery.

Hybrid modeling frameworks of tumor development and treatment

Tumors are complex multicellular heterogeneous systems comprised of components that interact with and modify one another. Tumor development depends on multiple factors: intrinsic, such as genetic mutations, altered signaling pathways, or variable receptor expression; and extrinsic, such as differences in nutrient supply, crosstalk with stromal or immune cells, or variable composition of the surrounding extracellular matrix. Tumors are also characterized by high cellular heterogeneity and dynamically changing tumor microenvironments. The complexity increases when this multiscale, multicomponent system is perturbed by anticancer treatments. Modeling such complex systems and predicting how tumors will respond to therapies require mathematical models that can handle various types of information and combine diverse theoretical methods on multiple temporal and spatial scales, that is, hybrid models. In this update, we discuss the progress that has been achieved during the last 10 years in the area of the hybrid modeling of tumors. The classical definition of hybrid models refers to the coupling of discrete descriptions of cells with continuous descriptions of microenvironmental factors. To reflect on the direction that the modeling field has taken, we propose extending the definition of hybrid models to include of coupling two or more different mathematical frameworks. Thus, in addition to discussing recent advances in discrete/continuous modeling, we also discuss how these two mathematical descriptions can be coupled with theoretical frameworks of optimal control, optimization, fluid dynamics, game theory, and machine learning. All these methods will be illustrated with applications to tumor development and various anticancer treatments.

This article is characterized under:

Analytical and Computational Methods > Computational Methods

Translational, Genomic, and Systems Medicine > Therapeutic Methods

Models of Systems Properties and Processes > Organ, Tissue, and Physiological Models

Mathematical modeling in cancer nanomedicine: a review

Cancer continues to be among the leading healthcare problems worldwide, and efforts continue not just to find better drugs, but also better drug delivery methods. The need for delivering cytotoxic agents selectively to cancerous cells, for improved safety and efficacy, has triggered the application of nanotechnology in medicine. This effort has provided drug delivery systems that can potentially revolutionize cancer treatment. Nanocarriers, due to their capacity for targeted drug delivery, can shift the balance of cytotoxicity from healthy to cancerous cells. The field of cancer nanomedicine has made significant progress, but challenges remain that impede its clinical translation. Several biophysical barriers to the transport of nanocarriers to the tumor exist, and a much deeper understanding of nano-bio interactions is necessary to change the status quo. Mathematical modeling has been instrumental in improving our understanding of the physicochemical and physiological underpinnings of nanomaterial behavior in biological systems. Here, we present a comprehensive review of literature on mathematical modeling works that have been and are being employed towards a better understanding of nano-bio interactions for improved tumor delivery efficacy.

Computational Approaches in Theranostics: Mining and Predicting Cancer Data

The ability to understand the complexity of cancer-related data has been prompted by the applications of (1) computer and data sciences, including data mining, predictive analytics, machine learning, and artificial intelligence, and (2) advances in imaging technology and probe development. Computational modelling and simulation are systematic and cost-effective tools able to identify important temporal/spatial patterns (and relationships), characterize distinct molecular features of cancer states, and address other relevant aspects, including tumor detection and heterogeneity, progression and metastasis, and drug resistance. These approaches have provided invaluable insights for improving the experimental design of therapeutic delivery systems and for increasing the translational value of the results obtained from early and preclinical studies. The big question is: Could cancer theranostics be determined and controlled in silico? This review describes the recent progress in the development of computational models and methods used to facilitate research on the molecular basis of cancer and on the respective diagnosis and optimized treatment, with particular emphasis on the design and optimization of theranostic systems. The current role of computational approaches is providing innovative, incremental, and complementary data-driven solutions for the prediction, simplification, and characterization of cancer and intrinsic mechanisms, and to promote new data-intensive, accurate diagnostics and therapeutics.

Efficacy of Surface-Modified PLGA Nanoparticles as a Function of Cervical Cancer Type

PURPOSE

Hypovascularization of cervical tumors, coupled with intrinsic and acquired drug resistance, has contributed to marginal therapeutic outcomes by hindering chemotherapeutic transport and efficacy. Recently, the heterogeneous penetration and distribution of cell penetrating peptide (CPP, here MPG) and polyethylene glycol (PEG) modified poly(lactic-co-glycolic acid) (PLGA) nanoparticles (NPs) were evaluated as a function of tumor type and morphology in cervical cancer spheroids modeling hypovascularized tumor nodules. Building upon this work, this study investigates the efficacy imparted by surface-modified Doxorubicin-loaded NPs transported into hypovascularized tissue.

