Reoxygenation and Split-Dose Response to Radiation in a Tumour Model with Krogh-Type Vascular Geometry

After a single dose of radiation, transient changes caused by cell death are likely to occur in the oxygenation of surviving cells. Since cell radiosensitivity increases with oxygen concentration, reoxygenation is expected to increase the sensitivity of the cell population to a successive irradiation. In previous papers we proposed a model of the response to treatment of tumour cords (cylindrical arrangements of tumour cells growing around a blood vessel of the tumour). The model included the motion of cells and oxygen diffusion and consumption. By assuming parallel and regularly spaced tumour vessels, as in the Krogh model of microcirculation, we extend our previous model to account for the action of irradiation and the damage repair process, and we study the time course of the oxygenation and the cellular response. By means of simulations of the response to a dose split in two equal fractions, we investigate the dependence of tumour response on the time interval between the fractions and on the main parameters of the system. The influence of reoxygenation on a therapeutic index that compares the effect of a split dose on the tumour and on the normal tissue is also investigated.     

Modelling the Cell Cycle and Cell Movement in Multicellular Tumour Spheroids

This paper analyses a recent mathematical model of avascular tumour spheroid growth which accounts for both cell cycle dynamics and chemotactic driven cell movement. The model considers cells to exist in one of two compartments: proliferating and quiescent, as well as accounting for necrosis and apoptosis. One particular focus of this paper is the behaviour created when proliferating and quiescent cells have different chemotactic responses to an extracellular nutrient supply. Two very different steady-state behaviours are identified corresponding to those cases where proliferating cells move either more quickly or more slowly than quiescent cells in response to a gradient in the extracellular nutrient supply. The case where proliferating cells move more rapidly leads to the commonly accepted spheroid structure of a thin layer of proliferating cells surrounding an inner quiescent core. In the case where proliferating cells move more slowly than quiescent cells the model predicts an interesting structure of a thin layer of quiescent cells surrounding an inner core of proliferating and quiescent cells. The sensitivity of this tumour structure to the cell cycle model parameters is also discussed. In particular variations in the steady-state size of the tumour and the types of transient behaviour are explored. The model reveals interesting transient behaviour with sharply delineated regions of proliferating and quiescent cells.     

Cell kinetics in a tumour cord

In some tumours, the viable cells grow around blood vessels forming cylindrical structures called tumour cords, which are surrounded by regions of necrosis. In the present paper, we propose a mathematical model for the cell kinetics in a tumour cord at the stationary state. Both proliferating cells and quiescent cells are considered, and the proliferating cell population is structured by age. Cell migration towards cord periphery is accounted for from a continuum viewpoint. The age distribution of proliferating cells, the fraction of cells in S phase, the growth fraction and the velocity along the cord radius are computed. The predictions of the model are compared with literature data obtained from two experimental rat hepatomas. The model was used to compute the profile of the oxygen tension within the cord. Possible modifications and extensions are also presented.     

