Quantitative Cancer Modeling Research Group

Staff	Research Interests
Philip Hahnfeldt, Ph.D. Principal Investigator	cancer growth dynamcis radiotherapeutic and chemotherapeutic dosing DNA damage and repair tumor angiogenesis modeling gene interaction networks
Lynn Hlatky, Ph.D.	cell-cell interactions self-organization and emergence stability criteria for interaction subpopulations evolutionary dynamics
Heiko Enderling, Ph.D. Associate Investigator	cellular automaton models basic cancer cell kinetics in tumor dormancy and progression cancer stem cell and progenitor dynamics tumor morphological evolution invadopodia formation and cancer-microenvironment interaction tissue architecture evolution and wound healing
Xuefeng (Ryan) Gao, Ph.D. Postdoctoral Fellow	modeling tumor growth, tumor angiogenesis, and invasion Darwin evolution of cancer cells: the emergence and distribution of cancer cell phenotypes modeling cancer gene therapies (e.g., virotherapy, bacterial therapy)
Charles Morton, Ph.D. Postdoctoral Fellow	mathematical modeling of the tumor-microenvironment milieu
Kathleen Wilkie, Ph.D. Research Associate	cell adhesion and the extracellular matrix tissue-matrix remodelling the effects of mechanical stresses on cells heterogeneous cell populations in cancer progression growth, development, and aging effects on biological tissues mechanical properties of biological tissues
Rainer Sachs, Ph.D. Associate Investigator	radiation induced carcinogenesis cosmic radiation risk estimation for astronauts second cancers after radiotherapy radiation induced chromosome aberrations

 

Mathematical research at the CCSB

embraces the principle that cancer is not just a disease of cells but is facilitated at the population and inter-tissue levels. Accordingly, a multi-level approach must be implemented to fully understand its origin and course. Initial events in carcinogenesis occur within cells at the molecular level as repair and proliferation dysfunctions, leading to genomic instability, aneuploidy and final transformation. But after cancer cell creation, the clone advances to encounter additional molding and fate-determining events defined by cell-cell interactions. The associated stroma (fibroblasts and extracellular matrix) plays a critical role in cancer progression, as does induced tumor vascularization (angiogenesis). Both act to determine whether a nascent cancer advances to become symptomatic disease. Without stromal activation and angiogenesis, tumor development is halted early. Under NASA Specialized Centers of Research (NSCOR) funding, these studies are focusing on the determination of cancer risk to astronauts who will be exposed to harmful solar particle events (SPEs) and galactic cosmic radiations (GCRs) during long-term space flight. By extension we hope to better understand the carcinogenesis process more generally, and discover new therapeutic interventions for improved cancer treatment.

The origin of cancer may be attributed to events that alter the repair machinery of the cell and destabilize its genome. Of active interest in this regard is how nucleotide-level DNA damage and repair translates into chromosome aberrations, as chromosome-level misrepair is the feature most closely identified with carcinogenic transformation. By developing a revised theory for double-strand break repair/misrepair following ionizing radiation, we have found it possible to improve upon the commonly-accepted repair models. Starting from carcinogenesis-initiating lesions to DNA, we have gone on to link this action to the first population-level bottleneck to the growth of the resultant hyperplastic clones - self-limited cell growth. The resulting deterministic model for early carcinogenesis has proven to be competitive with the current stochastic standard in explaining major epidemiological data sets on radiation-induced carcinogenesis.

A second bottleneck encountered early in carcinogenesis is nutrient availability. Without angiogenesis, a tumor cannot grow beyond approximately 1mm in size. This obstacle to tumor growth requires the development of angiogenic potential within the growing clone of tumor cells - an 'angiogenic switch'. Interestingly, it was discovered quite by accident some time ago while performing autopsies on adults who died of non-cancer causes (Black and Welch 1993), that most middle-aged people harbor dormant, non-threatening cancer lesions. Held back by the failure to initiate angiogenesis, the tumors remained harmless throughout these individuals' lifetimes. One major objective of our Center is to understand how such a stasis may be maintained, and perhaps re-established as part of a novel therapeutic approach. We have made inroads into quantitatively understanding this natural control in tumor growth, and how antiangiogenic therapy might best be applied to achieve this goal.

Basic cell kinetics, cancer stem cells and tumor morphology.