METHODS

NP efficacy was measured in HeLa, CaSki, and SiHa cells. NP internalization and association, and associated cell viability, were determined in monolayer and spheroid models.

RESULTS

MPG and PEG-NP co-treatment was most efficacious in HeLa cells, while PEG NPs were most efficacious in CaSki cells. NP surface-modifications were unable to improve efficacy, relative to unmodified NPs, in SiHa cells.

CONCLUSIONS

The results highlight the dependence of efficacy on tumor type and the associated microenvironment. The results further relate previous NP transport studies to efficacy, as a function of surface-modification and cell type. Longer-term, this information may help guide the design of NP-mediated strategies to maximize efficacy based on patient-specific cervical tumor origin and characteristics.

Pharmacokinetics and Pharmacodynamics Modeling and Simulation Systems to Support the Development and Regulation of Liposomal Drugs

Liposomal formulations have been developed to improve the therapeutic index of encapsulated drugs by altering the balance of on- and off-targeted distribution. The improved therapeutic efficacy of liposomal drugs is primarily attributed to enhanced distribution at the sites of action. The targeted distribution of liposomal drugs depends not only on the physicochemical properties of the liposomes, but also on multiple components of the biological system. Pharmacokinetic⁻pharmacodynamic (PK⁻PD) modeling has recently emerged as a useful tool with which to assess the impact of formulation- and system-specific factors on the targeted disposition and therapeutic efficacy of liposomal drugs. The use of PK⁻PD modeling to facilitate the development and regulatory reviews of generic versions of liposomal drugs recently drew the attention of the U.S. Food and Drug Administration. The present review summarizes the physiological factors that affect the targeted delivery of liposomal drugs, challenges that influence the development and regulation of liposomal drugs, and the application of PK⁻PD modeling and simulation systems to address these challenges.

Pharmacokinetic analysis reveals limitations and opportunities for nanomedicine targeting of endothelial and extravascular compartments of tumours

Targeting of nanoparticles to tumours can potentially improve the specificity of imaging and treatments. We have developed a multicompartmental pharmacokinetic model in order to analyse some of the factors that control efficiency of targeting to intravascular (endothelium) and extravascular (tumour cells and stroma) compartments. We make the assumption that transport across tumour endothelium is an important step for subsequent nanoparticle accumulation in the tumour (area-under-the-curve, AUC) regardless of entry route (interendothelial and transendothelial routes) and study this through a multicompartmental simulation. Our model reveals that increasing endothelial targeting efficiency has a much stronger effect on the AUC than increasing extravascular targeting efficiency. Furthermore, our analysis reveals that both extravasation and intratumoral diffusion rates need to be increased in order to significantly increase the AUC of extravascular-targeted nanoparticles. Increasing the nanoparticle circulation half-life increases the AUC independently of extravasation and intratumoral diffusion. Targeting the extravascular compartment leads to a buildup in the first layer surrounding blood vessels at the expense of deeper layers (binding site barrier). This model explains some of the limitations of tumour targeting and provides important guidelines for the design of targeted nanomedicines.

Design Optimization of Tumor Vasculature-Bound Nanoparticles

Nanotherapy may constitute a promising approach to target tumors with anticancer drugs while minimizing systemic toxicity. Computational modeling can enable rapid evaluation of nanoparticle (NP) designs and numerical optimization. Here, an optimization study was performed using an existing tumor model to find NP size and ligand density that maximize tumoral NP accumulation while minimizing tumor size. Optimal NP avidity lies at lower bound of feasible values, suggesting reduced ligand density to prolong NP circulation. For the given set of tumor parameters, optimal NP diameters were 288 nm to maximize NP accumulation and 334 nm to minimize tumor diameter, leading to uniform NP distribution and adequate drug load. Results further show higher dependence of NP biodistribution on the NP design than on tumor morphological parameters. A parametric study with respect to drug potency was performed. The lower the potency of the drug, the bigger the difference is between the maximizer of NP accumulation and the minimizer of tumor size, indicating the existence of a specific drug potency that minimizes the differential between the two optimal solutions. This study shows the feasibility of applying optimization to NP designs to achieve efficacious cancer nanotherapy, and offers a first step towards a quantitative tool to support clinical decision making.

