14 results on '"Hlatky L"'
Search Results
2. Mathematical Modeling of Tumor-Tumor Distant Interactions Supports a Systemic Control of Tumor Growth.
- Author
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Benzekry S, Lamont C, Barbolosi D, Hlatky L, and Hahnfeldt P
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- Animals, Carcinoma, Lewis Lung blood supply, Male, Mice, Mice, Inbred C57BL, Neoplasm Metastasis, Tumor Cells, Cultured, Carcinoma, Lewis Lung pathology, Cell Proliferation, Models, Biological, Models, Theoretical, Neovascularization, Pathologic pathology
- Abstract
Interactions between different tumors within the same organism have major clinical implications, especially in the context of surgery and metastatic disease. Three main explanatory theories (competition, angiogenesis inhibition, and proliferation inhibition) have been proposed, but precise determinants of the phenomenon remain poorly understood. Here, we formalized these theories into mathematical models and performed biological experiments to test them with empirical data. In syngeneic mice bearing two simultaneously implanted tumors, growth of only one of the tumors was significantly suppressed (61% size reduction at day 15, P < 0.05). The competition model had to be rejected, whereas the angiogenesis inhibition and proliferation inhibition models were able to describe the data. Additional models including a theory based on distant cytotoxic log-kill effects were unable to fit the data. The proliferation inhibition model was identifiable and minimal (four parameters), and its descriptive power was validated against the data, including consistency in predictions of single tumor growth when no secondary tumor was present. This theory may also shed new light on single cancer growth insofar as it offers a biologically translatable picture of how local and global action may combine to control local tumor growth and, in particular, the role of tumor-tumor inhibition. This model offers a depiction of concomitant resistance that provides an improved theoretical basis for tumor growth control and may also find utility in therapeutic planning to avoid postsurgery metastatic acceleration. Cancer Res; 77(18); 5183-93. ©2017 AACR ., (©2017 American Association for Cancer Research.)
- Published
- 2017
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3. Host mediated inflammatory influence on glioblastoma multiforme recurrence following high-dose ionizing radiation.
- Author
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McDonald JT, Gao X, Steber C, Lee Breed J, Pollock C, Ma L, and Hlatky L
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- Animals, Brain Neoplasms pathology, Brain Neoplasms radiotherapy, Glioblastoma pathology, Glioblastoma radiotherapy, Humans, Inflammation pathology, Inflammation radiotherapy, Male, Mice, Mice, Nude, Neoplasm Recurrence, Local pathology, Neoplasm Recurrence, Local radiotherapy, Radiation, Ionizing, Tumor Cells, Cultured, Xenograft Model Antitumor Assays, Brain Neoplasms immunology, Glioblastoma immunology, Inflammation immunology, Neoplasm Recurrence, Local immunology
- Abstract
Despite optimal clinical treatment, glioblastoma multiforme (GBM) inevitably recurs. Standard treatment of GBM, exposes patients to radiation which kills tumor cells, but also modulates the molecular fingerprint of any surviving tumor cells and the cross-talk between those cells and the host. Considerable investigation of short-term (hours to days) post-irradiation tumor cell response has been undertaken, yet long-term responses (weeks to months) which are potentially even more informative of recurrence, have been largely overlooked. To better understand the potential of these processes to reshape tumor regrowth, molecular studies in conjunction with in silico modeling were used to examine short- and long-term growth dynamics. Despite survival of 2.55% and 0.009% following 8 or 16Gy, GBM cell populations in vitro showed a robust escape from cellular extinction and a return to pre-irradiated growth rates with no changes in long-term population doublings. In contrast, these same irradiated GBM cell populations injected in vivo elicited tumors which displayed significantly suppressed growth rates compared to their pre-irradiated counterparts. Transcriptome analysis days to weeks after irradiation revealed, 281 differentially expressed genes with a robust increase for cytokines, histones and C-C or C-X-C motif chemokines in irradiated cells. Strikingly, this same inflammatory signature in vivo for IL1A, CXCL1, IL6 and IL8 was increased in xenografts months after irradiation. Computational modeling of tumor cell dynamics indicated a host-mediated negative pressure on the surviving cells was a source of inhibition consistent with the findings resulting in suppressed tumor growth. Thus, tumor cells surviving irradiation may shift the landscape of population doubling through inflammatory mediators interacting with the host in a way that impacts tumor recurrence and affects the efficacy of subsequent therapies. Clues to more effective therapies may lie in the development and use of pre-clinical models of post-treatment response to target the source of inflammatory mediators that significantly alter cellular dynamics and molecular pathways in the early stages of tumor recurrence.