Tumors are intrinsically heterogeneous. The majority of the tumor cells have limited life span and replicative potential, and only a small minority (so-called cancer stem cells) live forever, divide infinitely and potentially produce more such stem cells. It is these stem cells that determine tumor formation, and their dynamics is counterintutively inhibited by their non-stem progeny. Only a high migration rate can liberate stem cells and enable their migration to seed new clones in the vicinity of the original cluster. In this manner, the tumour continually 'self-metastasises'.
We use cellular automaton models to define the behavior of single cells, and then let single cells populate a compuational domain. As the number of cancer cell increases over time competition for environmental resources (such as space) defines population dynamics. A result is a cancer cell population (a tumor) growing sub-exponentially. Tumor progession is dictated by the ability of stem cells to form self-metastases that together form a malignant invasive morphology.

Modeling DNA damage and repair, and chromosome geometry.

The chromosome damage/repair studies have interrelated results on cytogenetics and interphase chromosome localization and geometry. By developing a revised theory for double-strand break repair/misrepair following ionizing radiation,we found it possible to improve upon the commonly-accepted repair models, in the process obtaining information on how chromosomes are packaged within the nucleus. Incomplete exchange models developed from these studies were also able to explain the relation between acentric and dicentric counts and the excess dispersion (variance/mean) for the number of acentric fragments relative to dicentrics seen in human lymphocytes exposed to various radiation types and doses.

Angiogenesis modeling and anti-angigenic therapy.

Extending from collaboration with the late Dr. Judah Folkman of Children's Hospital, Boston, we are exploring the unique tumor/vascular regression kinetics of anti-angiogenic therapy. The indirect means by which tumor suppression is here accomplished, coupled with the recent finding that tumors both stimulate and inhibit their own vascularization, points to a need to formulate tumor-vascular models that properly capture the dynamics. We use sets of differential equations that simultaneously consider vascular response to anti-angiogenic agents and subsequent suppression of tumor growth. The result is a formalism that is proving to be both explanatory and clinically predictive. This work is an example of quantitative translational research, a "workstation-to-bench-to-bedside" research strategy embraced by the CCSB. An important dynamic to surface from these studies is the self-imposed Gompertz restriction on growth imposed by a tumor on itself. Implications for the general organogenic control of tissue mass are suggested. Another study of dose rate effects addresses an as yet un-quantified effect -- the utility of so-called "metronomic" (small, evenly-spaced) dosing on the treatment response of a tumor population. It was shown considering the response of a heterogeneous target to various dosing protocols that: 1) metronomic dosing does indeed offer the best tumor suppression, and 2) the shift to metronomic dosing from more traditional "up-front" dosing regimens favors the endothelial cell compartment. The theory offers one explanation for numerous reports of an antiangiogenic response using the metronomic scheme.

Tumor heterogeneity.

A unifying theme in both the DNA repair and angiogenesis studies is the role tumor heterogeneity and inter-tissue interactions play in carcinogenesis risk and cancer treatment response. Under our NASA NSCOR Program Project dedicated to examining how inter-cellular interactions modulate carcinogenesis, we are currently employing quantitative methods to understand the unifying mechanisms more precisely. A deterministic carcinogenesis risk model that incorporates cell-cell interactions was developed which compares favorably to the current stochastic model standard in explaining epidemiologic data on atom bomb survivors. Additional unpublished studies are now showing that inter-cellular interactions may even decide the course of cancer after the fact of tumor cell creation, proving these interactions to be a vital augment to current cell-centric focuses on cancer origin and treatment response.

 

Representative publications:

