Philip S. Crooke, III, Ph.D.

Research Professor

phil.crooke@vanderbilt.edu

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Faculty Appointments
Research Professor of Mathematics Professor of Mathematics, Emeritus
Education
Ph.D., Applied Mathematics, Cornell University, Ithaca, New YorkB.S., Stevens Institute of Technology, Hoboken, New Jersey
Office Address
SC 1324
Department of Mathematics
Nashville, TN 37240
Research Description
Pulmonary Medicine: mathematical modeling of mechanical ventilation.

Estrogen Metabolism Pathways: multicompartment kinetic model for oxidative metabolism of estradiol.

Gene Expression Analysis: bioinformatics approaches to diagnosing autoimmune disease

Research Keywords
Mathematical models in biology. Breast cancer risk. Gene expression and auto-immune diseases.
Publications
Heinrich MJ, Purcell CA, Pruijssers AJ, Zhao Y, Spurlock CF, Sriram S, Ogden KM, Dermody TS, Scholz MB, Crooke PS, Karijolich J, Aune TM. Endogenous double-stranded Alu RNA elements stimulate IFN-responses in relapsing remitting multiple sclerosis. J. Autoimmun [print-electronic]. 2019 Feb 2/27/2019; PMID: 30826177, PII: S0896-8411(18)30699-1, DOI: 10.1016/j.jaut.2019.02.003, ISSN: 1095-9157.

Parl FF, Dupont WD, Crooke PS. Interchromosomal Translocations as a Means to Map Chromosome Territories in Breast Cancer. Cancer Inform. 2019; 18: 1176935119842573. PMID: 31019364, PMCID: PMC6469281, PII: 10.1177_1176935119842573, DOI: 10.1177/1176935119842573, ISSN: 1176-9351.

Parl FF, Crooke PS, Plummer WD, Dupont WD. Genomic-Epidemiologic Evidence That Estrogens Promote Breast Cancer Development. Cancer Epidemiol. Biomarkers Prev [print-electronic]. 2018 Aug; 27(8): 899-907. PMID: 29789325, PMCID: PMC6072561, PII: 1055-9965.EPI-17-1174, DOI: 10.1158/1055-9965.EPI-17-1174, ISSN: 1538-7755.

Spurlock CF, Shaginurova G, Tossberg JT, Hester JD, Chapman N, Guo Y, Crooke PS, Aune TM. Profiles of Long Noncoding RNAs in Human Naive and Memory T Cells. J. Immunol [print-electronic]. 2017 Jun 6/9/2017; PMID: 28600289, PII: jimmunol.1700232, DOI: 10.4049/jimmunol.1700232, ISSN: 1550-6606.

Aune TM, Crooke PS, Patrick AE, Tossberg JT, Olsen NJ, Spurlock CF. Expression of long non-coding RNAs in autoimmunity and linkage to enhancer function and autoimmune disease risk genetic variants. J. Autoimmun [print-electronic]. 2017 Apr 4/15/2017; PMID: 28420548, PII: S0896-8411(17)30070-7, DOI: 10.1016/j.jaut.2017.03.014, ISSN: 1095-9157.

Spurlock CF, Crooke PS, Aune TM. Biogenesis and Transcriptional Regulation of Long Noncoding RNAs in the Human Immune System. J. Immunol. 2016 Dec 12/15/2016; 197(12): 4509-17. PMID: 27913643, PMCID: PMC5140008, PII: 197/12/4509, DOI: 10.4049/jimmunol.1600970, ISSN: 1550-6606.

Aune TM, Crooke PS, Spurlock CF. Long noncoding RNAs in T lymphocytes. J. Leukoc. Biol [print-electronic]. 2016 Jan; 99(1): 31-44. PMID: 26538526, PII: jlb.1RI0815-389R, DOI: 10.1189/jlb.1RI0815-389R, ISSN: 1938-3673.

