Effects of cellular pharmacology on drug distribution in tissues

Analyze impact of tumor-associated kinetics on antibody delivery in solid tumors with a physiologically based pharmacokinetics/pharmacodynamics model

Monoclonal antibody (mAb)-based drugs are critical anti-cancer therapies. Unfortunately, therapeutic efficacy can be compromised by spatially heterogeneous intratumoral Ab deposition. Binding-site barriers arising from Ab and tumor-associated kinetics often underlie this phenomenon. Quantitative insight into these issues may lead to more efficient drug delivery. Difficulties in addressing this issue include (1) lack of techniques to quantify critical kinetic events, (2) lack of a pharmacokinetic/pharmacodynamic (PK/PD) model to assess important parameters for specific tumor types, and (3) uncertainty or variability of critical kinetic factors even within a single tumor type. This study developed a mechanism-based PK/PD model to profile heterogeneous distribution of Ab within tumors and tested this model using real-life experimental data. Model simulations incorporating several uncertainties were used to determine how mAb and tumor-associated kinetics influence receptor occupancy. Simulations were also used to predict the potential impact of these findings in preclinical tumor models and human tumors. We found significant differences in tumor-associated kinetics between groups in which mAb therapy was effective versus groups in which it was ineffective. These kinetic differences included rates of tumor-associated antigen (TAA) degradation, TAA expression, apparent flow rates of interstitial fluid, and ratios of Ab-TAA complex internalization to TAA degradation. We found less significant differences in mAb kinetics, including rates of clearance or affinity for target antigens. In conclusion, our mechanism-based PK/PD model suggests that TAA-associated kinetic factors participate more significantly than those associated with the Ab in generating barriers to mAb delivery and distribution in tumors.

Thermosensitive Liposome-Mediated Drug Delivery in Chemotherapy: Mathematical Modelling for Spatio-temporal Drug Distribution and Model-Based Optimisation

Thermosensitive liposome-mediated drug delivery has shown promising results in terms of improved therapeutic efficacy and reduced side effects compared to conventional chemotherapeutics. In order to facilitate our understanding of the transport mechanisms and their complex interplays in the drug delivery process, computational models have been developed to simulate the multiple steps involved in liposomal drug delivery to solid tumours. In this study we employ a multicompartmental model for drug-loaded thermosensitive liposomes, with an aim to identify the key transport parameters in determining therapeutic dosing and outcomes. The computational model allows us to not only examine the temporal and spatial variations of drug concentrations in the different compartments by utilising the tumour cord concept, but also assess the therapeutic efficacy and toxicity. In addition, the influences of key factors on systemic plasma concentration and intracellular concentration of the active drug are investigated; these include different chemotherapy drugs, release rate constants and heating duration. Our results show complex relationships between these factors and the predicted therapeutic outcome, making it difficult to identify the "best" parameter set. To overcome this challenge, a model-based optimisation method is proposed in an attempt to find a set of release rate constants and heating duration that can maximise intracellular drug concentration while minimising systemic drug concentration. Optimisation results reveal that under the operating conditions and ranges examined, the best outcome would be achieved with a low drug release rate at physiological temperature, combined with a moderate to high release rate at mild hyperthermia and 1 h heating after injection.

High-resolution mapping of fluoroquinolones in TB rabbit lesions reveals specific distribution in immune cell types

Understanding the distribution patterns of antibiotics at the site of infection is paramount to selecting adequate drug regimens and developing new antibiotics. Tuberculosis (TB) lung lesions are made of various immune cell types, some of which harbor persistent forms of the pathogen, Mycobacterium tuberculosis. By combining high resolution MALDI MSI with histology staining and quantitative image analysis in rabbits with active TB, we have mapped the distribution of a fluoroquinolone at high resolution, and identified the immune-pathological factors driving its heterogeneous penetration within TB lesions, in relation to where bacteria reside. We find that macrophage content, distance from lesion border and extent of necrosis drive the uneven fluoroquinolone penetration. Preferential uptake in macrophages and foamy macrophages, where persistent bacilli reside, compared to other immune cells present in TB granulomas, was recapitulated in vitro using primary human cells. A nonlinear modeling approach was developed to help predict the observed drug behavior in TB lesions. This work constitutes a methodological advance for the co-localization of drugs and infectious agents at high spatial resolution in diseased tissues, which can be applied to other diseases with complex immunopathology.