• Enderling H, Hlatky L, Hahnfeldt P. Tumor morphological evolution: directed migration and gain and loss of the self-metastatic phenotype. Biol Direct 5(1):23, 2010.
• Fakir H, Hofmann W, Sachs RK. Modeling progression in radiation-induced lung adenocarcinomas. Radiat Environ Biophys. Accepted, Nov. 2009.
• Enderling H, Anderson AR, Chaplain MA, Beheshti A, Hlatky L, Hahnfeldt P. Paradoxical dependencies of tumor dormancy and progression on basic cell kinetics. Cancer Res. 2009 Nov 15;69(22):8814-21.
• Fakir H, Tan WY, Hlatky L, Hahnfeldt P, Sachs RK. Stochastic population dynamic effects for lung cancer progression. Radiat Res. 2009 Sep;172(3):383-93.
• Shuryak I, Hahnfeldt P, Hlatky L, Sachs RK, Brenner DJ. A new view of radiation-induced cancer: integrating short- and long-term processes. Part I: approach. Radiat Environ Biophys. 2009 Aug;48(3):263-74.
• Shuryak I, Hahnfeldt P, Hlatky L, Sachs RK, Brenner DJ. A new view of radiation-induced cancer: integrating short- and long-term processes. Part II: second cancer risk estimation. Radiat Environ Biophys. 2009 Aug;48(3):275-86.
• Enderling H, Hlatky L, Hahnfeldt P. Migration rules: tumours are conglomerates of self-metastases. Br J Cancer. 2009 Jun 16;100(12):1917-25.
• Enderling H, Park D, Hlatky L, Hahnfeldt P. The importance of spatial distribution of stemness and proliferation state in determining tumor radioresponse. Math Model Nat Phenom. 2009;4(3):117-33.
• Fakir H, Hofmann W, Tan WY, Sachs RK. Triggering-response model for radiation-induced bystander effects. Radiat Res. 2009 Mar;171(3):320-31.
• Brenner D, Shuryak I, Sachs R. Radiotherapy-Induced Carcinogenesis and Leukemogenesis: Mechanisms and Quantitative Modeling. In: ALERT Adverse Late Effects of Cancer Treatment. Volume 1: General Concepts and Principles (P. Rubin, L. S. Constine, L. B. Marks, J. P. Williams, and J. T. Hansen, eds.), Springer, New York. In Series: Medical Radiology -- Radiation Oncology, Brady LW, Heilmann H-P, Molls M, Nieder C (Series Editors), 2009.
• Li L, McCormack AA, Nicholson JM, Fabarius A, Hehlmann R, Sachs RK, Duesberg PH. Cancer-causing karyotypes: chromosomal equilibria between destabilizing aneuploidy and stabilizing selection for oncogenic function. Cancer Genet Cytogenet. 2009 Jan 1;188(1):1-25.
• Enderling H, Alexander NR, Clark ES, Branch KM, Estrada L, Crooke C, Jourquin J, Lobdell N, Zaman MH, Guelcher SA, Anderson AR, Weaver AM. Dependence of invadopodia function on collagen fiber spacing and cross-linking: computational modeling and experimental evidence. Biophys J. 2008 Sep;95(5):2203-18.
• Feinendegen L, Hahnfeldt P, Schadt EE, Stumpf M, Voit EO. Systems biology and its potential role in radiobiology. Radiat Environ Biophys. 2008 Feb;47(1):5-23.
• Piotrowska MJ, Enderling H an der Heiden U, Mackey MC. Mathematcial modelling of stem cells related to cancer. In: STEM CELLS AND CANCER (eds. T. Dittmar et al), 2008.
• Shuryak I, Sachs RK, Brenner DJ. Biophysical models of radiation bystander effects: 1. Spatial effects in three-dimensional tissues. Radiat Res. 2007 Dec;168(6):741-9.
• Sachs RK, Shuryak I, Brenner D, Fakir H, Hlatky L, Hahnfeldt P. Second cancers after fractionated radiotherapy: stochastic population dynamics effects. J Theor Biol. 2007 Dec 7;249(3):518-31.
• Hodgson DC, Koh ES, Tran TH, Heydarian M, Tsang R, Pintilie M, Xu T, Huang L, Sachs RK, Brenner DJ. Individualized estimates of second cancer risks after contemporary radiation therapy for Hodgkin lymphoma. Cancer. 2007 Dec 1;110(11):2576-86.
• Brenner DJ, Shuryak I, Russo S, Sachs RK. Reducing second breast cancers: a potential role for prophylactic mammary irradiation. J Clin Oncol. 2007 Nov 1;25(31):4868-72.
• Enderling H, Chaplain MA, Anderson AR, Vaidya JS. A mathematical model of breast cancer development, local treatment and recurrence. J Theor Biol. 2007 May 21;246(2):245-59.