Mazzitelli D, Fischlein T, Rankin JS, Choi YH, Stamm C, Pfeiffer S, Pirk J, Detter C, Kroll J, Beyersdorf F, Griffin CD, Shrestha M, Nöbauer C, Crooke PS, Schreiber C, Lange R. Geometric ring annuloplasty as an adjunct to aortic valve repair: clinical investigation of the HAART 300 device. Eur J Cardiothorac Surg [print-electronic]. 2015 Jul 7/8/2015; PMID: 26156945, PII: ezv234, DOI: 10.1093/ejcts/ezv234, ISSN: 1873-734X.

Crooke PS, Beavan LA, Griffin CD, Mazzitelli D, Rankin JS. A geometric model of the normal human aortic root and design of a fully anatomic aortic root graft. Innovations (Phila). 2015 Jan; 10(1): 57-62. PMID: 25628255, DOI: 10.1097/IMI.0000000000000125, ISSN: 1559-0879.

Spurlock CF, Tossberg JT, Guo Y, Sriram S, Crooke PS, Aune TM. Defective structural RNA processing in relapsing-remitting multiple sclerosis. Genome Biol. 2015; 16: 58. PMID: 25885816, PMCID: PMC4403723, PII: 10.1186/s13059-015-0629-x, DOI: 10.1186/s13059-015-0629-x, ISSN: 1474-760X.

Spurlock CF, Tossberg JT, Guo Y, Collier SP, Crooke PS, Aune TM. Expression and functions of long noncoding RNAs during human T helper cell differentiation. Nat Commun. 2015; 6: 6932. PMID: 25903499, PMCID: PMC4410435, PII: ncomms7932, DOI: 10.1038/ncomms7932, ISSN: 2041-1723.

Spurlock CF, Tossberg JT, Guo Y, Sriram S, Crooke PS, Aune TM. Defective structural RNA processing in relapsing-remitting multiple sclerosis. Genome Biol. 2015; 16: 58. PMID: 25885816, PMCID: PMC4403723, PII: 10.1186/s13059-015-0629-x, DOI: 10.1186/s13059-015-0629-x, ISSN: 1474-760X.

Calmelet C, Hotchkiss J, Crooke P. A mathematical model for antibiotic control of bacteria in peritoneal dialysis associated peritonitis. Math Biosci Eng. 2014 Dec; 11(6): 1449-64. PMID: 25365600, ISSN: 1551-0018.

Rankin JS, Nöbauer C, Crooke PS, Schreiber C, Lange R, Mazzitelli D. Techniques of autologous pericardial leaflet replacement for aortic valve reconstruction. Ann. Thorac. Surg. 2014 Aug; 98(2): 743-5. PMID: 25087813, PII: S0003-4975(14)00125-8, DOI: 10.1016/j.athoracsur.2013.11.086, ISSN: 1552-6259.

Mazzitelli D, Stamm C, Rankin JS, Nöbauer C, Pirk J, Meuris B, Crooke PS, Wagner A, Beavan LA, Griffin CD, Powers D, Nasseri B, Schreiber C, Hetzer R, Lange R. Hemodynamic outcomes of geometric ring annuloplasty for aortic valve repair: a 4-center pilot trial. J. Thorac. Cardiovasc. Surg [print-electronic]. 2014 Jul; 148(1): 168-75. PMID: 24113022, PII: S0022-5223(13)00951-3, DOI: 10.1016/j.jtcvs.2013.08.031, ISSN: 1097-685X.

Mazzitelli D, Nöbauer C, Rankin JS, Badiu CC, Dorfmeister M, Crooke PS, Wagner A, Schreiber C, Lange R. Early results of a novel technique for ring-reinforced aortic valve and root restoration. Eur J Cardiothorac Surg [print-electronic]. 2014 Mar; 45(3): 426-30. PMID: 23959743, PII: ezt407, DOI: 10.1093/ejcts/ezt407, ISSN: 1873-734X.

Crooke PS, Beavan LA, Griffin CD, Mazzitelli D, Rankin JS. Design characteristics of a three-dimensional geometric aortic valve annuloplasty ring. Innovations (Phila). 2013 Sep; 8(5): 364-70. PMID: 24346586, PII: 01243895-201309000-00008, DOI: 10.1097/IMI.0000000000000026, ISSN: 1559-0879.