Evaluation of Drug-Loaded Gold Nanoparticle Cytotoxicity as a Function of Tumor Vasculature-Induced Tissue Heterogeneity

The inherent heterogeneity of tumor tissue presents a major challenge to nanoparticle-mediated drug delivery. This heterogeneity spans from the molecular (genomic, proteomic, metabolomic) to the cellular (cell types, adhesion, migration) and to the tissue (vasculature, extra-cellular matrix) scales. In particular, tumor vasculature forms abnormally, inducing proliferative, hypoxic, and necrotic tumor tissue regions. As the vasculature is the main conduit for nanotherapy transport into tumors, vasculature-induced tissue heterogeneity can cause local inadequate delivery and concentration, leading to subpar response. Further, hypoxic tissue, although viable, would be immune to the effects of cell-cycle specific drugs. In order to enable a more systematic evaluation of such effects, here we employ computational modeling to study the therapeutic response as a function of vasculature-induced tumor tissue heterogeneity. Using data with three-layered gold nanoparticles loaded with cisplatin, nanotherapy is simulated interacting with different levels of tissue heterogeneity, and the treatment response is measured in terms of tumor regression. The results quantify the influence that varying levels of tumor vascular density coupled with the drug strength have on nanoparticle uptake and washout, and the associated tissue response. The drug strength affects the proportion of proliferating, hypoxic, and necrotic tissue fractions, which in turn dynamically affect and are affected by the vascular density. Higher drug strengths may be able to achieve stronger tumor regression but only if the intra-tumoral vascular density is above a certain threshold that affords sufficient transport. This study establishes an initial step towards a more systematic methodology to assess the effect of vasculature-induced tumor tissue heterogeneity on the response to nanotherapy.

Nanoparticle localization in blood vessels: dependence on fluid shear stress, flow disturbances, and flow-induced changes in endothelial physiology

Nanoparticles in the bloodstream are subjected to complex fluid forces as they move through the curves and branches of healthy or tumor vasculature. While nanoparticles are known to preferentially accumulate in angiogenic vessels, little is known about the flow conditions in these vessels and how these conditions may influence localization. Here, we report a methodology which combines confocal imaging of nanoparticle-injected transgenic zebrafish embryos, 3D modeling of the vasculature, particle mapping, and computational fluid dynamics, to quantitatively assess the effects of fluid forces on nanoparticle distribution in vivo. Six-fold lower accumulation was found in zebrafish arteries compared to the lower velocity veins. Nanoparticle localization varied inversely with shear stress. Highest accumulation was present in regions of disturbed flow found at branch points and curvatures in the vasculature. To further investigate cell-particle association under flow, human endothelial cells were exposed to nanoparticles under hemodynamic conditions typically found in human vessels. Physiological adaptations of endothelial cells to 20 hours of flow enhanced nanoparticle accumulation in regions of disturbed flow. Overall our results suggest that fluid shear stress magnitude, flow disturbances, and flow-induced changes in endothelial physiology modulate nanoparticle localization in angiogenic vessels.

Nanoparticle-mediated drug delivery to treat infections in the female reproductive tract: evaluation of experimental systems and the potential for mathematical modeling

A variety of drug-delivery platforms have been employed to deliver therapeutic agents across cervicovaginal mucus (CVM) and the vaginal mucosa, offering the capability to increase the longevity and retention of active agents to treat infections of the female reproductive tract (FRT). Nanoparticles (NPs) have been shown to improve retention, diffusion, and cell-specific targeting via specific surface modifications, relative to other delivery platforms. In particular, polymeric NPs represent a promising option that has shown improved distribution through the CVM. These NPs are typically fabricated from nontoxic, non-inflammatory, US Food and Drug Administration-approved polymers that improve biocompatibility. This review summarizes recent experimental studies that have evaluated NP transport in the FRT, and highlights research areas that more thoroughly and efficiently inform polymeric NP design, including mathematical modeling. An overview of the in vitro, ex vivo, and in vivo NP studies conducted to date – whereby transport parameters are determined, extrapolated, and validated – is presented first. The impact of different NP design features on transport through the FRT is summarized, and gaps that exist due to the limitations of iterative experimentation alone are identified. The potential of mathematical modeling to complement the characterization and evaluation of diffusion and transport of delivery vehicles and active agents through the CVM and mucosa is discussed. Lastly, potential advancements combining experimental and mathematical knowledge are suggested to inform next-generation NP designs, such that infections in the FRT may be more effectively treated.