• Levy D, Reeder C, Loucas B, Hlatky L, Chen A, Cornforth M, Sachs R. Interpreting chromosome aberration spectra. J Comput Biol. 2007 Mar;14(2):144-55.
• Ponomarev AL, Belli M, Hahnfeldt PJ, Hlatky L, Sachs RK, Cucinotta FA. Subtraction of background damage in PFGE experiments on DNA fragment-size distributions. Radiat Environ Biophys. 2007 Jun;46(2):155-60.
• Enderling H, Anderson AR, Chaplain MA, Rowe GW. Visualisation of the Numerical Solution of Partial Differential Equation Systems in Three Space Dimensions and its Importance for Mathematical Models in Biology. Math Biosci Eng. 2006 3(4), 571-82.
• Enderling H, Anderson AR, Chaplain MA, Vaidya JS. Mathematical Modelling of Radiotherapy Strategies for Early Breast Cancer. J Theor Biol. 2006 241(1):158-71.
• Koh ES, Tran TH, Heydarian M, Sachs RK, Tsang RW, Brenner DJ, Pintilie M, XuT, Chung J, Paul N, Hodgson DC. A comparison of mantle versus involved-field radiotherapy for Hodgkin's lymphoma: reduction in normal tissue dose and second cancer risk. Radiat Oncol. 2007 Mar 15;2:13.
• Shuryak I, Sachs RK, Hlatky L, Little MP, Hahnfeldt P, Brenner DJ. Radiation-induced leukemia at doses relevant to radiation therapy: modeling mechanisms and estimating risks. J Natl Cancer Inst. 2006 Dec 20;98(24):1794-806.
• Ponomarev AL, Belli M, Hahnfeldt PJ, Hlatky L, Sachs RK, Cucinotta FA. A robust procedure for removing background damage in assays of radiation-induced DNA fragment distributions. Radiat Res. 2006 Dec;166(6):908-16.
• Fakir H, Sachs RK, Stenerlöw B, Hofmann W. Clusters of DNA double-strand breaks induced by different doses of nitrogen ions for various LETs: experimental measurements and theoretical analyses. Radiat Res. 2006 Dec;166(6):917-27.
• Brenner DJ, Sachs RK. Estimating radiation-induced cancer risks at very low doses: rationale for using a linear no-threshold approach. Radiat Environ Biophys. 2006 Mar;44(4):253-6.
• Plan Y, Hlatky L, Hahnfeldt P, Sachs R, Loucas B, Cornforth M. Full-color painting reveals an excess of radiation-induced dicentrics involving homologous chromosomes. Int J Radiat Biol. 2005 Aug;81(8):613-20.
• Li R, Hehlman R, Sachs R, Duesberg P. Chromosomal alterations cause the high rates and wide ranges of drug resistance in cancer cells. Cancer Genet Cytogenet. 2005 Nov;163(1):44-56.
• Sachs RK, Brenner DJ. Solid tumor risks after high doses of ionizing radiation. Proc Natl Acad Sci USA. 2005 Sep 13;102(37):13040-5. Epub 2005 Sep 6.
• Sachs RK, Chan M, Hlatky L, Hahnfeldt P. Modeling intercellular interactions during carcinogenesis. Radiat Res. 2005 Sep;164(3):324-31.
• Sachs RK, Brenner DJ. Chromosome Aberrations Produced by Ionizing Radiation: Quantitative Studies. Beta-test version of part of an NCBI Bookshelf Internet Textbook; PubMed, National Center for Biotechnology Information, NLM, NIH. link:http://radiobiology.math.berkeley.edu/, 2005.
• Vives S, Loucas B, Vazquez M, Brenner DJ, Sachs RK, Hlatky L, Cornforth M, Arsuaga J. SCHIP: statistics for chromosome interphase positioning based on interchange data. Bioinformatics. 2005 Jul 15;21(14):3181-2.
• Mestres M, Caballin MR, Schmid E, Stephan G, Sachs R, Barrios L, Barquinero JF. Analysis of alpha-particle induced chromosome aberrations in human lymphocytes, using pan-centromeric and pan-telomeric probes. Int J Radiat Biol. 2004 Oct;80(10):737-44.
• Levy D, Vazquez M, Cornforth M, Loucas B, Sachs RK, Arsuaga J. Comparing DNA damage-processing pathways by computer analysis of chromosome painting data. J Comput Biol. 2004;11(4):626-41.
• Arsuaga J, Greulich-Bode KM, Vazquez M, Bruckner M, Hahnfeldt P, Brenner DJ, Sachs R, Hlatky L. Chromosome spatial clustering inferred from radiogenic aberrations. Int J Radiat Biol. 2004 Jul;80(7):507-15.
• Sachs RK, Levy D, Hahnfeldt P, Hlatky L. Quantitative analysis of radiation-induced chromosome aberrations. Cytogenet Genome Res. 2004;104(1-4):142-8. Review.
