{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T01:21:01Z","timestamp":1760145661088,"version":"build-2065373602"},"reference-count":23,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T00:00:00Z","timestamp":1723507200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Union","award":["T2E\u0394K-03717"],"award-info":[{"award-number":["T2E\u0394K-03717"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["MPs"],"abstract":"<jats:p>Pressure ulcers are a frequent issue involving localized damage to the skin and underlying tissues, commonly arising from prolonged hospitalization and immobilization. This paper introduces a mathematical model designed to elucidate the mechanics behind pressure ulcer formation, aiming to predict its occurrence and assist in its prevention. Utilizing differential geometry and elasticity theory, the model represents human skin and simulates its deformation under pressure. Additionally, a system of ordinary differential equations is employed to predict the outcomes of these deformations, estimating the cellular death rate in skin tissues and underlying layers. The model also incorporates changes in blood flow resulting from alterations in skin geometry. This comprehensive approach provides new insights into the optimal bed surfaces required to prevent pressure ulcers and offers a general predictive method to aid healthcare personnel in making informed decisions for at-risk patients. Compared to existing models in the literature, our model delivers a more thorough prediction method that aligns well with current data. It can forecast the time required for an immobilized individual to develop an ulcer in various body parts, considering different initial health conditions and treatment strategies.<\/jats:p>","DOI":"10.3390\/mps7040062","type":"journal-article","created":{"date-parts":[[2024,8,13]],"date-time":"2024-08-13T10:54:54Z","timestamp":1723546494000},"page":"62","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["A Mathematical Model of Pressure Ulcer Formation to Facilitate Prevention and Management"],"prefix":"10.3390","volume":"7","author":[{"given":"Ioannis G.","family":"Violaris","sequence":"first","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Western Macedonia, 50131 Kozani, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7711-5194","authenticated-orcid":false,"given":"Konstantinos","family":"Kalafatakis","sequence":"additional","affiliation":[{"name":"Faculty of Medicine and Dentistry (Malta Campus), Queen Mary University of London, VCT 2520 Victoria, Malta"},{"name":"Human Computer Interaction Laboratory (HCILab), Department of Informatics and Telecommunications, School of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0615-783X","authenticated-orcid":false,"given":"Nikolaos","family":"Giannakeas","sequence":"additional","affiliation":[{"name":"Human Computer Interaction Laboratory (HCILab), Department of Informatics and Telecommunications, School of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9043-1290","authenticated-orcid":false,"given":"Alexandros T.","family":"Tzallas","sequence":"additional","affiliation":[{"name":"Human Computer Interaction Laboratory (HCILab), Department of Informatics and Telecommunications, School of Informatics and Telecommunications, University of Ioannina, 47100 Arta, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6757-1698","authenticated-orcid":false,"given":"Markos","family":"Tsipouras","sequence":"additional","affiliation":[{"name":"Department of Electrical and Computer Engineering, University of Western Macedonia, 50131 Kozani, Greece"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2024,8,13]]},"reference":[{"key":"ref_1","unstructured":"Timoshenko, S., and Goodier, J.N. (1976). Theory of Elasticity, McGraw-Hill. [3rd ed.]."},{"key":"ref_2","unstructured":"Washizu, K. (1968). Variational Methods in Elasticity and Plasticity, Pergamon Press."},{"key":"ref_3","unstructured":"Do Carmo, M.P. (1970). Differential Geometry of Curves and Surfaces, Prentice-Hall."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"023602","DOI":"10.1063\/1.3072796","article-title":"Estimation of volume flow in curved tubes based on analytical and computational analysis of axial velocity profiles","volume":"21","author":"Verkaik","year":"2009","journal-title":"Phys. Fluids"},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"80","DOI":"10.1016\/j.mechrescom.2019.05.003","article-title":"Towards understanding pressure ulcer formation: Coupling an inflammation regulatory network to a tissue scale finite element model","volume":"97","author":"Sree","year":"2019","journal-title":"Mech. Res. Commun."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"195","DOI":"10.1080\/10739680590905062","article-title":"Oxygen Partial Pressure in Outer Layers of Skin: Simulation Using Three-Dimensional Multilayered Models","volume":"12","author":"Wang","year":"2005","journal-title":"Microcirculation"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"264","DOI":"10.1007\/s004210100484","article-title":"Human body surface area: Measurement and prediction using three dimensional body scans","volume":"85","author":"Tikuisis","year":"2001","journal-title":"Eur. J. Appl. Physiol."