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- 2017
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4. Therapeutic Effectiveness of Anticancer Phytochemicals on Cancer Stem Cells.
- Author
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Oh J, Hlatky L, Jeong YS, and Kim D
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- Animals, Biomarkers, Tumor metabolism, Humans, Molecular Targeted Therapy, Neoplasms metabolism, Neoplasms pathology, Neoplastic Stem Cells metabolism, Neoplastic Stem Cells pathology, Phenotype, Signal Transduction drug effects, Antineoplastic Agents, Phytogenic therapeutic use, Neoplasms drug therapy, Neoplastic Stem Cells drug effects, Phytochemicals therapeutic use
- Abstract
Understanding how to target cancer stem cells (CSCs) may provide helpful insights for the development of therapeutic or preventive strategies against cancers. Dietary phytochemicals with anticancer properties are promising candidates and have selective impact on CSCs. This review summarizes the influence of phytochemicals on heterogeneous cancer cell populations as well as on specific targeting of CSCs.
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- 2016
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5. Radiation-Induced Reprogramming of Pre-Senescent Mammary Epithelial Cells Enriches Putative CD44(+)/CD24(-/low) Stem Cell Phenotype.
- Author
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Gao X, Sishc BJ, Nelson CB, Hahnfeldt P, Bailey SM, and Hlatky L
- Abstract
The enrichment of putative CD44(+)/CD24(-/low) breast stem cell populations following exposure to ionizing radiation (IR) has been ascribed to their inherent radioresistance and an elevated frequency of symmetric division during repopulation. However, recent studies demonstrating radiation-induced phenotypic reprogramming (the transition of non-CD44(+)/CD24(-/low) cells into the CD44(+)/CD24(-/low) phenotype) as a potential mechanism of CD44(+)/CD24(-/low) cell enrichment have raised the question of whether a higher survival and increased self-renewal of existing CD44(+)/CD24(-/low) cells or induced reprogramming is an additional mode of enrichment. To investigate this question, we combined a cellular automata model with in vitro experimental data using both MCF-10A non-tumorigenic human mammary epithelial cells and MCF-7 breast cancer cells, with the goal of identifying the mechanistic basis of CD44(+)/CD24(-/low) stem cell enrichment in the context of radiation-induced cellular senescence. Quantitative modeling revealed that incomplete phenotypic reprogramming of pre-senescent non-stem cells (reprogramming whereby the CD44(+)/CD24(-/low) phenotype is conveyed, along with the short-term proliferation capacity of the original cell) could be an additional mode of enriching the CD44(+)/CD24(-/low) subpopulation. Furthermore, stem cell enrichment in MCF-7 cells occurs both at lower doses and earlier time points, and has longer persistence, than that observed in MCF-10A cells, suggesting that phenotypic plasticity appears to be less regulated in breast cancer cells. Taken together, these results suggest that reprogramming of pre-senescent non-stem cells may play a significant role in both cancer and non-tumorigenic mammary epithelial populations following exposure to IR, a finding with important implications for both radiation therapy and radiation carcinogenesis.
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- 2016
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6. Proteasomal Inhibition by Ixazomib Induces CHK1 and MYC-Dependent Cell Death in T-cell and Hodgkin Lymphoma.