Monitoring therapeutic monoclonal antibodies in brain tumor

Bevacizumab induces normalization of abnormal blood vessels, making them less leaky. By binding to vascular endothelial growth factor, it indirectly attacks the vascular tumor mass. The optimal delivery of targeted therapies including monoclonal antibodies or anti-angiogenesis drugs to the target tissue highly depends on the blood-brain barrier permeability. It is therefore critical to investigate how drugs effectively reach the tumor. In situ investigation of drug distribution could provide a better understanding of pharmacological agent action and optimize chemotherapies for solid tumors. We developed an imaging method coupled to protein identification using matrix-assisted laser desorption/ionization mass spectrometry. This approach monitored bevacizumab distribution within the brain structures, and especially within the tumor, without any labeling.

Mathematical and computational models of drug transport in tumours

The ability to predict how far a drug will penetrate into the tumour microenvironment within its pharmacokinetic (PK) lifespan would provide valuable information about therapeutic response. As the PK profile is directly related to the route and schedule of drug administration, an in silico tool that can predict the drug administration schedule that results in optimal drug delivery to tumours would streamline clinical trial design. This paper investigates the application of mathematical and computational modelling techniques to help improve our understanding of the fundamental mechanisms underlying drug delivery, and compares the performance of a simple model with more complex approaches. Three models of drug transport are developed, all based on the same drug binding model and parametrized by bespoke in vitro experiments. Their predictions, compared for a 'tumour cord' geometry, are qualitatively and quantitatively similar. We assess the effect of varying the PK profile of the supplied drug, and the binding affinity of the drug to tumour cells, on the concentration of drug reaching cells and the accumulated exposure of cells to drug at arbitrary distances from a supplying blood vessel. This is a contribution towards developing a useful drug transport modelling tool for informing strategies for the treatment of tumour cells which are 'pharmacokinetically resistant' to chemotherapeutic strategies.

Current advances in mathematical modeling of anti-cancer drug penetration into tumor tissues

Delivery of anti-cancer drugs to tumor tissues, including their interstitial transport and cellular uptake, is a complex process involving various biochemical, mechanical, and biophysical factors. Mathematical modeling provides a means through which to understand this complexity better, as well as to examine interactions between contributing components in a systematic way via computational simulations and quantitative analyses. In this review, we present the current state of mathematical modeling approaches that address phenomena related to drug delivery. We describe how various types of models were used to predict spatio-temporal distributions of drugs within the tumor tissue, to simulate different ways to overcome barriers to drug transport, or to optimize treatment schedules. Finally, we discuss how integration of mathematical modeling with experimental or clinical data can provide better tools to understand the drug delivery process, in particular to examine the specific tissue- or compound-related factors that limit drug penetration through tumors. Such tools will be important in designing new chemotherapy targets and optimal treatment strategies, as well as in developing non-invasive diagnosis to monitor treatment response and detect tumor recurrence.

Endocytic Relay as a Potential Means for Enhancing Ligand Transport through Cellular Tissue Matrices: Analysis and Possible Implications for Drug Delivery

