{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,6]],"date-time":"2026-10-06T05:50:25Z","timestamp":1791265825418,"version":"4.1.0"},"reference-count":43,"publisher":"Springer Science and Business Media LLC","issue":"4","license":[{"start":{"date-parts":[[2019,11,18]],"date-time":"2019-11-18T00:00:00Z","timestamp":1574035200000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"},{"start":{"date-parts":[[2019,11,18]],"date-time":"2019-11-18T00:00:00Z","timestamp":1574035200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0"}],"funder":[{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["EP\/M508147\/1"],"award-info":[{"award-number":["EP\/M508147\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000266","name":"EPSRC","doi-asserted-by":"crossref","award":["EP\/M000303\/1"],"award-info":[{"award-number":["EP\/M000303\/1"]}],"id":[{"id":"10.13039\/501100000266","id-type":"DOI","asserted-by":"crossref"}]},{"DOI":"10.13039\/501100000287","name":"Royal Academy of Engineering","doi-asserted-by":"crossref","award":["RF\/130"],"award-info":[{"award-number":["RF\/130"]}],"id":[{"id":"10.13039\/501100000287","id-type":"DOI","asserted-by":"crossref"}]}],"content-domain":{"domain":["link.springer.com"],"crossmark-restriction":false},"short-container-title":["Biomech Model Mechanobiol"],"published-print":{"date-parts":[[2020,8]]},"abstract":"<jats:title>Abstract<\/jats:title>\n                  <jats:p>In post-amputation rehabilitation, a common goal is to return to ambulation using a prosthetic limb, suspended by a customised socket. Prosthetic socket design aims to optimise load transfer between the residual limb and mechanical limb, by customisation to the user. This is a time-consuming process, and with the increase in people requiring these prosthetics, it is vital that these personalised devices can be produced rapidly while maintaining excellent fit, to maximise function and comfort. Prosthetic sockets are designed by capturing the residual limb\u2019s shape and applying a series of geometrical modifications, called rectifications. Expert knowledge is required to achieve a comfortable fit in this iterative process. A variety of rectifications can be made, grouped into established strategies [e.g. in transtibial sockets: patellar tendon bearing (PTB) and total surface bearing (TSB)], creating a complex design space. To date, adoption of advanced engineering solutions to support fitting has been limited. One method is numerical optimisation, which allows the designer a number of likely candidate solutions to start the design process. Numerical optimisation is commonly used in many industries but not prevalent in the design of prosthetic sockets. This paper therefore presents candidate shape optimisation methods which might benefit the prosthetist and the limb user, by blending the state of the art from prosthetic mechanical design, surrogate modelling and evolutionary computation. The result of the analysis is a series of prosthetic socket designs that preferentially load and unload the pressure tolerant and intolerant regions of the residual limb. This spectrum is bounded by the general forms of the PTB and TSB designs, with a series of variations in between that represent a compromise between these accepted approaches. This results in a difference in pressure of up to 31\u00a0kPa over the fibula head and 14\u00a0kPa over the residuum tip. The presented methods would allow a trained prosthetist to rapidly assess these likely candidates and then to make final detailed modifications and fine-tuning. Importantly, insights gained about the design should be seen as a compliment, not a replacement, for the prosthetist\u2019s skill and experience. We propose instead that this method might reduce the time spent on the early stages of socket design and allow prosthetists to focus on the most skilled and creative tasks of fine-tuning the design, in face-to-face consultation with their client.