Advances in Glioblastoma Multiforme Treatment: New Models for Nanoparticle Therapy

The most lethal form of brain cancer, glioblastoma multiforme, is characterized by rapid growth and invasion facilitated by cell migration and degradation of the extracellular matrix. Despite technological advances in surgery and radio-chemotherapy, glioblastoma remains largely resistant to treatment. New approaches to study glioblastoma and to design optimized therapies are greatly needed. One such approach harnesses computational modeling to support the design and delivery of glioblastoma treatment. In this paper, we critically summarize current glioblastoma therapy, with a focus on emerging nanomedicine and therapies that capitalize on cell-specific signaling in glioblastoma. We follow this summary by discussing computational modeling approaches focused on optimizing these emerging nanotherapeutics for brain cancer. We conclude by illustrating how mathematical analysis can be used to compare the delivery of a high potential anticancer molecule, delphinidin, in both free and nanoparticle loaded forms across the blood-brain barrier for glioblastoma.

Activation of the HGF/c-Met axis in the tumor microenvironment: A multispecies model

The tumor microenvironment is an integral component in promoting tumor development. Cancer-associated fibroblasts (CAFs), which reside in the tumor stroma, produce Hepatocyte Growth Factor (HGF), an important trigger for invasive and metastatic tumor behavior. HGF contributes to a pro-tumorigenic environment by activating its cognate receptor, c-Met, on tumor cells. Tumor cells, in turn, secrete growth factors that upregulate HGF production in CAFs, thereby establishing a dynamic tumor-host signaling program. Using a spatiotemporal multispecies model of tumor growth, we investigate how the development and spread of a tumor is impacted by the initiation of a dynamic interaction between tumor-derived growth factors and CAF-derived HGF. We show that establishment of such an interaction results in increased tumor growth and morphological instability, the latter due in part to increased cell species heterogeneity at the tumor-host boundary. Invasive behavior is further increased if the tumor lowers responsiveness to paracrine pro-differentiation signals, which is a hallmark of neoplastic development. By modeling anti-HGF and anti-c-Met therapy, we show how disruption of the HGF/c-Met axis can reduce tumor invasiveness and growth, thereby providing theoretical evidence that targeting tumor-microenvironment interactions is a promising avenue for therapeutic development.

Nanomaterials for In Vivo Imaging

In vivo imaging, which enables us to peer deeply within living subjects, is producing tremendous opportunities both for clinical diagnostics and as a research tool. Contrast material is often required to clearly visualize the functional architecture of physiological structures. Recent advances in nanomaterials are becoming pivotal to generate the high-resolution, high-contrast images needed for accurate, precision diagnostics. Nanomaterials are playing major roles in imaging by delivering large imaging payloads, yielding improved sensitivity, multiplexing capacity, and modularity of design. Indeed, for several imaging modalities, nanomaterials are now not simply ancillary contrast entities, but are instead the original and sole source of image signal that make possible the modality's existence. We address the physicochemical makeup/design of nanomaterials through the lens of the physical properties that produce contrast signal for the cognate imaging modality-we stratify nanomaterials on the basis of their (i) magnetic, (ii) optical, (iii) acoustic, and/or (iv) nuclear properties. We evaluate them for their ability to provide relevant information under preclinical and clinical circumstances, their in vivo safety profiles (which are being incorporated into their chemical design), their modularity in being fused to create multimodal nanomaterials (spanning multiple different physical imaging modalities and therapeutic/theranostic capabilities), their key properties, and critically their likelihood to be clinically translated.

3D nano- and micro-patterning of biomaterials for controlled drug delivery

Recently, there has been an emerging interest in controlling 3D structures and designing novel 3D shapes for drug carriers at nano- and micro-scales. Certain 3D shapes and structures of drug particles enable transportation of the drugs to desired areas of the body, allow drugs to target specific cells and tissues, and influence release kinetics. Advanced nano- and micro-manufacturing methods including 3D printing, photolithography-based processes, microfluidics and DNA origami have been developed to generate defined 3D shapes and structures for drug carriers. This paper reviews the importance of 3D structures and shapes on controlled drug delivery, and the current state-of-the-art technologies that allow the creation of novel 3D drug carriers at nano- and micro-scales.