The transport of peptide ligands, such as cytokines, through tissue is complicated by resistances due to cell multilayers and holdup in extracellular matrix. To determine whether it is possible for receptor-mediated endocytic trafficking to enhance ligand transport, we have developed a mathematical model of ligand flux through tissue containing cells possessing complementary receptors. Tissue is considered as two phases: the cell phase and the matrix phase; thus tissue is modeled as analogous to a packed bed reactor. This model allows calculation of steady-state flux of intact and degraded peptide through a one-dimensional cell/tissue matrix. Both environmental and molecular parameters were considered in this study. Results predict that three quantities should have a major influence on growth factor flux: the ratio of matrix diffusivity to intracellular "diffusivity" (D(m)/D(i)), the extracellular matrix proteolysis rate constant (k (prot)), and the fraction of internalized growth factor degraded (f(1)). For basal levels of intracellular degradation (0 < f(1) >/= 0.05) but no extracellular proteolysis, significant enhancement is possible only for D(m)/D(i) >/=1. f(1) increases, enhancement is only possible up to f(1)= 0.07 even for D(m)/D(i) < 1. For significant levels of extracellular proteolysis (k (prot) > 0), the requirements for D(m)/D(i) and f(1) to permit transport enhancement encompass a broader range with the exact values dependent on k (prot). These insights may be helpful for delivery of ligands generated from controlled-release devices or genetically modified autocrine cells, and may also provide better understanding of cytokine transport in embryonic development.

Identification of key processes that control tumor necrosis factor availability in a tuberculosis granuloma

Tuberculosis (TB) granulomas are organized collections of immune cells comprised of macrophages, lymphocytes and other cells that form in the lung as a result of immune response to Mycobacterium tuberculosis (Mtb) infection. Formation and maintenance of granulomas are essential for control of Mtb infection and are regulated in part by a pro-inflammatory cytokine, tumor necrosis factor-α (TNF). To characterize mechanisms that control TNF availability within a TB granuloma, we developed a multi-scale two compartment partial differential equation model that describes a granuloma as a collection of immune cells forming concentric layers and includes TNF/TNF receptor binding and trafficking processes. We used the results of sensitivity analysis as a tool to identify experiments to measure critical model parameters in an artificial experimental model of a TB granuloma induced in the lungs of mice following injection of mycobacterial antigen-coated beads. Using our model, we then demonstrated that the organization of immune cells within a TB granuloma as well as TNF/TNF receptor binding and intracellular trafficking are two important factors that control TNF availability and may spatially coordinate TNF-induced immunological functions within a granuloma. Further, we showed that the neutralization power of TNF-neutralizing drugs depends on their TNF binding characteristics, including TNF binding kinetics, ability to bind to membrane-bound TNF and TNF binding stoichiometry. To further elucidate the role of TNF in the process of granuloma development, our modeling and experimental findings on TNF-associated molecular scale aspects of the granuloma can be incorporated into larger scale models describing the immune response to TB infection. Ultimately, these modeling and experimental results can help identify new strategies for TB disease control/therapy.

Tuberculosis is a common and deadly infectious disease caused by a highly successful bacterium, Mycobacterium tuberculosis (Mtb). Multiple host immune factors control the formation of a self-organizing aggregate of immune cells termed a granuloma in the lungs after inhalation of Mtb. One such factor, tumor necrosis factor-α (TNF), is a protein that regulates inflammatory immune responses. Availability of TNF within a TB granuloma has been proposed to have a critical role in the protective immunity against TB. However, direct measurement of the level of TNF in a granuloma is not experimentally feasible. Therefore, we develop a mathematical model based on an experimental model of granuloma developed in mice to predict TNF availability in a granuloma. We measure values of critical model parameters and explore mechanisms that influence TNF availability in the granuloma. We find that cellular organization in a granuloma and intracellular trafficking of TNF control TNF availability in a granuloma. Further, our model analysis also highlights anti-TNF drug properties that determine their TNF neutralization power. Our findings complement and extend those of recent studies on the role of TNF in the immune response against TB.

Antibody tumor penetration: transport opposed by systemic and antigen-mediated clearance

Antibodies have proven to be effective agents in cancer imaging and therapy. One of the major challenges still facing the field is the heterogeneous distribution of these agents in tumors when administered systemically. Large regions of untargeted cells can therefore escape therapy and potentially select for more resistant cells. We present here a summary of theoretical and experimental approaches to analyze and improve antibody penetration in tumor tissue.