Rankin JS, Crooke PS, Lange R, Mazzitelli D. Techniques of autologous pericardial leaflet replacement for bicuspid aortic valve endocarditis. J. Heart Valve Dis. 2013 Sep; 22(5): 724-31. PMID: 24383388, ISSN: 0966-8519.

Rankin JS, Bone MC, Fries PM, Aicher D, Schäfers HJ, Crooke PS. A refined hemispheric model of normal human aortic valve and root geometry. J. Thorac. Cardiovasc. Surg [print-electronic]. 2013 Jul; 146(1): 103-108.e1. PMID: 22858429, PII: S0022-5223(12)00722-2, DOI: 10.1016/j.jtcvs.2012.06.043, ISSN: 1097-685X.

Mazzitelli D, Nöbauer C, Rankin JS, Badiu CC, Krane M, Crooke PS, Cohn WE, Opitz A, Schreiber C, Lange R. Early results after implantation of a new geometric annuloplasty ring for aortic valve repair. Ann. Thorac. Surg [print-electronic]. 2013 Jan; 95(1): 94-7. PMID: 23063198, PII: S0003-4975(12)01865-6, DOI: 10.1016/j.athoracsur.2012.08.034, ISSN: 1552-6259.

Paladino JD, Crooke PS, Brackney CR, Kaynar AM, Hotchkiss JR. Medical practices display power law behaviors similar to spoken languages. BMC Med Inform Decis Mak. 2013; 13: 102. PMID: 24007376, PMCID: PMC3766655, PII: 1472-6947-13-102, DOI: 10.1186/1472-6947-13-102, ISSN: 1472-6947.

Tossberg JT, Crooke PS, Henderson MA, Sriram S, Mrelashvili D, Vosslamber S, Verweij CL, Olsen NJ, Aune TM. Using biomarkers to predict progression from clinically isolated syndrome to multiple sclerosis. J Clin Bioinforma. 2013; 3(1): 18. PMID: 24088512, PMCID: PMC3850501, PII: 2043-9113-3-18, DOI: 10.1186/2043-9113-3-18, ISSN: 2043-9113.

Tossberg JT, Crooke PS, Henderson MA, Sriram S, Mrelashvili D, Chitnis S, Polman C, Vosslamber S, Verweij CL, Olsen NJ, Aune TM. Gene-expression signatures: biomarkers toward diagnosing multiple sclerosis. Genes Immun [print-electronic]. 2012 Feb; 13(2): 146-54. PMID: 21938015, PMCID: PMC3291793, PII: gene201166, DOI: 10.1038/gene.2011.66, ISSN: 1476-5470.

Crooke PS, Tossberg JT, Horst SN, Tauscher JL, Henderson MA, Beaulieu DB, Schwartz DA, Olsen NJ, Aune TM. Using gene expression data to identify certain gastro-intestinal diseases. J Clin Bioinforma. 2012; 2(1): 20. PMID: 23171526, PMCID: PMC3599448, PII: 2043-9113-2-20, DOI: 10.1186/2043-9113-2-20, ISSN: 2043-9113.

Crooke P, Hotchkiss J, Lenbury Y, McKinney B. Mathematical modeling of patient care [editorial]. Comput Math Methods Med [print-electronic]. 2012; 2012: 563287. PMID: 22693538, PMCID: PMC3368168, DOI: 10.1155/2012/563287, ISSN: 1748-6718.

Crooke PS, Tossberg JT, Horst SN, Tauscher JL, Henderson MA, Beaulieu DB, Schwartz DA, Olsen NJ, Aune TM. Using gene expression data to identify certain gastro-intestinal diseases. J Clin Bioinforma. 2012; 2(1): 20. PMID: 23171526, PMCID: PMC3599448, PII: 2043-9113-2-20, DOI: 10.1186/2043-9113-2-20, ISSN: 2043-9113.