- Author
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Ravi D, Beheshti A, Abermil N, Passero F, Sharma J, Coyle M, Kritharis A, Kandela I, Hlatky L, Sitkovsky MV, Mazar A, Gartenhaus RB, and Evens AM
- Subjects
- Animals, Biomarkers, Tumor genetics, Biomarkers, Tumor metabolism, Blotting, Western, Cell Proliferation drug effects, Checkpoint Kinase 1 genetics, Chromatin Immunoprecipitation, Gene Expression Profiling, Glycine pharmacology, Hodgkin Disease drug therapy, Hodgkin Disease metabolism, Humans, Lymphoma, T-Cell drug therapy, Lymphoma, T-Cell metabolism, Mice, Mice, SCID, Proteasome Endopeptidase Complex metabolism, Proto-Oncogene Proteins c-myc genetics, RNA, Messenger genetics, Real-Time Polymerase Chain Reaction, Reverse Transcriptase Polymerase Chain Reaction, Tumor Cells, Cultured, Xenograft Model Antitumor Assays, Apoptosis drug effects, Boron Compounds pharmacology, Checkpoint Kinase 1 metabolism, Glycine analogs & derivatives, Hodgkin Disease pathology, Lymphoma, T-Cell pathology, Proteasome Endopeptidase Complex chemistry, Proteasome Inhibitors pharmacology, Proto-Oncogene Proteins c-myc metabolism
- Abstract
Proteasome-regulated NF-κB has been shown to be important for cell survival in T-cell lymphoma and Hodgkin lymphoma models. Several new small-molecule proteasome inhibitors are under various stages of active preclinical and clinical development. We completed a comprehensive preclinical examination of the efficacy and associated biologic effects of a second-generation proteasome inhibitor, ixazomib, in T-cell lymphoma and Hodgkin lymphoma cells and in vivo SCID mouse models. We demonstrated that ixazomib induced potent cell death in all cell lines at clinically achievable concentrations. In addition, it significantly inhibited tumor growth and improved survival in T-cell lymphoma and Hodgkin lymphoma human lymphoma xenograft models. Through global transcriptome analyses, proteasomal inhibition showed conserved overlap in downregulation of cell cycle, chromatin modification, and DNA repair processes in ixazomib-sensitive lymphoma cells. The predicted activity for tumor suppressors and oncogenes, the impact on "hallmarks of cancer," and the analysis of key significant genes from global transcriptome analysis for ixazomib strongly favored tumor inhibition via downregulation of MYC and CHK1, its target genes. Furthermore, in ixazomib-treated lymphoma cells, we identified that CHK1 was involved in the regulation of MYC expression through chromatin modification involving histone H3 acetylation via chromatin immunoprecipitation. Finally, using pharmacologic and RNA silencing of CHK1 or the associated MYC-related mechanism, we demonstrated synergistic cell death in combination with antiproteasome therapy. Altogether, ixazomib significantly downregulates MYC and induces potent cell death in T-cell lymphoma and Hodgkin lymphoma, and we identified that combinatorial therapy with anti-CHK1 treatment represents a rational and novel therapeutic approach. Cancer Res; 76(11); 3319-31. ©2016 AACR., (©2016 American Association for Cancer Research.)
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- 2016
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7. Evaluating biomarkers to model cancer risk post cosmic ray exposure.
- Author
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Sridharan DM, Asaithamby A, Blattnig SR, Costes SV, Doetsch PW, Dynan WS, Hahnfeldt P, Hlatky L, Kidane Y, Kronenberg A, Naidu MD, Peterson LE, Plante I, Ponomarev AL, Saha J, Snijders AM, Srinivasan K, Tang J, Werner E, and Pluth JM
- Subjects
- Dose-Response Relationship, Radiation, Evaluation Studies as Topic, Humans, Neoplasms, Radiation-Induced etiology, Neoplasms, Radiation-Induced metabolism, Risk Assessment, Biomarkers metabolism, Cosmic Radiation adverse effects, Neoplasms, Radiation-Induced diagnosis
- Abstract
Robust predictive models are essential to manage the risk of radiation-induced carcinogenesis. Chronic exposure to cosmic rays in the context of the complex deep space environment may place astronauts at high cancer risk. To estimate this risk, it is critical to understand how radiation-induced cellular stress impacts cell fate decisions and how this in turn alters the risk of carcinogenesis. Exposure to the heavy ion component of cosmic rays triggers a multitude of cellular changes, depending on the rate of exposure, the type of damage incurred and individual susceptibility. Heterogeneity in dose, dose rate, radiation quality, energy and particle flux contribute to the complexity of risk assessment. To unravel the impact of each of these factors, it is critical to identify sensitive biomarkers that can serve as inputs for robust modeling of individual risk of cancer or other long-term health consequences of exposure. Limitations in sensitivity of biomarkers to dose and dose rate, and the complexity of longitudinal monitoring, are some of the factors that increase uncertainties in the output from risk prediction models. Here, we critically evaluate candidate early and late biomarkers of radiation exposure and discuss their usefulness in predicting cell fate decisions. Some of the biomarkers we have reviewed include complex clustered DNA damage, persistent DNA repair foci, reactive oxygen species, chromosome aberrations and inflammation. Other biomarkers discussed, often assayed for at longer points post exposure, include mutations, chromosome aberrations, reactive oxygen species and telomere length changes. We discuss the relationship of biomarkers to different potential cell fates, including proliferation, apoptosis, senescence, and loss of stemness, which can propagate genomic instability and alter tissue composition and the underlying mRNA signatures that contribute to cell fate decisions. Our goal is to highlight factors that are important in choosing biomarkers and to evaluate the potential for biomarkers to inform models of post exposure cancer risk. Because cellular stress response pathways to space radiation and environmental carcinogens share common nodes, biomarker-driven risk models may be broadly applicable for estimating risks for other carcinogens., (Copyright © 2016 The Committee on Space Research (COSPAR). All rights reserved.)