Modeling recombinant immunotoxin efficacies in solid tumors

Effectiveness of cancer therapy is improved by the use of recombinant immunotoxins (RITs) that target membrane proteins unique to malignant tumor cells. Although RIT antitumor activity in vivo can always be improved with larger doses, clinical restriction on the dose toleration makes it critical to explore how RIT antitumor activity can be maximized without resorting to dose elevation. In this work, a mathematical model was developed to explore functional correlations between the properties of several recombinant immunotoxins and their antitumor efficacies in vivo. Simulations were compared with experimental data of human tumor xenografts grown on nude mice to assess parameters critical to optimal antitumor activity. We dissected out or held constant as many parameters of the model as possible to investigate the effect of the remaining parameters on the behavior of the system as a whole. Empirical correlations between immunotoxin binding affinity and the target binding site density were obtained for several recombinant immunotoxins targeting either human A431 carcinoma or CD46 Burkitt's lymphoma. Simulations reinforced the idea of binding site barrier for drug diffusion and suggested that optimal antitumor activity was achieved when the binding affinity is logarithmically dependent on the target binding site density.

Target-mediated drug disposition and dynamics

Nonlinear pharmacokinetics and pharmacodynamics may result from several capacity-limited processes and often represent complicating factors in characterizing the pharmacological properties of drugs. Target-mediated drug disposition (TMDD) corresponds to a special case wherein a significant proportion of a drug (relative to dose) is bound with high affinity to a pharmacological target, such that this interaction is reflected in the pharmacokinetic properties of the drug. Dose-dependent effects on apparent pharmacokinetic parameters may manifest, including the steady-state volume of distribution and total systemic clearance. Although a few small molecular weight compounds have been identified to exhibit TMDD, the incidence of TMDD is likely to increase particularly among emerging biotechnology pharmaceuticals. The goal of this commentary is to describe the basic tenets of TMDD and discuss several mathematical modeling approaches for characterizing this phenomenon. Whereas traditional pharmacokinetic/pharmacodynamic models assume that the amount of the drug-target complex is negligible relative to the total amount of drug in the body, integrated mechanism-based models of TMDD incorporate the binding and stoichiometry of drug-target binding. These models may be utilized to infer the time-course of inaccessible system variables, such as the in vivo density of the drug-target complex, and provide a suitable platform for ascertaining the apparent pharmacodynamic implications of TMDD.

Resonance energy transfer for assessing the molecular integrity of proteins for local delivery

It remains unclear whether the limitations to the therapeutic potential of angiogenic growth factors stem from pharmacokinetic concerns related to inadequate delivery or from a reduced sensitivity of target tissues. Here, we report a novel method using resonance energy transfer to assess the molecular integrity of proteins after local delivery. As an example, we labeled fibroblast growth factor-2 with a fluorescent donor and nonfluorescent acceptor pair, tetramethylrhodamine and QSY-7, and demonstrate in an ex vivo bovine carotid artery model that this growth factor is not limited by proteolytic constraints imposed by the tissue. Our data indicate that FGF-2 is unlikely to be degraded within the arterial wall and suggest that pharmacokinetic limitations alone cannot fully explain the muted response seen thus far in therapeutic angiogenesis. In general, resonance energy transfer may serve as a novel approach to assess the molecular integrity of protein-based therapies in local delivery.

Impact of transport and drug properties on the local pharmacology of drug-eluting stents

Drugs released from stents are driven by physiological transport forces, principally solvent-driven flow (convection) and random molecular agitation (diffusion). The relative strength of these two forces determines drug penetration and distribution in the arterial wall. Drug physicochemical factors can induce critical modulations to the primary distribution, both transiently and at steady state. Hydrophobic interactions and nonspecific binding, for example, can both result in tissue drug concentrations severalfold above administered concentration. Drug interaction with native proteins may also interfere with drug transfer at the stent-artery interface. These transport forces and tissue interactions can induce local drug concentrations even at steady state to vary by one or more orders of magnitude over the span of a few cells. To account for significant local variations in drug concentrations following stent-based delivery, rational design of vascular delivery systems requires consideration of drug distribution and tissue interactions on a local, continuum basis. Continuum analysis adapts traditional pharmacokinetics to the local environment by supplementing discrete global parameters of drug content with continuous local values of concentration, transport and binding. The interplay of these parameters with local flux conditions and drug and tissue properties defines the local drug distribution in space and over time. This type of analysis may well become increasingly relevant given the trend toward stent-based drug therapy in cardiovascular care.

