Crooke, Philip

Hotchkiss, John

Lenbury, Yongwimon

McKinney, Brett

Computational and Mathematical Methods in Medicine

English

PubMed

Philip Crooke

John Hotchkiss

Yongwimon Lenbury

Brett McKinney

Crossref

Hindawi Publishing CorporationComputational and Mathematical Methods in MedicineVolume 2012, Article ID 563287, 2 pagesdoi:10.1155/2012/563287EditorialMathematical Modeling of Patient CarePhilip Crooke,1 John Hotchkiss,2 Yongwimon Lenbury,3 and Brett McKinney41 Department of Mathematics, Vanderbilt University, Nashville, TN, USA2 Department of Critical Care Medicine and Department of Medicine, Pittsburgh Veterans Aﬀairs Healthcare System,University of Pittsburgh Medical Center, Pittsburgh, PA, USA3 Department of Mathematics, Faculty of Science, Centre of Excellence in Mathematics (CHE), Mahidol University,Bangkok 10400, Thailand4 Tandy School of Computer Science and Department of Mathematics, Rayzor Hall, University of Tulsa, Tulsa, OK 74104, USACorrespondence should be addressed to Philip Crooke, philip.s.crooke@vanderbilt.eduReceived 28 March 2012; Accepted 28 March 2012Copyright © 2012 Philip Crooke et al. This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.In our call for papers for this special issue, we requestedtopics that ranged from mathematical models of physio-logical systems to macroeconomic models of the healthcareindustry. Although the response to this broad invitation wasmuted, we did receive a nice cross-section of papers withinthis spectrum of topics. In the following, we summarize thesix papers included in this volume.D. T. Grima et al. investigated the impact of antibiotics ontreating Clostridium diﬃcile-associated diseases (CDAD) onthe emergence of antibiotic-resistant bacteria using mathe-matical model describing the impact of in-hospital antibioticuse. Themodel is a system of nonlinear diﬀerential equationsarising from a compartment network of uncolonized andcolonized patients with and without antibiotic treatment.The model leads to a very important conclusion: there maybe a substantial reduction in antibiotic-resistant prevalencewhen nonantibiotic strategies are employed for CDAD. Thisis a perfect example of how mathematical modeling can leadto a practical change in treatment and impact on patienthealth and a reduction in costs.Advances in mathematical modeling have led to variouseﬀective tools for early diagnosis, such as the application ofthermometry ultrasonic techniques. Before implementationof the ultrasonic noninvasive estimation of thermal gradientsinto tissues based on spectral changes, rigorous analyses, overtransient echotraces acquired fromwell-controlled biologicaland computational phantoms, must be still made in orderto improve resolutions and evaluate clinic limitations. I.Bazan et al. applied this technique to computationallymodeled echotraces from scattered biological phantoms,attaining high resolution (better than 0.1◦C). They alsoprovided computer methods for viability evaluation ofthermal estimation from echoes with distinct noise levels,making it diﬃcult to interpret the readings. As a result oftheir analyses, the technique has been evaluated as a possibleeﬀective diagnosis tool for scattered tissues applications.Such research and analyses are of great importance sincethe ability to detect changes of thermal origin in ultrasonicecho spectra means the achievement of precise noninvasivetemperature estimations that could be very useful as an earlycomplementary indicator of infections, inflammations, orcancer.Obstructive sleep apnea (OSA) is an important healthissue and has been subject to diﬀerent modeling investiga-tions. C. T. Su et al. have applied a Mutliclass Mahalanobis-Taguchi System (MMTS) to the problem of prediagnosingthe condition using readily available patient information.Their model results in a better than 84% accuracy. Thisstatistical diagnostic/predictive method comes from patterninformation technology and demonstrates an importantapplication of a little used modeling paradigm in biology.The paper by C. Pagel et al. addresses a problem ofgrowing relevance with an aging population, dwindlingresources, and a declining number of healthcare providers:that of optimal scheduling in the context of a steppedcare. This topic is of considerable interest, not only in thedomain addressed by the authors, but in other populationsrequiring complex, highly specialized care. The author’smodel includes stratified levels of intensity of care, andcan be used to analyze expected changes in waiting times2 Computational and Mathematical Methods in Medicineand throughput under diﬀerent allocations of scheduledslots. This quantitative model will be of highly operationalinterest—particularly to large, integrated healthcare systemsconfronted with a growing mental healthcare population.Moreover, since the model is suﬃciently flexible, it may beadapted to address queuing systems germane to other highlycomplex medical conditions.Healthcare providers and networks face more thanresource limitations: increased oversight and an emphasison the quality of care are wending their way towardreimbursement (“pay for performance”) as well as publicaccess to quality “report cards.” In this context, establishingthat the metrics of quality accurately reflect the performanceof the hospital, rather than diﬀerences in patient populations,is of paramount importance. The paper by D. Shine directlyaddresses this issue, focusing on the modulation of riskby comorbid conditions. Shine illustrates a spreadsheet-based approach for capturing high impact comorbiditiesand identifies those having the greatest impact on risk. Thisgeneral approach could improve the accuracy of expectedmortality estimates, thus also the ratio of observed mortalityto expected mortality. Such considerations will have a clearimpact not only on quality reports but also eventually onequitable reimbursement.HIV/AIDS is a global pandemic of disastrous pro-portions, in which the virus can rapidly develop resis-tance to antiretrovirals, and subsequently, lifelong therapyis required, and many at-risk individuals live in austereenvironments where compliance with complex treatmentregimens may prove problematic. These medications areoften toxic, and attenuation of treatment intensity dueeither to toxicity or to regimen complexity can promotethe development of drug resistance. The development ofnew antiretroviral agents or formulations is both costlyand critical in the setting of a virus prone to very rapidmutation. M. L. Branham et al. illustrate the use of artificialneural networks (ANN), primed with drug physicochemicaland bioaccumulation characteristics, to predict maximumrecommended therapeutic doses of antiretroviral agents.They note particular utility of the ANN approach whenthe medications evaluated are poorly soluble in water. Thistype of computational analyses should prove useful as drugdevelopers balance bioavailability and ease of administrationagainst tolerable doses, a balance with implications forcompliance and the potential for eﬀective treatment.We are convinced of the utility of mathematics and otherquantitative approaches to provide better healthcare. Thesix papers in this volume demonstrate that mathematicalmodeling can play a central role in patient care innovations.Philip CrookeJohn HotchkissYongwimon LenburyBrett McKinneySubmit your manuscripts athttp://www.hindawi.comStem CellsInternationalHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014MEDIATORSINFLAMMATIONofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Behavioural NeurologyEndocrinologyInternational Journal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Disease MarkersHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014BioMed Research InternationalOncologyJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Oxidative Medicine and Cellular LongevityHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014PPAR ResearchThe Scientific World JournalHindawi Publishing Corporation http://www.hindawi.com Volume 2014Immunology ResearchHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Journal ofObesityJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014 Computational and  Mathematical Methods in MedicineOphthalmologyJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Diabetes ResearchJournal ofHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Hindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Research and TreatmentAIDSHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Gastroenterology Research and PracticeHindawi Publishing Corporationhttp://www.hindawi.com Volume 2014Parkinson’s DiseaseEvidence-Based Complementary and Alternative MedicineVolume 2014Hindawi Publishing Corporationhttp://www.hindawi.com

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