Spurlock CF, Aune ZT, Tossberg JT, Collins PL, Aune JP, Huston JW, Crooke PS, Olsen NJ, Aune TM. Increased sensitivity to apoptosis induced by methotrexate is mediated by JNK. Arthritis Rheum. 2011 Sep; 63(9): 2606-16. PMID: 21618198, PMCID: PMC3165146, DOI: 10.1002/art.30457, ISSN: 1529-0131.

Crooke PS, Justenhoven C, Brauch H, , Dawling S, Roodi N, Higginbotham KS, Plummer WD, Schuyler PA, Sanders ME, Page DL, Smith JR, Dupont WD, Parl FF. Estrogen metabolism and exposure in a genotypic-phenotypic model for breast cancer risk prediction. Cancer Epidemiol. Biomarkers Prev [print-electronic]. 2011 Jul; 20(7): 1502-15. PMID: 21610218, PMCID: PMC3472969, PII: 1055-9965.EPI-11-0060, DOI: 10.1158/1055-9965.EPI-11-0060, ISSN: 1538-7755.

Hota S, Crooke P, Hotchkiss J. A Monte Carlo analysis of peritoneal antimicrobial pharmacokinetics. Adv. Exp. Med. Biol. 2011; 696: 401-10. PMID: 21431580, DOI: 10.1007/978-1-4419-7046-6_40, ISSN: 0065-2598.

Crooke PS, Parl FF. A mathematical model for DNA damage and repair. J Nucleic Acids. 2010; 2010: PMID: 20725623, PMCID: PMC2915813, DOI: 10.4061/2010/352603, ISSN: 2090-021X.

Paladino, J, Kaynar, AM, Crooke, PS, Hotchkiss, JR. The language of caring: Quantitating medical practice patterns using symbolic dynamics. Math Mod Nat Phen. 2010; 4((3)): 165-72.

Calmelet, C, Prokop, A, Mensah, J, McCawley, Crooke, PS. Modeling the cancer stem cell hypothesis. Math Mod Nat Phen. 2010; 4((3)): 40-62.

Crooke, PS, Kaynar, AM, Hotchkiss, JR. Lecture Notes in Control and Information Sciences. [place unknown: publisher unknown]; 2010. (407). Available from: http://www.springerlink.com/content/978-3-642-16134-6/#section=792859&page=1&locus=34.

Crooke PS, Parl FF. A mathematical model for DNA damage and repair. J Nucleic Acids. 2010; 2010: PMID: 20725623, PMCID: PMC2915813, DOI: 10.4061/2010/352603, ISSN: 2090-021X.

Adalja AA, Crooke PS, Hotchkiss JR. Influenza Transmission in Preschools: Modulation by contact landscapes and interventions. Math Model Nat Phenom. 2010 Jan 1/1/2010; 5(3): 3-14. PMID: 20967134, PMCID: PMC2956988, DOI: 10.1051/mmnp/20105301, ISSN: 0973-5348.

Paladino J, Kaynar AM, Crooke PS, Hotchkiss JR. The Language of Caring: Quantitating Medical Practice Patterns using Symbolic Dynamics. Math Model Nat Phenom [print-electronic]. 2010; 5(3): 165-72. PMID: 30542241, PMCID: PMC6287919, DOI: 10.1051/mmnp/20105310, ISSN: 0973-5348.

Parl FF, Dawling S, Roodi N, Crooke PS. Estrogen metabolism and breast cancer: a risk model. Ann. N. Y. Acad. Sci. 2009 Feb; 1155: 68-75. PMID: 19250193, PII: NYAS03676, DOI: 10.1111/j.1749-6632.2008.03676.x, ISSN: 1749-6632.

Parl FF, Egan KM, Li C, Crooke PS. Estrogen exposure, metabolism, and enzyme variants in a model for breast cancer risk prediction. Cancer Inform. 2009; 7: 109-21. PMID: 19718449, PMCID: PMC2730178, ISSN: 1176-9351.

Rankin JS, Dalley AF, Crooke PS, Anderson RH. A 'hemispherical' model of aortic valvar geometry. J. Heart Valve Dis. 2008 Mar; 17(2): 179-86. PMID: 18512488, ISSN: 0966-8519.