Optimising non-viral gene delivery in a tumour spheroid model

BACKGROUND: Our current understanding of how the unique tumour microenvironment influences the efficacy of gene delivery is limited. The current investigation systematically examines the efficiency of several non-viral gene transfer agents to transfect multicellular tumour spheroids (MCTS), an in vitro model that displays a faithful three-dimensional (3D) representation of solid tumour tissue. METHODS: Using a luciferase reporter assay, gene transfer to MCTS was optimised for 22 kDa linear and 25 kDa branched polyethyleneimine (PEI), the cationic lipids Lipofectamine(trade mark) and DCChol : DOPE, and the physical approach of tissue electroporation. Confocal microscopy was used to take optical tissue slices to identify the tissue localisation of green fluorescent protein (GFP) reporter gene expression and the distribution of fluorescently labelled complexes. A MCTS model of quiescent tumour regions was used to establish the influence of cellular proliferation status on gene transfer efficiency. RESULTS: Of the polyplexes tested, 22 kDa linear PEI provided optimal gene delivery, with gene expression peaking at 46 h. Despite being the optimal vector tested, PEI-mediated transfection was limited to cells at the MCTS periphery. Using fluorescent PEI, it was found that complexes could only penetrate the outer 3-5 proliferating cell layers of the MCTS, sparing the deeper quiescent cells. Gene delivery in an MCTS model comprised entirely of quiescent cells demonstrated that in addition to being inaccessible to the vector, quiescent tumour regions are inherently less susceptible to PEI-mediated transfection than proliferating regions. This 'resistance' to transfection observed in quiescent cells was overcome through the use of electroporation. Despite the improved efficacy of electroporation in quiescent tissue, the gene expression was still confined to the outer regions of MCTS. The results suggest that limited access to central regions of an MCTS remain a significant barrier to gene delivery. CONCLUSIONS: This data provides new insights into tumour-specific factors affecting non-viral gene transfer and highlights the difficulties in delivering genes to avascular tumour regions. The MCTS model is a useful system for the initial screening of future gene therapy strategies for solid tumours.     

Quiescent fibroblasts are protected from proteasome inhibition-mediated toxicity

Proteasome inhibition is used as a treatment strategy for multiple types of cancers. Although proteasome inhibition can induce apoptotic cell death in actively proliferating cells, it is less effective in quiescent cells. In this study, we used primary human fibroblasts as a model system to explore the link between the proliferative state of a cell and proteasome inhibition-mediated cell death. We found that proliferating and quiescent fibroblasts have strikingly different responses to MG132, a proteasome inhibitor; proliferating cells rapidly apoptosed, whereas quiescent cells maintained viability. Moreover, MG132 treatment of proliferating fibroblasts led to increased superoxide anion levels, juxtanuclear accumulation of ubiquitin- and p62/SQSTM1-positive protein aggregates, and apoptotic cell death, whereas MG132-treated quiescent cells displayed fewer juxtanuclear protein aggregates, less apoptosis, and higher levels of mitochondrial superoxide dismutase. In both cell states, reducing reactive oxygen species with N-acetylcysteine lessened protein aggregation and decreased apoptosis, suggesting that protein aggregation promotes apoptosis. In contrast, increasing cellular superoxide levels with 2-methoxyestradiol treatment or inhibition of autophagy/lysosomal pathways with bafilomycin A1 sensitized serum-starved quiescent cells to MG132-induced apoptosis. Thus, antioxidant defenses and the autophagy/lysosomal pathway protect serum-starved quiescent fibroblasts from proteasome inhibition-induced cytotoxicity.     

Experimental chemotherapy and concepts related to the cell cycle

Scheduling of chemotherapy is limited by damage to normal tissues, and tolerated schedules are dependent on normal tissue recovery. Most anticancer drugs are more toxic to proliferating cells and the fall and recovery of granulocyte counts after chemotherapy may be explained by the effect of drugs on rapidly proliferating precursor cells in the bone marrow. It is argued that serious toxicity due to myelosuppression most often occurs because of damage to proliferating precursors that may be recognized in bone marrow rather than to stem cells. In contrast, therapy that is aimed at producing cure or long-term remission of tumours must be directed at killing tumour stem cells. The evidence that tumours contain a limited population of cells which can repopulate the tumour after treatment (and are therefore tumour stem cells) is reviewed critically. While there is quite strong evidence for a limited population of target cells, evidence from studies on metastases suggests that the tumour cells which may express this stem cell property may change with time. The stem cell concept has major implications for predictive assays. Although colony-forming assays appear to have a sound biological background for predicting tumour response, technical problems prevent them from being used routinely in patient management. Cells in tumours are known to be heterogeneous and at least three types of heterogeneity may influence tumour response to drug treatment: the development of subclones with differing properties including drug resistance; variation in cellular properties due to differentiation during clonal expansion; and variation in properties due to nutritional status and micro-anatomy. Heterogeneity in drug distribution within solid tumours may occur because of limited drug penetration from blood vessels, and nutrient-deprived cells in solid tumours may be expected to escape the toxicity of some anticancer drugs as well as being resistant to radiation because of hypoxia. This may occur both because nutrient-deprived cells have a low rate of cell proliferation, and also because of poor drug penetration to them. There is a need for improved understanding of the mechanisms that lead to cell death in tumours. If these mechanisms were understood, it might be possible to simulate them by therapeutic manoeuvres. Recent research from our laboratory suggests that the combination of low extracellular pH and hypoxia may be very toxic to cells in nutrient-deprived regions. Drugs which limit the cell's ability to survive in regions of acid pH may provide strategy for therapy of nutrient-deprived cells.     