<\/jats:p>","DOI":"10.1007\/s10237-019-01258-7","type":"journal-article","created":{"date-parts":[[2019,11,18]],"date-time":"2019-11-18T18:01:55Z","timestamp":1574100115000},"page":"1347-1360","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":44,"title":["Predictive prosthetic socket design: part 2\u2014generating person-specific candidate designs using multi-objective genetic algorithms"],"prefix":"10.1007","volume":"19","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-6288-1347","authenticated-orcid":false,"given":"J. W.","family":"Steer","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0635-3125","authenticated-orcid":false,"given":"P. A.","family":"Grudniewski","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5184-050X","authenticated-orcid":false,"given":"M.","family":"Browne","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0145-5042","authenticated-orcid":false,"given":"P. R.","family":"Worsley","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6880-8338","authenticated-orcid":false,"given":"A. J.","family":"Sobey","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9647-1944","authenticated-orcid":false,"given":"A. S.","family":"Dickinson","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2019,11,18]]},"reference":[{"issue":"8","key":"1258_CR1","doi-asserted-by":"crossref","first-page":"10348","DOI":"10.3390\/s130810348","volume":"13","author":"EA Al-Fakih","year":"2013","unstructured":"Al-Fakih EA, Osman NAA, Eshraghi A, Adikan FRM (2013) The capability of fiber Bragg grating sensors to measure amputees' trans-tibial stump\/socket interface pressures. Sensors (Switzerland) 13(8):10348\u201310357","journal-title":"Sensors (Switzerland)"},{"issue":"6A","key":"1258_CR2","doi-asserted-by":"crossref","first-page":"821","DOI":"10.1682\/JRRD.2003.09.0146","volume":"41","author":"TL Beil","year":"2004","unstructured":"Beil TL, Street GM (2004) Comparison of interface pressures with pin and suction suspension systems. J Rehabil Res Dev 41(6A):821\u2013828","journal-title":"J Rehabil Res Dev"},{"issue":"6","key":"1258_CR3","first-page":"693","volume":"39","author":"TL Beil","year":"2002","unstructured":"Beil TL, Street GM, Covey SJ (2002) Interface pressures during ambulation using suction and vacuum-assisted prosthetic sockets. J Rehabil Res Dev 39(6):693\u2013700","journal-title":"J Rehabil Res Dev"},{"issue":"Suppl","key":"1258_CR4","first-page":"1","volume":"43","author":"JL Bramley","year":"2019","unstructured":"Bramley JL, Worsley PR, Bostan L, Bader DL, Dickinson AS (2019) Investigating the effects of simulated prosthetic loading on intact and trans-tibial residual limb dermal tissues. Prosthet Orthot Intl 43(Suppl):1","journal-title":"Prosthet Orthot Intl"},{"issue":"2","key":"1258_CR5","doi-asserted-by":"crossref","first-page":"97","DOI":"10.1080\/17452759.2013.797230","volume":"8","author":"G Colombo","year":"2013","unstructured":"Colombo G, Facoetti G, Regazzoni D, Rizzi C (2013) A full virtual approach to design and test lower limb prosthesis. Virtual Phys Prototyp 8(2):97\u2013111","journal-title":"Virtual Phys Prototyp"},{"issue":"2","key":"1258_CR6","doi-asserted-by":"crossref","first-page":"182","DOI":"10.1109\/4235.996017","volume":"6","author":"K