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- 2016
- Full Text
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8. Capturing the Driving Role of Tumor-Host Crosstalk in a Dynamical Model of Tumor Growth.
- Author
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Benzekry S, Beheshti A, Hahnfeldt P, and Hlatky L
- Abstract
In 1999, Hahnfeldt et al . proposed a mathematical model for tumor growth as dictated by reciprocal communications between tumor and its associated vasculature, introducing the idea that a tumor is supported by a dynamic, rather than a static, carrying capacity. In this original paper, the carrying capacity was equated with the variable tumor vascular support resulting from the net effect of tumor-derived angiogenesis stimulators and inhibitors. This dynamic carrying capacity model was further abstracted and developed in our recent publication to depict the more general situation where there is an interaction between the tumor and its supportive host tissue; in that case, as a function of host aging (Benzekry et al. , 2014). This allowed us to predict a range of host changes that may be occurring with age that impact tumor dynamics. More generally, the basic formalism described here can be (and has been), extended to the therapeutic context using additional optimization criteria (Hahnfeldt et al. , 1999). The model depends on three parameters: One for the tumor cell proliferation kinetics, one for the stimulation of the stromal support, and one for its inhibition, as well as two initial conditions. We describe here the numerical method to estimate these parameters from longitudinal tumor volume measurements.
- Published
- 2015
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9. Tumor-host signaling interaction reveals a systemic, age-dependent splenic immune influence on tumor development.
- Author
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Beheshti A, Wage J, McDonald JT, Lamont C, Peluso M, Hahnfeldt P, and Hlatky L
- Subjects
- Age Factors, Animals, Cell Proliferation, Disease Progression, Humans, Mice, Neoplasms, Signal Transduction, Spleen pathology, Tumor Microenvironment, Spleen immunology
- Abstract
The concept of age-dependent host control of cancer development raises the natural question of how these effects manifest across the host tissue/organ types with which a tumor interacts, one important component of which is the aging immune system. To investigate this, changes in the spleen, an immune nexus in the mouse, was examined for its age-dependent interactive influence on the carcinogenesis process. The model is the C57BL/6 male mice (adolescent, young adult, middle-aged, and old or 68, 143, 551 and 736 days old respectively) with and without a syngeneic murine tumor implant. Through global transcriptome analysis, immune-related functions were found to be key regulators in the spleen associated with tumor progression as a function of age with CD2, CD3ε, CCL19, and CCL5 being the key molecules involved. Surprisingly, other than CCL5, all key factors and immune-related functions were not active in spleens from non-tumor bearing old mice. Our findings of age-dependent tumor-spleen signaling interaction suggest the existence of a global role of the aging host in carcinogenesis. Suggested is a new avenue for therapeutic improvement that capitalizes on the pervasive role of host aging in dictating the course of this disease.
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- 2015
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10. Proton irradiation impacts age-driven modulations of cancer progression influenced by immune system transcriptome modifications from splenic tissue.