Murine mammary tumour cells in vitro. I. The development of a quiescent state

Three mouse mammary tumour lines (66, 67, and 68H) derived from a single mouse mammary tumour were investigated for their growth kinetics and development of quiescent cells in unfed monolayer cultures. All three lines develop pure quiescent populations when grown in unfed plateau cultures. A dramatic cell-cycle redistribution accompanied the proliferating (P) to quiescent (Q) transition, with the percentage of cells having a G1 DNA content increasing from 50% in the P state to greater than 97% in the Q state. As the cultures progressed from exponential to plateau growth, a decrease of greater than or equal to 50% in cellular RNA was observed in all three lines. This property enables the clear identification of P v. Q cells by flow cytometry using the two-step acridine orange assay. Autoradiographic data verified that these plateau cells were quiescent since less than 2.5% of the cells incorporated [3H]TdR when labelled for approximately two doubling times. Further comparison of the P and Q cells showed that: (a) the Coulter volume of Q cells was approximately half that of P cells in all three lines; (b) viability, as measured by dye exclusion was greater than 95% in all cultures regardless of their proliferative state; and (c) colony-forming ability decreased as the cells entered the quiescent state. In each of these cell lines the development of Q-cell populations was marked by similar changes in all measured parameters. These quiescent tumour cells provide a relatively simple model to evaluate what, if any, important differences exist between the response of P v. Q cells to various therapeutic agents.     

Regression and regrowth of tumour cords following single-dose anticancer treatment

In this paper, the evolution of a tumour cord after treatment is investigated by extensive numerical simulations on the basis of a mathematical model developed by Bertuzzi et al. (submitted). The model is formulated in cylindrical symmetry adopting the continuum approach, and takes into account the influence of oxygen level on the proliferation and death rate of cells, the volume reduction due to disgregation of dead cells, and the cell killing effects of radiation and drugs. Some extensions of the model are proposed to represent more accurately the radioresistance of hypoxic cells and the cytotoxic action of anticancer drugs. The steady state of the cord, and the cord evolution from the steady state after the delivery of a single dose of an anticancer agent, are computed for various combinations of model parameters and for different choices of the functions describing the effects of treatments. The results of the numerical computations show that, in spite of its many simplifications, the model behaviour appears to be reasonable in view of the available experimental observations. The model allows having a better insight into some complex treatment-related events, such as cell reoxygenation and repopulation.     

Why is the partial oxygen pressure of human tissues a crucial parameter? Small molecules and hypoxia

Oxygen supply and diffusion into tissues are necessary for survival. The oxygen partial pressure (pO(2)), which is a key component of the physiological state of an organ, results from the balance between oxygen delivery and its consumption. In mammals, oxygen is transported by red blood cells circulating in a well-organized vasculature. Oxygen delivery is dependent on the metabolic requirements and functional status of each organ. Consequently, in a physiological condition, organ and tissue are characterized by their own unique 'tissue normoxia' or 'physioxia' status. Tissue oxygenation is severely disturbed during pathological conditions such as cancer, diabetes, coronary heart disease, stroke, etc., which are associated with decrease in pO(2), i.e. 'hypoxia'. In this review, we present an array of methods currently used for assessing tissue oxygenation. We show that hypoxia is marked during tumour development and has strong consequences for oxygenation and its influence upon chemotherapy efficiency. Then we compare this to physiological pO(2) values of human organs. Finally we evaluate consequences of physioxia on cell activity and its molecular modulations. More importantly we emphasize the discrepancy between in vivo and in vitro tissue and cells oxygen status which can have detrimental effects on experimental outcome. It appears that the values corresponding to the physioxia are ranging between 11% and 1% O(2) whereas current in vitro experimentations are usually performed in 19.95% O(2), an artificial context as far as oxygen balance is concerned. It is important to realize that most of the experiments performed in so-called normoxia might be dangerously misleading.     