Facilitating the Clinical Integration of Nanomedicines: The Roles of Theoretical and Computational Scientists

Since the launch of multiple research initiatives on nanotechnology applied to medicine in the early 2000s, a plethora of nanomedicines have been developed that exhibit great therapeutic efficacy in preclinical models but yet minimal impact in daily clinical practice. The successful and complete clinical fruition of nanomedicines requires addressing three major technical challenges: improving loading efficacy and on-command release, modulating recognition and sequestration by immune cells, and maximizing accumulation at biological targets. In this Perspective, I describe how theoretical and computational models can help address each of these challenges. This armamentarium represents an ideal tool for maximizing the therapeutic efficacy of nanomedicines, thus facilitating their integration into daily clinical operations.

Generalized plasma skimming model for cells and drug carriers in the microvasculature

In microvascular transport, where both blood and drug carriers are involved, plasma skimming has a key role on changing hematocrit level and drug carrier concentration in capillary beds after continuous vessel bifurcation in the microvasculature. While there have been numerous studies on modeling the plasma skimming of blood, previous works lacked in consideration of its interaction with drug carriers. In this paper, a generalized plasma skimming model is suggested to predict the redistributions of both the cells and drug carriers at each bifurcation. In order to examine its applicability, this new model was applied on a single bifurcation system to predict the redistribution of red blood cells and drug carriers. Furthermore, this model was tested at microvascular network level under different plasma skimming conditions for predicting the concentration of drug carriers. Based on these results, the applicability of this generalized plasma skimming model is fully discussed and future works along with the model's limitations are summarized.

Impact of wall shear stress and ligand avidity on binding of anti-CD146-coated nanoparticles to murine tumor endothelium under flow

The endothelial phenotype of tumor blood vessels differs from the liver and forms an important base for endothelium-specific targeting by antibody-coated nanoparticles. Although differences of shear stress and ligand avidity can modulate the nanoparticle binding to endothelium, these mechanisms are still poorly studied. This study analyzed the binding of antibody-coated nanoparticles to tumor and liver endothelium under controlled flow conditions and verified this binding in tumor models in vivo. Binding of anti-CD146-coated nanoparticles, but not of antibody was significantly reduced under increased wall shear stress and the degree of nanoparticle binding correlated with the avidity of the coating. The intravascular wall shear stress favors nanoparticle binding at the site of higher avidity of endothelial epitope which additionally promotes the selectivity to tumor endothelium. After intravenous application in vivo, pegylated self-coated nanoparticles showed specific binding to tumor endothelium, whereas the nanoparticle binding to the liver endothelium was very low. This study provides a rationale that selective binding of mAb-coated nanoparticles to tumor endothelium is achieved by two factors: higher expression of endothelial epitope and higher nanoparticle shearing from liver endothelium. The combination of endothelial marker targeting and the use of shear stress-controlled nanoparticle capture can be used for selective intratumoral drug delivery.

Theory and Experimental Validation of a Spatio-temporal Model of Chemotherapy Transport to Enhance Tumor Cell Kill

It has been hypothesized that continuously releasing drug molecules into the tumor over an extended period of time may significantly improve the chemotherapeutic efficacy by overcoming physical transport limitations of conventional bolus drug treatment. In this paper, we present a generalized space- and time-dependent mathematical model of drug transport and drug-cell interactions to quantitatively formulate this hypothesis. Model parameters describe: perfusion and tissue architecture (blood volume fraction and blood vessel radius); diffusion penetration distance of drug (i.e., a function of tissue compactness and drug uptake rates by tumor cells); and cell death rates (as function of history of drug uptake). We performed preliminary testing and validation of the mathematical model using in vivo experiments with different drug delivery methods on a breast cancer mouse model. Experimental data demonstrated a 3-fold increase in response using nano-vectored drug vs. free drug delivery, in excellent quantitative agreement with the model predictions. Our model results implicate that therapeutically targeting blood volume fraction, e.g., through vascular normalization, would achieve a better outcome due to enhanced drug delivery.

Mathematical Based Calculation of Drug Penetration Depth in Solid Tumors

Cancer is a class of diseases characterized by out-of-control cells' growth which affect cells and make them damaged. Many treatment options for cancer exist. Chemotherapy as an important treatment option is the use of drugs to treat cancer. The anticancer drug travels to the tumor and then diffuses in it through capillaries. The diffusion of drugs in the solid tumor is limited by penetration depth which is different in case of different drugs and cancers. The computation of this depth is important as it helps physicians to investigate about treatment of infected tissue. Although many efforts have been made on studying and measuring drug penetration depth, less works have been done on computing this length from a mathematical point of view. In this paper, first we propose phase lagging model for diffusion of drug in the tumor. Then, using this model on one side and considering the classic diffusion on the other side, we compute the drug penetration depth in the solid tumor. This computed value of drug penetration depth is corroborated by comparison with the values measured by experiments.