Xie J, Crooke PS, McKinney BA, Soltman J, Brandt SJ. A computational model of quantitative chromatin immunoprecipitation (ChIP) analysis. Cancer Inform [print-electronic]. 2008; 6: 138-46. PMID: 18458756, PMCID: PMC2367313, ISSN: 1176-9351.

Hotchkiss JR, Holley P, Crooke PS. Analyzing pathogen transmission in the dialysis unit: time for a (schedule) change?. Clin J Am Soc Nephrol. 2007 Nov; 2(6): 1176-85. PMID: 17962421, PII: CJN.00130107, DOI: 10.2215/CJN.00130107, ISSN: 1555-905X.

Mogal AP, van der Meer R, Crooke PS, Abdulkadir SA. Haploinsufficient prostate tumor suppression by Nkx3.1: a role for chromatin accessibility in dosage-sensitive gene regulation. J. Biol. Chem [print-electronic]. 2007 Aug 8/31/2007; 282(35): 25790-800. PMID: 17602165, PII: M702438200, DOI: 10.1074/jbc.M702438200, ISSN: 0021-9258.

Hotchkiss JR, Sanders MH, Clermont G, Crooke PS. Preventing "bored-lung disease" when treating patients with ventilatory failure [editorial]. Crit. Care Med. 2007 Jul; 35(7): 1797-9. PMID: 17581375, PII: 00003246-200707000-00040, DOI: 10.1097/01.CCM.0000269360.74281.1D, ISSN: 0090-3493.

Fossey SC, Vnencak-Jones CL, Olsen NJ, Sriram S, Garrison G, Deng X, Crooke PS, Aune TM. Identification of molecular biomarkers for multiple sclerosis. J Mol Diagn. 2007 Apr; 9(2): 197-204. PMID: 17384211, PMCID: PMC1867435, PII: S1525-1578(10)60380-7, DOI: 10.2353/jmoldx.2007.060147, ISSN: 1525-1578.

Puttasontiphot T, Lenbury Y, Rattanakul C, Rattanamongkonkul S, Hotchkiss JR, Crooke PS. Dynamic processes permitting stable coexistence of antimicrobial resistant and non-resistant organisms in a gastrointestinal tract model. ScienceAsia. 2007; 33: 197-206.

Crooke PS, Ritchie MD, Hachey DL, Dawling S, Roodi N, Parl FF. Estrogens, enzyme variants, and breast cancer: a risk model. Cancer Epidemiol. Biomarkers Prev. 2006 Sep; 15(9): 1620-9. PMID: 16985022, PII: 15/9/1620, DOI: 10.1158/1055-9965.EPI-06-0198, ISSN: 1055-9965.

Hota S, Crooke PS, Adams AB, Hotchkiss JR. Optimal phasic tracheal gas insufflation timing: an experimental and mathematical analysis. Crit. Care Med. 2006 May; 34(5): 1408-14. PMID: 16557158, DOI: 10.1097/01.CCM.0000214515.45727.21, ISSN: 0090-3493.

McKinney BA, Crowe JE, Voss HU, Crooke PS, Barney N, Moore JH. Hybrid grammar-based approach to nonlinear dynamical system identification from biological time series. Phys Rev E Stat Nonlin Soft Matter Phys [print-electronic]. 2006 Feb; 73(2 Pt 1): 21912. PMID: 16605367, DOI: 10.1103/PhysRevE.73.021912, ISSN: 1539-3755.

Hotchkiss JR, Strike DG, Crooke PS. Pathogen transmission and clinic scheduling. Emerging Infect. Dis. 2006 Jan; 12(1): 159-62. PMID: 16494737, PMCID: PMC3291384, DOI: 10.3201/eid1201.050349, ISSN: 1080-6040.

Rattanakul C, Lenbury Y, Bell J, Chatsudthipong V, Triampo W, Crooke PS. Spatial turing-type pattern formation in a model of signal transduction involving membrane-based receptors coupled by g proteins. Cancer Inform. 2006; 2: 329-43. PMID: 19458775, PMCID: PMC2675512, ISSN: 1176-9351.