Cell kinetics and radiation biology

The cell cycle, the growth fraction and cell loss influence the response of cells to radiation in many ways. The variation in radiosensitivity around the cell cycle, and the extent of radiation-induced delay in cell cycle progression have both been clearly demonstrated in vitro. This translates into a variable time of expression of radiation injury in different normal tissues, ranging from a few days in intestine to weeks, months or even years in slowly proliferating tissues like lung, kidney, bladder and spinal cord. The radiosensitivity of tumours, to single doses, is dominated by hypoxic cells which arise from the imbalance between tumour cell production and the proliferation and branching of the blood vessels needed to bring oxygen and other nutrients to each cell. The response to fractionated radiation schedules is also influenced by the cell kinetic parameters of the cells comprising each tissue or tumour. This is described in terms of repair, redistribution, reoxygenation and repopulation. Slowly cycling cells show much more curved underlying cell survival curves, leading to more dramatic changes with fractionation, dose rate or l.e.t. Rapidly cycling cells redistribute around the cell cycle when the cells in sensitive phases have been killed, and experience less mitotic delay than slowly proliferating cells. Reoxygenation seems more effective in tumours with rapidly cycling cells and high natural cell loss rates. Compensatory repopulation within a treatment schedule may spare skin and mucosa but does not spare slowly proliferating tissues. Furthermore, tumour cell proliferation during fractionated radiotherapy may be an important factor limiting the overall success of treatment.     

Mechanisms of regulating cell topology in proliferating epithelia: impact of division plane, mechanical forces, and cell memory

Regulation of cell growth and cell division has a fundamental role in tissue formation, organ development, and cancer progression. Remarkable similarities in the topological distributions were found in a variety of proliferating epithelia in both animals and plants. At the same time, there are species with significantly varied frequency of hexagonal cells. Moreover, local topology has been shown to be disturbed on the boundary between proliferating and quiescent cells, where cells have fewer sides than natural proliferating epithelia. The mechanisms of regulating these topological changes remain poorly understood. In this study, we use a mechanical model to examine the effects of orientation of division plane, differential proliferation, and mechanical forces on animal epithelial cells. We find that regardless of orientation of division plane, our model can reproduce the commonly observed topological distributions of cells in natural proliferating animal epithelia with the consideration of cell rearrangements. In addition, with different schemes of division plane, we are able to generate different frequency of hexagonal cells, which is consistent with experimental observations. In proliferating cells interfacing quiescent cells, our results show that differential proliferation alone is insufficient to reproduce the local changes in cell topology. Rather, increased tension on the boundary, in conjunction with differential proliferation, can reproduce the observed topological changes. We conclude that both division plane orientation and mechanical forces play important roles in cell topology in animal proliferating epithelia. Moreover, cell memory is also essential for generating specific topological distributions.     

Combining Gompertzian growth and cell population dynamics

A two-compartment model of cancer cells population dynamics proposed by Gyllenberg and Webb includes transition rates between proliferating and quiescent cells as non-specified functions of the total population, N. We define the net inter-compartmental transition rate function: Phi(N). We assume that the total cell population follows the Gompertz growth model, as it is most often empirically found and derive Phi(N). The Gyllenberg-Webb transition functions are shown to be characteristically related through Phi(N). Effectively, this leads to a hybrid model for which we find the explicit analytical solutions for proliferating and quiescent cell populations, and the relations among model parameters. Several classes of solutions are examined. Our model predicts that the number of proliferating cells may increase along with the total number of cells, but the proliferating fraction appears to be a continuously decreasing function. The net transition rate of cells is shown to retain direction from the proliferating into the quiescent compartment. The death rate parameter for quiescent cell population is shown to be a factor in determining the proliferation level for a particular Gompertz growth curve.     