Effect of therapeutic macromolecules in spheroids

Recent advances in biotechnology have allowed the production of new types of macromolecular therapeutic agents (antibodies, immunotoxins, cytokines, extracellular matrix molecule (ECM) proteins, vectors) that may eventually find broad clinical applications in the treatment of human tumors and other diseases. The model of the Multicellular Tumor Spheroids (MTS) represents a valuable tool to test the therapeutic potential of these new pharmacologic agents in a 3-D context. Specific questions pertaining to the behaviour in a 3-D setting of some of the macromolecules under evaluation for in vivo applications can also be addressed in the MTS model (e.g. 'binding site barrier', role of cell-cell and cell-ECM interactions). This paper reviews the most significant contributions regarding the delivery of macromolecules to MTS, the penetration and therapeutic effects of antibodies, radiolabelled antibodies, immunotoxins and other macromolecular compounds.

Aggressive administration of recombinant oncotoxin AR209 (anti-ErbB-2) in athymic nude mice implanted with orthotopic human non-small cell lung tumours

Lung cancer remains a significant public health problem in the U.S.A. and will result in an estimated 160,400 deaths in 1997. This appalling number is due in large part to the lack of adequate treatment for tumours that are refractory to surgery with curable intent, or of an adequate salvage therapy for those patients who recur after surgical resection. Because non-small cell lung cancer is refractory to traditional chemotherapy, non-traditional therapies have been developed to treat patients with this disease. Recombinant oncotoxins have been designed to target cells that express certain proteins as part of their cellular membrane. One such oncotoxin, AR209 (formerly OLX-209 [e23(Fv)PE38KDEL]), has the specificity of an anti-ErbB-2 antibody contained within a single-chain antibody domain (e23v) coupled to a portion of the Pseudomonas exotoxin A (PE38KDEL). Previous studies demonstrate that this drug is capable of significantly reducing the size of orthotopic lung tumour xenografts. However, most of the treated mice developed tumours once therapy was removed. In this study, mice were treated aggressively using one of four drug treatment schedules. Mice were treated with either intravenous or subcutaneous injections of AR209 over a 2 week period. The data indicate that AR209 significantly reduced the size of tumours and upon microscopic analysis at necropsy, some mice were cured. However, despite the treatment schedule used, many mice contained residual tumour. Residual tumours expressed the ErbB-2 protein, indicating that more aggressive treatment with AR209 may have resulted in higher rates of cure.

Antibody transport in cultured tumor cell layers

This review summarizes our recent in vitro studies of the factors affecting the tumor penetration of immunoconjugates. The studies were designed to probe the mechanisms of diffusion and convection, using a cultured layer of mouse melanoma cells as a model tumor cell layer and an antibody to the murine transferrin receptor as a model ligand. Transport of the binding antibody was observed to be slower than that of a non-binding control, a result that is consistent with the "binding site barrier" hypothesis (Fujimori et al., J. Nucl. Med., 31: 1191-1198, 1990). Internalization of the antibody/receptor complex was necessary for this effect to be observed, implying that intracellular trafficking is a determinant of net tumor transport rates. Convective fluid flow exhibited a dependence on cell density that is consistent with a Poiseuille flow model, suggesting that convective transport occurs as laminar flow in tortuous channels. Implications for immunoconjugate therapy, limitations of the approach, and future directions of the research program are discussed.

The pros and cons of drug 'trafficking'

Internalization of targeted therapeutics is often needed for efficacy, but also alters drug penetration of a tissue. A new model explores the trade-offs of intracellular drug trafficking.