• Brenner DJ, Doll R, Goodhead DT, Hall EJ, Land CE, Little JB, Lubin JH, Preston DL, Preston RJ, Puskin JS, Ron E, Sachs RK, Samet JM, Setlow RB, Zaider M. Cancer risks attributable to low doses of ionizing radiation: assessing what we really know. Proc Natl Acad Sci USA. 2003 Nov 25;100(24):13761-6.
• Brenner DJ, Sachs RK. Domestic radon risks may be dominated by bystander effects--but the risks are unlikely to be greater than we thought. Health Phys. 2003 Jul;85(1):103-8.
• Hahnfeldt P, Folkman J, Hlatky L. Minimizing long-term tumor burden: the logic for metronomic chemotherapeutic dosing and its antiangiogenic basis. J Theor Biol. 2003 Feb 21;220(4):545-54.
• Vazquez M, Greulich-Bode KM, Arsuaga J, Cornforth MN, Brückner M, Sachs RK, Hlatky L, Molls M, Hahnfeldt P. Computer analysis of mFISH chromosome aberration data uncovers an excess of very complicated metaphases. Int J Radiat Biol. 2002 Dec;78(12):1103-15.
• Cornforth MN, Greulich-Bode KM, Loucas BD, Arsuaga J, Vázquez M, Sachs RK, Brückner M, Molls M, Hahnfeldt P, Hlatky L, Brenner DJ. Chromosomes are predominantly located randomly with respect to each other in interphase human cells. J Cell Biol. 2002 Oct 28;159(2):237-44.
• Sachs RK, Arsuaga J, Vázquez M, Hlatky L, Hahnfeldt P. Using graph theory to describe and model chromosome aberrations. Radiat Res. 2002 Nov;158(5):556-67.
• Panigrahy D, Singer S, Shen LQ, Butterfield CE, Freedman DA, Chen EJ, Moses MA, Kilroy S, Duensing S, Fletcher C, Fletcher JA, Hlatky L, Hahnfeldt P, Folkman J, Kaipainen A. PPARgamma ligands inhibit primary tumor growth and metastasis by inhibiting angiogenesis. J Clin Invest. 2002 Oct;110(7):923-32.
• Hlatky L, Sachs RK, Vazquez M, Cornforth MN. Radiation-induced chromosome aberrations: insights gained from biophysical modeling. Bioessays. 2002 Aug;24(8):714-23. Review.
• Brenner DJ, Sachs RK. Do low dose-rate bystander effects influence domestic radon risks? Int J Radiat Biol. 2002 Jul;78(7):593-604.
• Radivoyevitch T, Kozubek S, Sachs RK. The risk of chronic myeloid leukemia: can the dose-response curve be U-shaped? Radiat Res. 2002 Jan;157(1):106-9.
• Ponomarev AL, Sachs RK. Radiation breakage of DNA: a model based on random-walk chromatin structure. J Math Biol. 2001 Oct;43(4):356-76.
• Sachs RK, Hlatky LR, Hahnfeldt P. Simple ODE models of tumor growth and anti-angiogenic or radiation treatment, Math Comp Modelling 2001;33:1297-305.
• Radivoyevitch T, Sachs RK, Nikiforov YE, Nikiforova MN, Little MP. On target cell numbers in radiation-induced H4-RET mediated papillary thyroid cancer. Radiat Environ Biophys. 2001 Sep;40(3):191-7.
• Radivoyevitch T, Kozubek S, Sachs RK. Biologically based risk estimation for radiation-induced CML. Inferences from BCR and ABL geometric distributions. Radiat Environ Biophys. 2001 Mar;40(1):1-9.
• Ponomarev AL, Sachs RK. Radiation breakage of DNA: A model based on random-walk chromatin structure. J Math Biol. 2001;43:356-76.
• Ponomarev AL, Cucinotta FA, Sachs RK, Brenner DJ. Monte Carlo predictions of DNA fragment-size distributions for large sizes after HZE particle irradiation. Phys Med. 2001;17 Suppl 1:153-6.
• Ponomarev AL, Cucinotta FA, Sachs RK, Brenner DJ, Peterson LE. Extrapolation of the dna fragment-size distribution after high-dose irradiation to predict effects at low doses. Radiat Res. 2001 Nov;156(5 Pt 2):594-7.
• Costes S, Sachs R, Hlatky L, Vannais D, Waldren C, Fouladi B. Large-mutation spectra induced at hemizygous loci by low-LET radiation: evidence for intrachromosomal proximity effects. Radiat Res. 2001 Nov;156(5 Pt 1):545-57.
• Brenner DJ, Little JB, Sachs RK. The bystander effect in radiation oncogenesis: II. A quantitative model. Radiat Res. 2001 Mar;155(3):402-8.
• Sachs RK, Levy D, Chen AM, Simpson PJ, Cornforth MN, Ingerman EA, Hahnfeldt P, Hlatky LR. Random breakage and reunion chromosome aberration formation model; an interaction-distance version based on chromatin geometry. Int J Radiat Biol. 2000 Dec;76(12):1579-88.