Murine Mammary Tumour Cells In Vitro. I. the Development of A Quiescent State

Abstract Three mouse mammary tumour lines (66, 67, and 68H) derived from a single mouse mammary tumour were investigated for their growth kinetics and development of quiescent cells in unfed monolayer cultures. All three lines develop pure quiescent populations when grown in unfed plateau cultures. A dramatic cell-cycle redistribution accompanied the proliferating (P) to quiescent (Q) transition, with the percentage of cells having a G₁ DNA content increasing from 50% in the P state to <97% in the Q state. As the cultures progressed from exponential to plateau growth, a decrease of 50% in cellular RNA was observed in all three lines. This property enables the clear identification of P v. Q cells by flow cytometry using the two-step acridine orange assay. Autoradiographic data verified that these plateau cells were quiescent since >2.5% of the cells incorporated [³H]TdR when labelled for approximately two doubling times. Further comparison of the P and Q cells showed that: (a) the Coulter volume of Q cells was approximately half that of P cells in all three lines; (b) viability, as measured by dye exclusion was >95% in all cultures regardless of their proliferative state; and (c) colony-forming ability decreased as the cells entered the quiescent state. In each of these cell lines the development of Q-cell populations was marked by similar changes in all measured parameters. These quiescent tumour cells provide a relatively simple model to evaluate what, if any, important differences exist between the response of P v. Q cells to various therapeutic agents.     

Spatio-Temporal Dynamics of Hypoxia during Radiotherapy

Tumour hypoxia plays a pivotal role in cancer therapy for most therapeutic approaches from radiotherapy to immunotherapy. The detailed and accurate knowledge of the oxygen distribution in a tumour is necessary in order to determine the right treatment strategy. Still, due to the limited spatial and temporal resolution of imaging methods as well as lacking fundamental understanding of internal oxygenation dynamics in tumours, the precise oxygen distribution map is rarely available for treatment planing. We employ an agent-based in silico tumour spheroid model in order to study the complex, localized and fast oxygen dynamics in tumour micro-regions which are induced by radiotherapy. A lattice-free, 3D, agent-based approach for cell representation is coupled with a high-resolution diffusion solver that includes a tissue density-dependent diffusion coefficient. This allows us to assess the space- and time-resolved reoxygenation response of a small subvolume of tumour tissue in response to radiotherapy. In response to irradiation the tumour nodule exhibits characteristic reoxygenation and re-depletion dynamics which we resolve with high spatio-temporal resolution. The reoxygenation follows specific timings, which should be respected in treatment in order to maximise the use of the oxygen enhancement effects. Oxygen dynamics within the tumour create windows of opportunity for the use of adjuvant chemotherapeutica and hypoxia-activated drugs. Overall, we show that by using modelling it is possible to follow the oxygenation dynamics beyond common resolution limits and predict beneficial strategies for therapy and in vitro verification. Models of cell cycle and oxygen dynamics in tumours should in the future be combined with imaging techniques, to allow for a systematic experimental study of possible improved schedules and to ultimately extend the reach of oxygenation monitoring available in clinical treatment.     

Engineering select physical properties of cross-linked red blood cells and a simple a priori estimation of their efficacy as an oxygen delivery vehicle within the context of a hepatic hollow fiber bioreactor