Deb","year":"2002","unstructured":"Deb K, Pratap A, Agarwal S, Meyarivan T (2002) A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans Evol Comput 6(2):182\u2013197","journal-title":"IEEE Trans Evol Comput"},{"issue":"10","key":"1258_CR7","doi-asserted-by":"crossref","first-page":"1067","DOI":"10.1016\/j.clinbiomech.2006.06.004","volume":"21","author":"P Dou","year":"2006","unstructured":"Dou P, Jia X, Suo S, Wang R, Zhang M (2006) Pressure distribution at the stump\/socket interface in transtibial amputees during walking on stairs, slope and non-flat road. Clin Biomech 21(10):1067\u20131073","journal-title":"Clin Biomech"},{"issue":"3","key":"1258_CR8","doi-asserted-by":"crossref","first-page":"405","DOI":"10.1682\/JRRD.2008.01.0015","volume":"46","author":"T Dumbleton","year":"2009","unstructured":"Dumbleton T et al (2009) Dynamic interface pressure distributions of two transtibial prosthetic socket concepts. J Rehabil Res Dev 46(3):405\u2013415","journal-title":"J Rehabil Res Dev"},{"key":"1258_CR9","unstructured":"Eklund A, Sexton S (2017) WHO standards for prosthetics and orthotics"},{"issue":"3","key":"1258_CR10","doi-asserted-by":"crossref","first-page":"237","DOI":"10.1016\/S0268-0033(02)00206-1","volume":"18","author":"JCH Goh","year":"2003","unstructured":"Goh JCH, Lee PVS, Chong SY (2003a) Stump\/socket pressure profiles of the pressure cast prosthetic socket. Clin Biomech 18(3):237\u2013243","journal-title":"Clin Biomech"},{"issue":"2","key":"1258_CR11","doi-asserted-by":"crossref","first-page":"121","DOI":"10.1243\/09544110360579330","volume":"217","author":"JCH Goh","year":"2003","unstructured":"Goh JCH, Lee PVS, Chong SY (2003b) Static and dynamic pressure profiles of a patellar-tendon-bearing (PTB) socket. Proc Inst Mech Eng H 217(2):121\u2013126","journal-title":"Proc Inst Mech Eng H"},{"issue":"3","key":"1258_CR12","first-page":"491","volume":"41","author":"JCH Goh","year":"2004","unstructured":"Goh JCH, Lee PVS, Chong SY (2004) Comparative study between patellar-tendon-bearing and pressure cast prosthetic sockets. J Rehabil Res Dev 41(3):491\u2013501","journal-title":"J Rehabil Res Dev"},{"issue":"6","key":"1258_CR13","doi-asserted-by":"crossref","first-page":"623","DOI":"10.1016\/j.clinbiomech.2005.02.005","volume":"20","author":"JCH Goh","year":"2005","unstructured":"Goh JCH, Lee PVS, Toh SL, Ooi CK (2005) Development of an integrated CAD-FEA process for below-knee prosthetic sockets. Clin Biomech 20(6):623\u2013629","journal-title":"Clin Biomech"},{"issue":"2","key":"1258_CR14","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1023\/A:1022602019183","volume":"3","author":"DE Goldberg","year":"1988","unstructured":"Goldberg DE, Holland JH (1988) Genetic algorithms and machine learning. Mach Learn 3(2):95\u201399","journal-title":"Mach Learn"},{"key":"1258_CR15","first-page":"1","volume":"44","author":"PA Grudniewski","year":"2018","unstructured":"Grudniewski PA, Sobey AJ (2018) Behaviour of multi-level selection genetic algorithm (MLSGA) using different individual-level selection mechanisms. Swarm Evol Comput 44:1\u201329","journal-title":"Swarm Evol Comput"},{"key":"1258_CR16","unstructured":"Grudniewski PA, Sobey AJ (2019) cMLSGA: co-evolutionary multi-level selection genetic algorithm. Swarm Evol Comput Under Rev"},{"issue":"7","key":"1258_CR17","doi-asserted-by":"crossref","first-page":"783","DOI":"10.1016\/S0003-9993(98)90356-2","volume":"79","author":"K Hachisuka","year":"1998","unstructured":"Hachisuka K, Dozono K, Ogata H, Ohmine S, Shitama H, Shinkoda K (1998) Total surface bearing below-knee prosthesis: advantages, disadvantages, and