• Brenner DJ, Sachs RK. Protraction effects in radiation studies: basic biophysics. Radiat Res. 2000 Dec;154(6):736-7.
• Ponomarev AL, Brenner D, Hlatky LR, Sachs RK. A polymer, random walk model for the size-distribution of large DNA fragments after high linear energy transfer radiation. Radiat Environ Biophys. 2000 Jun;39(2):111-20.
• Helmlinger G, Endo M, Ferrara N, Hlatky L, Jain RK. Formation of endothelial cell networks. Nature. 2000 May 11;405(6783):139-41.
• Sachs RK, Hlatky LR, Trask BJ. Radiation-produced chromosome aberrations: colourful clues. Trends Genet. 2000 Apr;16(4):143-6. Review.
• Sachs RK, Rogoff A, Chen AM, Simpson PJ, Savage JR, Hahnfeldt P, Hlatky LR. Underprediction of visibly complex chromosome aberrations by a recombinational-repair ('one-hit') model. Int J Radiat Biol. 2000 Feb;76(2):129-48.
• Ponomarev AL, Sachs RK. Polymer chromosome models and Monte Carlo simulations of radiation breaking DNA. Bioinformatics. 1999 Dec;15(12):957-64.
• Hahnfeldt P, Panigrahy D, Folkman J, Hlatky L. Tumor development under angiogenic signaling: a dynamical theory of tumor growth, treatment response, and postvascular dormancy. Cancer Res. 1999 Oct 1;59(19):4770-5.
• Sachs RK, Ponomarev AL, Hahnfeldt P, Hlatky LR. Locations of radiation-produced DNA double strand breaks along chromosomes: a stochastic cluster process formalism. Math Biosci. 1999 Jul;159(2):165-87.
• Sachs RK, Chen AM, Simpson PJ, Hlatky LR, Hahnfeldt P, Savage JR. Clustering of radiation-produced breaks along chromosomes: modelling the effects on chromosome aberrations. Int J Radiat Biol. 1999 Jun;75(6):657-72.
• Brenner DJ, Sachs RK. A more robust biologically based ranking criterion for treatment plans. Int J Radiat Oncol Biol Phys. 1999 Feb 1;43(3):697-8.
• Hardenbergh PH, Hahnfeldt P, Hlatky L, Takemoto C, Shimamura A, McGill G, Fung CY, Bodis S, Fisher DE. Distinct mathematical behavior of apoptotic versus non-apoptotic tumor cell death. Int J Radiat Oncol Biol Phys. 1999 Feb 1;43(3):601-5.
• Hahnfeldt P, Hlatky L. Cell resensitization during protracted dosing of heterogeneous cell populations. Radiat Res. 1998 Dec;150(6):681-7.
• Sachs RK, Brenner DJ. The mechanistic basis of the linear-quadratic formalism. Med Phys. 1998 Oct;25(10):2071-3. Review.
• Sachs RK, Brenner DJ, Hahnfeldt PJ, Hlatky LR. A formalism for analyzing large-scale clustering of radiation-induced breaks along chromosomes. Int J Radiat Biol. 1998 Aug;74(2):185-206.
• Brenner DJ, Hlatky LR, Hahnfeldt PJ, Huang Y, Sachs RK. The linear-quadratic model and most other common radiobiological models result in similar predictions of time-dose relationships. Radiat Res. 1998 Jul;150(1):83-91.
• Radivoyevitch T, Hoel DG, Hahnfeldt P, Sachs RK. Size distributions of misrejoining DNA fragments in irradiated cells. Math Biosci. 1998 May;149(2):107-36. Review.
• Wu H, Sachs RK, Yang TC. Radiation-induced total-deletion mutations in the human hprt gene: a biophysical model based on random walk interphase chromatin geometry. Int J Radiat Biol. 1998 Feb;73(2):149-56.
• Radivoyevitch T, Hoel DG, Chen AM, Sachs RK. Misrejoining of double-strand breaks after X irradiation: relating moderate to very high doses by a Markov model. Radiat Res. 1998 Jan;149(1):59-67.
• Radivoyevitch T, Hoel DG, Hahnfeldt PJ, Rydberg B, Sachs RK. Recent data obtained by pulsed-field gel electrophoresis suggest two types of double-strand breaks. Radiat Res. 1998 Jan;149(1):52-8.
• Chen AM, Lucas JN, Simpson PJ, Griffin CS, Savage JR, Brenner DJ, Hlatky LR, Sachs RK. Computer simulation of data on chromosome aberrations produced by X rays or alpha particles and detected by fluorescence in situ hybridization. Radiat Res. 1997 Nov;148(5 Suppl):S93-101.
• Sachs RK, Hahnfeld P, Brenner DJ. The link between low-LET dose-response relations and the underlying kinetics of damage production/repair/misrepair. Int J Radiat Biol. 1997 Oct;72(4):351-74. Review.