- Author
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Wage J, Ma L, Peluso M, Lamont C, Evens AM, Hahnfeldt P, Hlatky L, and Beheshti A
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- Animals, Carcinoma, Lewis Lung, Cell Cycle, Cell Line, Tumor, Cell Proliferation radiation effects, Disease Models, Animal, Disease Progression, Humans, Male, Mice, Mice, Inbred C57BL, Neoplasm Transplantation, Protons, Radiation, Ionizing, Spleen immunology, Spleen radiation effects, Age Factors, Immune System radiation effects, Neoplasms immunology, Neoplasms pathology, Spleen pathology, Transcriptome
- Abstract
Age plays a crucial role in the interplay between tumor and host, with additional impact due to irradiation. Proton irradiation of tumors induces biological modulations including inhibition of angiogenic and immune factors critical to 'hallmark' processes impacting tumor development. Proton irradiation has also provided promising results for proton therapy in cancer due to targeting advantages. Additionally, protons may contribute to the carcinogenesis risk from space travel (due to the high proportion of high-energy protons in space radiation). Through a systems biology approach, we investigated how host tissue (i.e. splenic tissue) of tumor-bearing mice was altered with age, with or without whole-body proton exposure. Transcriptome analysis was performed on splenic tissue from adolescent (68-day) versus old (736-day) C57BL/6 male mice injected with Lewis lung carcinoma cells with or without three fractionations of 0.5 Gy (1-GeV) proton irradiation. Global transcriptome analysis indicated that proton irradiation of adolescent hosts caused significant signaling changes within splenic tissues that support carcinogenesis within the mice, as compared with older subjects. Increases in cell cycling and immunosuppression in irradiated adolescent hosts with CDK2, MCM7, CD74 and RUVBL2 indicated these were the key genes involved in the regulatory changes in the host environment response (i.e. the spleen). Collectively, these results suggest that a significant biological component of proton irradiation is modulated by host age through promotion of carcinogenesis in adolescence and resistance to immunosuppression, carcinogenesis and genetic perturbation associated with advancing age., (© The Author 2015. Published by Oxford University Press on behalf of The Japan Radiation Research Society and Japanese Society for Radiation Oncology.)
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- 2015
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11. Fractionated Radiation Exposure of Rat Spinal Cords Leads to Latent Neuro-Inflammation in Brain, Cognitive Deficits, and Alterations in Apurinic Endonuclease 1.
- Author
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Suresh Kumar MA, Peluso M, Chaudhary P, Dhawan J, Beheshti A, Manickam K, Thapar U, Pena L, Natarajan M, Hlatky L, Demple B, and Naidu M
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- Animals, Biomarkers, Cognition Disorders metabolism, Cognition Disorders pathology, Encephalitis metabolism, Encephalitis pathology, Rats, Spinal Cord pathology, Time Factors, Cognition Disorders etiology, Cognition Disorders physiopathology, DNA-(Apurinic or Apyrimidinic Site) Lyase metabolism, Encephalitis etiology, Encephalitis physiopathology, Radiation Exposure, Radiation, Ionizing, Spinal Cord radiation effects
- Abstract
Ionizing radiation causes degeneration of myelin, the insulating sheaths of neuronal axons, leading to neurological impairment. As radiation research on the central nervous system has predominantly focused on neurons, with few studies addressing the role of glial cells, we have focused our present research on identifying the latent effects of single/ fractionated -low dose of low/ high energy radiation on the role of base excision repair protein Apurinic Endonuclease-1, in the rat spinal cords oligodendrocyte progenitor cells' differentiation. Apurinic endonuclease-1 is predominantly upregulated in response to oxidative stress by low- energy radiation, and previous studies show significant induction of Apurinic Endonuclease-1 in neurons and astrocytes. Our studies show for the first time, that fractionation of protons cause latent damage to spinal cord architecture while fractionation of HZE (28Si) induce increase in APE1 with single dose, which then decreased with fractionation. The oligodendrocyte progenitor cells differentiation was skewed with increase in immature oligodendrocytes and astrocytes, which likely cause the observed decrease in white matter, increased neuro-inflammation, together leading to the observed significant cognitive defects.
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- 2015
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12. Concepts and challenges in cancer risk prediction for the space radiation environment.
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Barcellos-Hoff MH, Blakely EA, Burma S, Fornace AJ Jr, Gerson S, Hlatky L, Kirsch DG, Luderer U, Shay J, Wang Y, and Weil MM
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- Animals, Astronauts, Humans, Mice, Neoplasms, Occupational Exposure, Space Flight, Cosmic Radiation adverse effects, Radiation Dosage, Radiation Injuries epidemiology, Radiation Protection methods
- Abstract
Cancer is an important long-term risk for astronauts exposed to protons and high-energy charged particles during travel and residence on asteroids, the moon, and other planets. NASA's Biomedical Critical Path Roadmap defines the carcinogenic risks of radiation exposure as one of four type I risks. A type I risk represents a demonstrated, serious problem with no countermeasure concepts, and may be a potential "show-stopper" for long duration spaceflight. Estimating the carcinogenic risks for humans who will be exposed to heavy ions during deep space exploration has very large uncertainties at present. There are no human data that address risk from extended exposure to complex radiation fields. The overarching goal in this area to improve risk modeling is to provide biological insight and mechanistic analysis of radiation quality effects on carcinogenesis. Understanding mechanisms will provide routes to modeling and predicting risk and designing countermeasures. This white paper reviews broad issues related to experimental models and concepts in space radiation carcinogenesis as well as the current state of the field to place into context recent findings and concepts derived from the NASA Space Radiation Program., (Copyright © 2015 The Committee on Space Research (COSPAR). Published by Elsevier Ltd. All rights reserved.)