clinical implications. Arch Phys Med Rehabil 79(7):783\u2013789","journal-title":"Arch Phys Med Rehabil"},{"issue":"15","key":"1258_CR18","doi-asserted-by":"crossref","first-page":"4063","DOI":"10.1088\/0031-9155\/53\/15\/004","volume":"53","author":"K Hoyt","year":"2008","unstructured":"Hoyt K, Kneezel T, Castaneda B, Parker KJ (2008) Quantitative sonoelastography for the in vivo assessment of skeletal muscle viscoelasticity. Phys Med Biol 53(15):4063\u20134080","journal-title":"Phys Med Biol"},{"issue":"12","key":"1258_CR19","doi-asserted-by":"crossref","first-page":"1498","DOI":"10.1111\/dme.12545","volume":"31","author":"M Kerr","year":"2014","unstructured":"Kerr M, Rayman G, Jeffcoate WJ (2014) Cost of diabetic foot disease to the National Health Service in England. Diabet Med 31(12):1498\u20131504","journal-title":"Diabet Med"},{"key":"1258_CR20","unstructured":"Kuhn GG (1966) Kondylen Bettung M\u00fcnster am Unterschenkel-Stumpf \u2018KBM-Prothese. Atlas d\u2019Appareillage Proth{\u00e9}tique et Orthop{\u00e9}dique 14"},{"issue":"July","key":"1258_CR21","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/j.gaitpost.2017.08.017","volume":"58","author":"S Laing","year":"2017","unstructured":"Laing S, Lythgo N, Lavranos J, Lee PVS (2017) Transtibial prosthetic socket shape in a developing country: a study to compare initial outcomes in pressure cast hydrostatic and patella tendon bearing designs. Gait Posture 58(July):363\u2013368","journal-title":"Gait Posture"},{"issue":"July","key":"1258_CR22","doi-asserted-by":"crossref","first-page":"88","DOI":"10.1016\/j.gaitpost.2018.08.022","volume":"66","author":"S Laing","year":"2018","unstructured":"Laing S, Lee PVS, Lavranos J, Lythgo N (2018) The functional, spatio-temporal and satisfaction outcomes of transtibial amputees with a hydrocast socket following an extended usage period in an under-resourced environment. Gait Posture 66(July):88\u201393","journal-title":"Gait Posture"},{"issue":"1","key":"1258_CR23","doi-asserted-by":"crossref","first-page":"132","DOI":"10.1016\/j.medengphy.2014.10.002","volume":"37","author":"P Laszczak","year":"2015","unstructured":"Laszczak P, Jiang L, Bader DL, Moser D, Zahedi S (2015) Development and validation of a 3D-printed interfacial stress sensor for prosthetic applications. Med Eng Phys 37(1):132\u2013137","journal-title":"Med Eng Phys"},{"key":"1258_CR24","unstructured":"Lee P, Goh J, Cheung S (2000) Biomechanical evaluation of the pressure cast (PCast) prosthetic socket for transtibial amputee. In: Proceedings of the World congress on medical physics & biomedical engineering"},{"issue":"1","key":"1258_CR25","first-page":"1","volume":"1","author":"M Li","year":"2018","unstructured":"Li M, Yao XIN (2018) Quality evaluation of solution sets in multiobjective optimisation: a survey. ACM Comput Surv 1(1):1\u201343","journal-title":"ACM Comput Surv"},{"issue":"5","key":"1258_CR26","first-page":"711","volume":"20","author":"Q Lin","year":"2016","unstructured":"Lin Q et al (2016) A hybrid evolutionary immune algorithm for multiobjective optimization problems. IEEE Trans Evol Comput 20(5):711\u2013729","journal-title":"IEEE Trans Evol Comput"},{"issue":"2","key":"1258_CR27","first-page":"161","volume":"38","author":"AF Mak","year":"2001","unstructured":"Mak AF, Zhang M, Boone DA (2001) State-of-the-art research in lower-limb prosthetic biomechanics-socket interface: a review. J Rehabil Res Dev 38(2):161\u2013174","journal-title":"J Rehabil Res Dev"},{"issue":"3","key":"1258_CR28","doi-asserted-by":"crossref","first-page":"095441191769076","DOI":"10.1177\/0954411917690764","volume":"231","author":"MP