• Sachs RK, Brenner DJ, Chen AM, Hahnfeldt P, Hlatky LR. Intra-arm and interarm chromosome intrachanges: tools for probing the geometry and dynamics of chromatin. Radiat Res. 1997 Oct;148(4):330-40. Review.
• Wu H, Durante M, Sachs RK, Yang TC. Centric rings, acentric rings and excess acentric fragments based on a random-walk interphase chromosome model. Int J Radiat Biol. 1997 May;71(5):487-96.
• Liu B, Sachs RK. A two-backbone polymer model for interphase chromosome geometry. Bull Math Biol. 1997 Mar;59(2):325-37.
• Sachs RK, Chen AM, Brenner DJ. Review: proximity effects in the production of chromosome aberrations by ionizing radiation. Int J Radiat Biol. 1997 Jan;71(1):1-19. Review.
• Sachs RK, Heidenreich WF, Brenner DJ. Dose timing in tumor radiotherapy: considerations of cell number stochasticity. Math Biosci. 1996 Dec;138(2):131-46. Review.
• Brenner DJ, Hahnfeldt P, Amundson SA, Sachs RK. Interpretation of inverse dose-rate effects for mutagenesis by sparsely ionizing radiation. Int J Radiat Biol. 1996 Oct;70(4):447-58.
• Brenner DJ, Sachs RK. Comments on "Comment on the ratio of chromosome-type dicentric interchanges to centric rings for track-clustered compared with random breaks" by Savage and Papworth (Radiat. Res. 146, 236-240, 1996). Radiat Res. 1996 Aug;146(2):241-2.
• Hlatky L, Hahnfeldt P, Tsionou C, Coleman CN. Vascular endothelial growth factor: environmental controls and effects in angiogenesis. Br J Cancer Suppl. 1996 Jul;27:S151-6. Review.
• Chen AM, Lucas JN, Hill FS, Brenner DJ, Sachs RK. Proximity effects for chromosome aberrations measured by FISH. Int J Radiat Biol. 1996 Apr;69(4):411-20.
• Hlatky L, Olesiak M, Hahnfeldt P. Measurement of potential doubling time for human tumor xenografts using the cytokinesis-block method. Cancer Res. 1996 Apr 1;56(7):1660-3.
• Lucas JN, Chen AM, Sachs RK. Theoretical predictions on the equality of radiation-produced dicentrics and translocations detected by chromosome painting. Int J Radiat Biol. 1996 Feb;69(2):145-53.
• Hahnfeldt P, Hlatky L. Resensitization due to redistribution of cells in the phases of the cell cycle during arbitrary radiation protocols. Radiat Res. 1996 Feb;145(2):134-43.
• Chen AM, Lucas JN, Hill FS, Brenner DJ, Sachs RK. Chromosome aberrations produced by ionizing radiation: Monte Carlo simulations and chromosome painting data. Comput Appl Biosci. 1995 Aug;11(4):389-97.
• Brenner DJ, Hlatky LR, Hahnfeldt PJ, Hall EJ, Sachs RK. A convenient extension of the linear-quadratic model to include redistribution and reoxygenation. Int J Radiat Oncol Biol Phys. 1995 May 15;32(2):379-90.
• Hlatky L, Van Buren T, Hahnfeldt P. Quantifying intracellular radioresponse diversity in irradiated sandwich cultures via micronucleus expression. Int J Radiat Biol. 1995 May;67(5):541-8.
• Chen PL, Brenner DJ, Sachs RK. Ionizing radiation damage to cells: effects of cell cycle redistribution. Math Biosci. 1995 Apr;126(2):147-70.
• Sachs RK, van den Engh G, Trask B, Yokota H, Hearst JE. A random-walk/giant-loop model for interphase chromosomes. Proc Natl Acad Sci USA. 1995 Mar 28;92(7):2710-4. PMC42288.
• Hahnfeldt P, Hlatky LR, Brenner DJ, Sachs RK. Chromosome aberrations produced by radiation: the relationship between excess acentric fragments and dicentrics. Radiat Res. 1995 Feb;141(2):136-52.
• Brenner DJ, Hall EJ, Huang Y, Sachs RK. Potential reduced late effects for pulsed brachytherapy compared with conventional LDR. Int J Radiat Oncol Biol Phys. 1995 Jan 1;31(1):201-2.
• Brenner DJ, Sachs RK. Chromosomal "fingerprints" of prior exposure to densely ionizing radiation. Radiat Res. 1994 Oct;140(1):134-42.
• Hlatky LR, Hahnfeldt P, Sachs RK. Influence of time-dependent stochastic heterogeneity on the radiation response of a cell population. Math Biosci. 1994 Aug;122(2):201-20.
• Brenner DJ, Hall EJ, Huang Y, Sachs RK. Optimizing the time course of brachytherapy and other accelerated radiotherapeutic protocols. Int J Radiat Oncol Biol Phys. 1994 Jul 1;29(4):893-901. Review.