Intravital Microscopy Imaging Approaches for Image-Guided Drug Delivery Systems

Rapid technical advances in the field of non-linear microscopy have made intravital microscopy a vital pre-clinical tool for research and development of imaging-guided drug delivery systems. The ability to dynamically monitor the fate of macromolecules in live animals provides invaluable information regarding properties of drug carriers (size, charge, and surface coating), physiological, and pathological processes that exist between point-of-injection and the projected of site of delivery, all of which influence delivery and effectiveness of drug delivery systems. In this Review, we highlight how integrating intravital microscopy imaging with experimental designs (in vitro analyses and mathematical modeling) can provide unique information critical in the design of novel disease-relevant drug delivery platforms with improved diagnostic and therapeutic indexes. The Review will provide the reader an overview of the various applications for which intravital microscopy has been used to monitor the delivery of diagnostic and therapeutic agents and discuss some of their potential clinical applications.

Enhanced uptake and transport of PLGA-modified nanoparticles in cervical cancer

BACKGROUND

Uncoordinated cellular proliferation and dysregulated angiogenesis in solid tumors are coupled with inadequate tissue, blood, and lymphatic vascularization. Consequently, tumors are often characterized by hypoxic regions with limited access to vascular-borne substances. In particular, systemically administered nanoparticles (NPs) targeting tumor cells and relying on vascular access to reach tumor tissue can suffer from limited therapeutic efficacy due to inhomogeneous intra-tumor distribution and insufficient cellular internalization of NPs. To circumvent these challenges, NP surfaces can be modified to facilitate tumor interstitial transport and cellular uptake.

RESULTS

We create poly(lactic-co-glycolic) acid NPs modified with MPG, polyethylene glycol (PEG), MPG/PEG, and Vimentin (VIM), and evaluate their cellular uptake in 2D (monolayer) cell culture of human cervical carcinoma (HeLa). We compare NP performance by evaluating uptake by non-cancerous vaginal (VK2) cells. We further assess NP interstitial transport in hypo-vascularized lesions by evaluating the effect of the various modifications on NP penetration in 3D cell culture of the HeLa cells. Results show that after 24 h incubation with HeLa cells in monolayer, MPG, MPG/PEG, PEG, and VIM NPs were internalized at 66×, 24×, 30×, and 15× that of unmodified NPs, respectively. In contrast, incubation with VK2 cells in monolayer showed that MPG , MPG/PEG , PEG , and VIM NPs internalized at 6.3×, 4.3×, 12.4×, and 3.0× that of unmodified NPs, respectively. Uptake was significantly enhanced in tumorigenic vs. normal cells, with internalization of MPG NPs by HeLa cells being twice that of PEG NPs by VK2 cells. After 24 h incubation in HeLa 3D cell culture, MPG and MPG/PEGNPs were internalized 2× and 3× compared to PEG and VIM NPs, respectively. Whereas MPG NPs were internalized mostly in the cell culture periphery (1.2×, 1.4×, and 2.7× that of PEG, MPG/PEG, and VIM NPs, respectively), PEG NPs at 250 μm penetrated 2× farther into the tissue culture than MPG NPs. For all NP types, cellular internalization was severely hindered in 3D compared to monolayer.

CONCLUSIONS

Although MPG surface modification enhances internalization and uptake in hypo-vascularized cervical tissue culture, coating with PEG reduces this internalization while enhancing penetration. A delivery strategy combining NPs with either modification may balance cellular internalization vs. tissue penetration in hypo-vascularized cervical cancer lesions.

The effect of nanoparticle size on in vivo pharmacokinetics and cellular interaction

Nanoparticle-based technologies offer exciting new approaches to disease diagnostics and therapeutics. To take advantage of unique properties of nanoscale materials and structures, the size, shape and/or surface chemistry of nanoparticles need to be optimized, allowing their functionalities to be tailored for different biomedical applications. Here we review the effects of nanoparticle size on cellular interaction and in vivo pharmacokinetics, including cellular uptake, biodistribution and circulation half-life of nanoparticles. Important features of nanoparticle probes for molecular imaging and modeling of nanoparticle size effects are also discussed.