Bovine red blood cells (bRBCs) can potentially provide a simplistic and economic means of improving oxygenation within hollow fiber (HF) bioreactor cell cultures. Bovine RBCs are also interesting since many of their physical properties can be altered as a result of glutaraldehyde (G) cross-linking. Cross-linking bRBCs produces an oxygen carrier that is expected to be beneficial under specific circumstances (i.e., delivery of oxygen to cells that are sensitive to free hemoglobin (Hb) and cells that require low inlet oxygen tensions). We have examined the osmotic stability and electrophoretic mobility of cross-linked bRBCs and observed that cross-linking improves osmotic stability while minimally impacting electrophoretic mobility. The oxygen binding/dissociation properties (P(50) and n) of cross-linked bRBCs were also measured, and under the reported reaction conditions, cross-linking increased the oxygen affinity and reduced the cooperativity of bRBCs. A basic Krogh tissue cylinder model was then utilized to provide a quick a priori estimate of oxygen delivery and release to hepatocytes housed within a HF bioreactor in order to demonstrate potential oxygenation benefits arising with both normal and cross-linked bRBC media supplementation. This model showed that bRBCs generally improved oxygen delivery and release to HF cell cultures and that cross-linked bRBCs are particularly beneficial in specifically targeting oxygen delivery to cells maintained at low inlet oxygen tensions. Additionally, the model showed that bRBC supplementation can significantly improve oxygen delivery without requiring extreme bRBC concentrations.     

Proliferating and quiescent cells exhibit different subcellular distribution of protein kinase C activity

The activity of calcium, phospholipid-dependent protein kinase (PKc), which is thought to play an important role in cell proliferation, has been measured in the particulate and soluble fractions of cultured cells, under different proliferative conditions. Our results indicate that proliferating cells display higher PKc activity than quiescent cells. Furthermore, in both normal and transformed cells, PKc is preferentially associated with the particulate fraction when the cells are proliferating, while in mitotically quiescent cells the majority of the enzyme activity is found in the soluble fraction. These data suggest tha PKc activity and subcellular distribution undergo spontaneous changes according to the proliferative state of the cells.     

Macrophage-Based Anti-Cancer Therapy: Modelling Different Modes of Tumour Targeting

Tumour hypoxia is associated with poor drug delivery and low rates of cell proliferation, factors that limit the efficacy of therapies that target proliferating cells. Since macrophages localise within hypoxic regions, a promising way to target hypoxic tumour cells involves engineering macrophages to express therapeutic genes under hypoxia. In this paper we develop mathematical models to compare the responses of avascular tumour spheroids to two modes of action: either the macrophages deliver an enzyme that activates an externally applied prodrug (bystander model), or they deliver cytotoxic factors directly (local model). The models we develop comprise partial differential equations for a multiphase mixture of tumour cells, macrophages and extracellular fluid, coupled to a moving boundary representing the spheroid surface. Chemical constituents, such as oxygen and drugs, diffuse within the multiphase mixture. Simulations of both models show the spheroid evolving to an equilibrium or to a travelling wave (multiple stable solutions are also possible). We uncover the parameter dependence of the wave speed and steady-state tumour size, and bifurcations between these solution forms. For some parameter sets, adding extra macrophages has a counterintuitive deleterious effect, triggering a bifurcation from bounded to unbounded tumour growth. While these features are common to the bystander and local models, the crucial difference is where cell death occurs. The bystander model is comparable to traditional chemotherapy, with poor targeting of hypoxic tumour cells; however, the local mode of action is more selective for hypoxic regions. We conclude that effective targeting of hypoxic tumour cells may require the use of drugs with limited mobility or whose action does not depend on cell proliferation.     

Stem cells in postnatal myogenesis: molecular mechanisms of satellite cell quiescence, activation and replenishment

Satellite cells are the primary stem cells in adult skeletal muscle, and are responsible for postnatal muscle growth, hypertrophy and regeneration. In mature muscle, most satellite cells are in a quiescent state, but they activate and begin proliferating in response to extrinsic signals. Following activation, a subset of satellite cell progeny returns to the quiescent state during the process of self-renewal. Here, we review recent studies of satellite cell biology and focus on the key transitions from the quiescent state to the state of proliferative activation and myogenic lineage progression and back to the quiescent state. The molecular mechanisms of these transitions are considered in the context of the biology of the satellite cell niche, changes with age, and interactions with established pathways of myogenic commitment and differentiation.