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1111\/j.1600-0846.2007.00269.x","article-title":"A nonlinear elastic behavior to identify the mechanical parameters of human skin in vivo","volume":"14","author":"Delalleau","year":"2008","journal-title":"Ski. Res. Technol."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"75","DOI":"10.1016\/j.compstruc.2017.05.003","article-title":"The mechanical behavior of skin: Structures and models for the finite element analysis","volume":"190","year":"2017","journal-title":"Comput. Struct."},{"key":"ref_10","doi-asserted-by":"crossref","unstructured":"Polyanin, A.D. (2002). Handbook of Linear Partial Differential Equations for Engineers and Scientists, CHAPMAN and HALL\/CRC.","DOI":"10.1201\/9781420035322"},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"443","DOI":"10.1146\/annurev-fluid-010816-060302","article-title":"Blood Flow in the Microcirculation","volume":"49","author":"Secomb","year":"2017","journal-title":"Annu. Rev. Fluid Mech."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1080\/00039896.1987.9935790","article-title":"Effects of tobacco smoke inhalation on capillary blood flow in human skin","volume":"42","author":"Richardson","year":"1987","journal-title":"Arch. Environ. Heal. Int. J."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"1295","DOI":"10.1136\/bmj.292.6531.1295","article-title":"Impaired microvascular hyperaemic response to minor skin trauma in type I diabetes","volume":"292","author":"Rayman","year":"1986","journal-title":"Br. Med. J. (Clin. Res. Ed.)"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"927","DOI":"10.1016\/j.ijnurstu.2006.02.011","article-title":"prePURSE-Study Group The prevalence and incidence of pressure ulcers in hospitalised patients in the Netherlands: A prospective inception cohort study","volume":"44","author":"Schoonhoven","year":"2007","journal-title":"Int. J. Nurs. Stud."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1002\/nur.10025","article-title":"Prevalence, prevention, and treatment of pressure ulcers: Descriptive study in 89 institutions in the Netherlands","volume":"25","author":"Bours","year":"2002","journal-title":"Res. Nurs. Health"},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"634","DOI":"10.1111\/iwj.13071","article-title":"The national cost of hospital-acquired pressure injuries in the United States","volume":"16","author":"Padula","year":"2019","journal-title":"Int. Wound J."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"103546","DOI":"10.1016\/j.ijnurstu.2020.103546","article-title":"Global prevalence and incidence of pressure injuries in hospitalised adult patients: A systematic review and meta-analysis","volume":"105","author":"Li","year":"2020","journal-title":"Int. J. Nurs. Stud."},{"key":"ref_18","doi-asserted-by":"crossref","unstructured":"Mishu, M.C., and Schroeder, J.W. (2015, January 28\u201330). Modelling of pressure ulcer (PU) risk prediction system. Proceedings of the 2015 Science and Information Conference (SAI), London, UK.","DOI":"10.1109\/SAI.2015.7237211"},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Ziraldo, C., Solovyev, A., Allegretti, A., Krishnan, S., Henzel, M.K., Sowa, G.A., and Vodovotz, Y. (2015). A computational, tissue-realistic model of pressure ulcer formation in individuals with spinal cord injury. PLoS Comput. Biol., 11.","DOI":"10.1371\/journal.pcbi.1004309"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"517","DOI":"10.1109\/TNSRE.2007.906967","article-title":"Finite element analysis for evaluation of pressure ulcer on the buttock: Development and validation","volume":"15","author":"Makhsous","year":"2007","journal-title":"IEEE Trans. Neural Syst. Rehabil. Eng."},{"key":"ref_21","first-page":"20170257","article-title":"Mathematical and computational modelling of skin biophysics: A review","volume":"473","author":"Limbert","year":"2017","journal-title":"Proc. Math. Phys. Eng. Sci."},{"key":"ref_22","doi-asserted-by":"crossref","unstructured":"Li, K., and Utyuzhnikov, S. (2023). Tensor Train-Based Higher-Order Dynamic Mode decomposition for dynamical systems. Mathematics, 11.","DOI":"10.3390\/math11081809"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"013031","DOI":"10.1088\/1367-2630\/ad1b29","article-title":"Information Cascade Prediction of complex networks based on Physics-informed Graph Convolutional Network","volume":"26","author":"Yu","year":"2024","journal-title":"New J. Phys."}],"container-title":["Methods and Protocols"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2409-9279\/7\/4\/62\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T15:35:53Z","timestamp":1760110553000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2409-9279\/7\/4\/62"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,8,13]]},"references-count":23,"journal-issue":{"issue":"4","published-online":{"date-parts":[[2024,8]]}},"alternative-id":["mps7040062"],"URL":"https:\/\/doi.org\/10.3390\/mps7040062","relation":{},"ISSN":["2409-9279"],"issn-type":[{"type":"electronic","value":"2409-9279"}],"subject":[],"published":{"date-parts":[[2024,8,13]]}}}