Crooke PS, Kongkul K, Lenbury Y, Adams AB, Carter CS, Marini JJ, Hotchkiss JR. Mathematical models for pressure controlled ventilation of oleic acid-injured pigs. Math Med Biol. 2005 Mar; 22(1): 99-112. PMID: 15716301, PII: 22/1/99, DOI: 10.1093/imammb/dqh023, ISSN: 1477-8599.

Hotchkiss JR, Strike DG, Simonson DA, Broccard AF, Crooke PS. An agent-based and spatially explicit model of pathogen dissemination in the intensive care unit. Crit. Care Med. 2005 Jan; 33(1): 168-76; discussion 253. PMID: 15644665, PII: 00003246-200501000-00025, ISSN: 0090-3493.

Hotchkiss JR, Hermsen ED, Hovde LB, Simonson DA, Rotschafer JC, Crooke PS. Dynamic analysis of peritoneal dialysis associated peritonitis. ASAIO J. 2004 Nov; 50(6): 568-76. PMID: 15672790, ISSN: 1058-2916.

Hotchkiss JR, Broccard AF, Crooke PS. Artificial neural network prediction of ventilator-induced lung edema formation [letter]. Crit. Care Med. 2003 Aug; 31(8): 2250. PMID: 12973193, DOI: 10.1097/01.CCM.0000087328.59341.FC, ISSN: 0090-3493.

P.S. Crooke, S. Hota, J.R. Hotchkiss, and J.J. Marini. Mathematical models of passive, pressure-controlled ventilation with different resistance assumptions. Mathematical and Computer Modeling. 2003; 38: 495-502.

T. Dumrongpokaphan, Y. Lenbury, and P.S. Crooke. The analysis of higher-order cascade systems with separation conditions on the slow components: Application to a model of migration for survival of the species. Mathematical and Computer Modeling. 2003; 38: 671-90.

Hotchkiss JR, Adams AB, Stone MK, Dries DJ, Marini JJ, Crooke PS. Oscillations and noise: inherent instability of pressure support ventilation?. Am. J. Respir. Crit. Care Med. 2002 Jan 1/1/2002; 165(1): 47-53. PMID: 11779729, DOI: 10.1164/ajrccm.165.1.2101025, ISSN: 1073-449X.

P.S. Crooke. Mathematical modeling of respiratory care. East-West Journal of Mathematics. 2002; 4: 203-14.

P.S. Crooke, J.R. Hotchkiss, and J.J. Marini. Modeling recruitment manoeuvres with a variable compliance model for pressure controlled ventilation. Journal of Theoretical Medicine. 2002; 4: 197-202.

P.S. Crooke, J.R. Hotchkiss and J.J. Marini. Linear and nonlinear mathematical models for noninvasive ventilation. Mathematical and Computer Modeling. 2002; 35: 1297-313.

Hotchkiss JR, Adams AB, Dries DJ, Marini JJ, Crooke PS. Dynamic behavior during noninvasive ventilation: chaotic support?. Am. J. Respir. Crit. Care Med. 2001 Feb; 163(2): 374-8. PMID: 11179109, DOI: 10.1164/ajrccm.163.2.2004004, ISSN: 1073-449X.

P.S. Crooke, S. Hota, J.R. Hotchkiss, and J.J. Marini. A mathematical model for carbon dioxide exchange during mechanical ventilation with tracheal gas insufflation (TGI). Mathematical and Computer Modeling. 1999; 29: 45-61.

Crooke PS, Head JD, Marini JJ, Hotchkiss JR. Patient-ventilator interaction: a general model for nonpassive mechanical ventilation. IMA J Math Appl Med Biol. 1998 Dec; 15(4): 321-37. PMID: 9951713, ISSN: 0265-0746.

Hotchkiss JR, Crooke PS, Marini JJ. Theoretical interactions between ventilator settings and proximal deadspace ventilation during tracheal gas insufflation. Intensive Care Med. 1996 Oct; 22(10): 1112-9. PMID: 8923080, ISSN: 0342-4642.