• Hahnfeldt P, Hlatky LR. A Monte Carlo/Markov chain model for the association of data for chromosome aberrations and formation of micronuclei. Radiat Res. 1994 May;138(2):239-45.
• Chen PL, Sachs R. Singular perturbation theory applied to Markov models for DNA damage caused by ionizing radiation. J Theor Biol. 1994 Jan 21;166(2):117-26.
• Brenner DJ, Ward JF, Sachs RK. Track structure, chromosome geometry and chromosome aberrations. Basic Life Sci. 1994;63:93-109; discussion 109-13.
• Sachs RK, Brenner DJ. Effect of LET on chromosomal aberration yields. I. Do long-lived, exchange-prone double strand breaks play a role? Int J Radiat Biol. 1993 Dec;64(6):677-88.
• Hahnfeldt P, Hearst JE, Brenner DJ, Sachs RK, Hlatky LR. Polymer models for interphase chromosomes. Proc Natl Acad Sci USA. 1993 Aug 15;90(16):7854-8.
• Hurwitz SJ, Hlatky L. Assessment of radiation response on a cell-by-cell basis using in situ densitometric imaging of micronuclei. Radiat Res. 1993 Apr;134(1):112-6.
• Sachs RK, Awa A, Kodama Y, Nakano M, Ohtaki K, Lucas JN. Ratios of radiation-produced chromosome aberrations as indicators of large-scale DNA geometry during interphase. Radiat Res. 1993 Mar;133(3):345-50.
• Lucas JN, Sachs RK. Using three-color chromosome painting to test chromosome aberration models. Proc Natl Acad Sci USA. 1993 Feb 15;90(4):1484-7.
• Sachs RK, Chen P, Hahnfeldt P, Lai D, Hlatky LR. DNA damage in non-proliferating cells subjected to ionizing irradiation at high or low dose rates. J Math Biol. 1993;31(3):291-315.
• Trask BJ, Allen S, Massa H, Fertitta A, Sachs R, van den Engh G, Wu M. Studies of metaphase and interphase chromosomes using fluorescence in situ hybridization. Cold Spring Harb Symp Quant Biol. 1993;58:767-75.
• Sachs RK, Chen PL, Hahnfeldt PJ, Hlatky LR. DNA damage caused by ionizing radiation. Math Biosci. 1992 Dec;112(2):271-303.
• Sachs RK, Yates BL, Tarver J, Morgan WF. Modelling the formation of polycentric chromosome aberrations. Int J Radiat Biol. 1992 Oct;62(4):449-60.
• van den Engh G, Sachs R, Trask BJ. Estimating genomic distance from DNA sequence location in cell nuclei by a random walk model. Science. 1992 Sep 4;257(5075):1410-2.
• Hlatky LR, Sachs RK, Hahnfeldt P. The ratio of dicentrics to centric rings produced in human lymphocytes by acute low-LET radiation. Radiat Res. 1992 Mar;129(3):304-8.
• Hahnfeldt P, Sachs RK, Hlatky LR. Evolution of DNA damage in irradiated cells. J Math Biol. 1992;30(5):493-511.
• Hlatky L, Sachs R, Hahnfeldt P. Reaction kinetics for the development of radiation-induced chromosome aberrations. Int J Radiat Biol. 1991 May;59(5):1147-72.
• Sachs RK, Hlatky L, Hahnfeldt P, Chen PL. Incorporating dose-rate effects in Markov radiation cell survival models. Radiat Res. 1990 Nov;124(2):216-26.
• Hlatky L, Ring CS, Sachs RK. Detection of an intrinsic marker in hypoxic cells. Cancer Res. 1989 Sep 15;49(18):5162-6.
• Hlatky L, Ring C, Sachs RK. Comparison of 3H-misonidazole binding between CHO and 9L cells using the sandwich system. Int J Radiat Oncol Biol Phys. 1989 Apr;16(4):943-7.
• Hlatky L, Sachs RK, Ring CS. Reducing the hypoxic fraction of a tumour model by growth in low glucose. Br J Cancer. 1989 Mar;59(3):375-80.
• Hlatky L, Ring CS, Sachs RK. 3H-misonidazole labeling and viability of hypoxic cells in the sandwich system, an in vitro tumor analogue. Int J Radiat Oncol Biol Phys. 1989 Jan;16(1):143-53.
• Hlatky L, Sachs RK, Alpen EL. Joint oxygen-glucose deprivation as the cause of necrosis in a tumor analog. J Cell Physiol. 1988 Feb;134(2):167-78.
• Hlatky L, Alpen EL, Yee MK. Differences in the X-ray sensitivity of cells in different regions of the sandwich, a diffusion-limited system for cell growth. Radiat Res. 1986 Oct;108(1):62-73.
• Hlatky L, Alpen EL. Two-dimensional diffusion limited system for cell growth. Cell Tissue Kinet. 1985 Nov;18(6):597-611.