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- 2015
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13. Host age is a systemic regulator of gene expression impacting cancer progression.
- Author
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Beheshti A, Benzekry S, McDonald JT, Ma L, Peluso M, Hahnfeldt P, and Hlatky L
- Subjects
- Age Factors, Animals, Cell Proliferation, Disease Progression, Male, Mice, Mice, Inbred C57BL, Transforming Growth Factor beta1 physiology, Aging, Gene Expression Regulation, Neoplasms etiology
- Abstract
Aging is the major determinant of cancer incidence, which, in turn, is likely dictated in large part by processes that influence the progression of early subclinical (occult) cancers. However, there is little understanding of how aging informs changes in aggregate host signaling that favor cancer progression. In this study, we provide direct evidence that aging can serve as an organizing axis to define cancer progression-modulating processes. As a model system to explore this concept, we employed adolescent (68 days), young adult (143 days), middle-aged (551 days), and old (736 days) C57BL/6 mice as syngeneic hosts for engraftment of Lewis lung cancer to identify signaling and functional processes varying with host age. Older hosts exhibited dysregulated angiogenesis, metabolism, and apoptosis, all of which are associated with cancer progression. TGFβ1, a central player in these systemic processes, was downregulated consistently in older hosts. Our findings directly supported the conclusion of a strong host age dependence in determining the host tumor control dynamic. Furthermore, our results offer initial mechanism-based insights into how aging modulates tumor progression in ways that may be actionable for therapy or prevention., (©2015 American Association for Cancer Research.)
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- 2015
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14. Stochastic process pharmacodynamics: dose timing in neonatal gentamicin therapy as an example.
- Author
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Radivoyevitch T, Siranart N, Hlatky L, and Sachs R
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- Administration, Intravenous, Anti-Bacterial Agents pharmacokinetics, Anti-Bacterial Agents pharmacology, Colony Count, Microbial, Escherichia coli drug effects, Escherichia coli Infections microbiology, Gentamicins pharmacokinetics, Gentamicins pharmacology, Humans, Infant, Newborn, Probability, Stochastic Processes, Anti-Bacterial Agents administration & dosage, Escherichia coli Infections drug therapy, Gentamicins administration & dosage, Models, Biological
- Abstract
We consider dosing regimens designed to cure patients by eradicating colony forming units (CFU) such as bacteria. In the field of "population" pharmaco-kinetics/dynamics (PK/PD), inter-individual variability (IIV) of patients is estimated using model parameter statistical distributions. We consider a more probabilistic approach to IIV called stochastic process theory, motivated by the fact that tumor treatment planning uses both approaches. Stochastic process PD can supply additional insights and suggest different dosing regimens due to its emphasis on the probability of complete CFU eradication and its predictions on "pure chance" fluctuations of CFU number per patient when treatment has reduced this integer to less than ~100. To exemplify the contrast between stochastic process PD models and standard deterministic PD models, which track only average CFU number, we analyze, neglecting immune responses, neonatal intravenous gentamicin dosing regimens directed against Escherichia coli. Our stochastic calculations predict that the first dose is crucial for CFU eradication. For example, a single 6 mg/kg dose is predicted to have a higher eradication probability than four daily 4 mg/kg doses. We conclude: (1) neonatal gentamicin dosing regimens with larger first doses but smaller total doses deserve investigation; (2) in general, if standard PK/PD models predict average CFU number drops substantially below 100, the models should be modified to incorporate stochastic effects more accurately, and will then usually make more favorable, or less unfavorable, predictions for front boosting ("hit hard early"). Various caveats against over-interpreting the calculations are given.
- Published
- 2015
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