P.S. Crooke, D. Head and J.J. Marini. A general two-compartment model for mechanical ventilation. Mathematical and Computer Modeling. 1996; 24: 1-18.

Valdivia, TD, Hotchkiss, JR, Crooke, PS, Marini, JJ. Simulating the Clinical Care of Patients: A Comprehensive Mathematical Model of Human Pathophysiology. Proc Annu Symp Comput Appl Med Care. 1995; 1014.

Hotchkiss JR, Crooke PS, Adams AB, Marini JJ. Implications of a biphasic two-compartment model of constant flow ventilation for the clinical setting. J Crit Care. 1994 Jun; 9(2): 114-23. PMID: 7920978, ISSN: 0883-9441.

Burke WC, Crooke PS, Marcy TW, Adams AB, Marini JJ. Comparison of mathematical and mechanical models of pressure-controlled ventilation. J. Appl. Physiol. 1993 Feb; 74(2): 922-33. PMID: 8458816, ISSN: 8750-7587.

Marini JJ, Crooke PS. A general mathematical model for respiratory dynamics relevant to the clinical setting. Am. Rev. Respir. Dis. 1993 Jan; 147(1): 14-24. PMID: 8420408, DOI: 10.1164/ajrccm/147.1.14, ISSN: 0003-0805.

P.S. Crooke and J.J. Marini. A general mathematical model for respiratory dynamics relevant to the clinical setting. American Review of Respiratory Disease. 1993; 147: 14-24.

P.S. Crooke and J.J. Marini. A nonlinear mathematical model of pressure preset ventilation: Description and limit values for key outcome variables. Mathematical Models and Methods in Applied Sciences. 1993; 3: 839-59.

W.C. Burke, P.S. Crooke, T.W. March, A.B. Adams, and J.J. Marini. Comparison of mathematical and mechanical models of pressure controlled ventilation. JOURNAL OF APPLIED PHYSIOLOGY. 1993; 74((2)): 922-33.

Nahum A, Burke WC, Ravenscraft SA, Marcy TW, Adams AB, Crooke PS, Marini JJ. Lung mechanics and gas exchange during pressure-control ventilation in dogs. Augmentation of CO2 elimination by an intratracheal catheter. Am. Rev. Respir. Dis. 1992 Oct; 146(4): 965-73. PMID: 1416426, DOI: 10.1164/ajrccm/146.4.965, ISSN: 0003-0805.

Marini JJ, Crooke PS, Truwit JD. Determinants and limits of pressure-preset ventilation: a mathematical model of pressure control. J. Appl. Physiol. 1989 Sep; 67(3): 1081-92. PMID: 2676950, ISSN: 8750-7587.

P. Crooke, R.D. Tanner, and Y. Lenbury. Investigation of the volume effect on a simple batch fermentation process. Mathematical and Computer Modeling. 1989; 12((12)): 1521-30.

Hong K, Tanner RD, Crooke PS, Malaney GW. Semisolid state fermentation of baker's yeast in an air-fluidized bed fermentor. Appl. Biochem. Biotechnol. 1988 Aug; 18: 3-17. PMID: 3052296, ISSN: 0273-2289.

Crooke PS, Tanner RD, Park DH. Time Dependent Differential Yield as a Scale-up Parameter in Enzyme and Fermentation Reactors. Biotechnol. Prog. 1986 Mar; 2(1): 40-7. PMID: 20568184, DOI: 10.1002/btpr.5420020108, ISSN: 8756-7938.

Lenbury Y, Crooke PS, Tanner RD. Relating damped oscillations to sustained limit cycles describing real and ideal batch fermentation processes. BioSystems. 1986; 19(1): 15-22. PMID: 3521759, ISSN: 0303-2647.

Yongwimon Lenbury and Philip Crooke. The effect of the specific growth rates and the yield expressions on oscillations in a two-tank fermentor. Journal of the Science Society of Thailand. 1986; 12: 171-86.