McGrath","year":"2017","unstructured":"McGrath MP et al (2017) Development of a residuum\/socket interface simulator for lower limb prosthetics. Proc Inst Mech Eng Part H J Eng Med 231(3):095441191769076","journal-title":"Proc Inst Mech Eng Part H J Eng Med"},{"key":"1258_CR29","first-page":"231","volume":"19","author":"G Murdoch","year":"1964","unstructured":"Murdoch G (1964) The \u2018Dundee\u2019 socket\u2014a total contact socket for the below-knee amputation. Orthop Prosthet Appl J 19:231\u2013234","journal-title":"Orthop Prosthet Appl J"},{"issue":"5","key":"1258_CR30","doi-asserted-by":"crossref","first-page":"782","DOI":"10.1115\/1.2264395","volume":"128","author":"A Palevski","year":"2006","unstructured":"Palevski A, Glaich I, Portnoy S, Linder-Ganz E, Gefen A (2006) Stress relaxation of porcine gluteus muscle subjected to sudden transverse deformation as related to pressure sore modeling. J Biomech Eng 128(5):782","journal-title":"J Biomech Eng"},{"issue":"12","key":"1258_CR31","doi-asserted-by":"crossref","first-page":"2583","DOI":"10.1007\/s10439-009-9801-3","volume":"37","author":"S Portnoy","year":"2009","unstructured":"Portnoy S, Siev-Ner I, Yizhar Z, Kristal A, Shabshin N, Gefen A (2009) Surgical and morphological factors that affect internal mechanical loads in soft tissues of the transtibial residuum. Ann Biomed Eng 37(12):2583\u20132605","journal-title":"Ann Biomed Eng"},{"key":"1258_CR32","first-page":"16","volume":"6","author":"CW Radcliffe","year":"1962","unstructured":"Radcliffe CW (1962) The biomechanics of below-knee prostheses in normal, level, bipedal walking. Artif Limbs 6:16\u201324","journal-title":"Artif Limbs"},{"issue":"5","key":"1258_CR33","doi-asserted-by":"crossref","first-page":"509","DOI":"10.1682\/JRRD.2014.08.0184","volume":"52","author":"MR Safari","year":"2015","unstructured":"Safari MR, Meier MR (2015a) Systematic review of effects of current transtibial prosthetic socket designs\u2014Part 2: quantitative outcomes. J Rehabil Res Dev 52(5):509\u2013526","journal-title":"J Rehabil Res Dev"},{"issue":"5","key":"1258_CR34","doi-asserted-by":"crossref","first-page":"491","DOI":"10.1682\/JRRD.2014.08.0183","volume":"52","author":"MR Safari","year":"2015","unstructured":"Safari MR, Meier MR (2015b) Systematic review of effects of current transtibial prosthetic socket designs\u2014Part 1: qualitative outcomes. J Rehabil Res Dev 52(5):491\u2013508","journal-title":"J Rehabil Res Dev"},{"key":"1258_CR35","unstructured":"Sobey A, Blanchard J, Grudniewski P, Savasta T (2019) There\u2019s no free lunch: a study of Genetic Algorithm use in Maritime Applications. In: Conference on computer applications and information technology in the maritime industries"},{"issue":"3","key":"1258_CR36","first-page":"118","volume":"11","author":"T Staats","year":"1987","unstructured":"Staats T, Lundt J (1987) The UCLA total surface bearing suction below-knee prosthesis. Clin Prosthet Orthot 11(3):118\u2013130","journal-title":"Clin Prosthet Orthot"},{"key":"1258_CR37","doi-asserted-by":"crossref","unstructured":"Steer JW, Browne M, Worsley PR, Dickinson AS (2019) Predictive prosthetic socket design. Part 1: population-based evaluation of transtibial prosthetic sockets by FEA-driven surrogate modelling. Biomech Model Mechanobiol","DOI":"10.1007\/s10237-019-01195-5"},{"key":"1258_CR38","unstructured":"Tseng LY, Chen C (2007) Multiple trajectory search for multiobjective optimization. In: 2007 IEEE congress on evolutionary computation, CEC 2007, vol 758, pp 3609\u20133616"},{"issue":"June","key":"1258_CR39","doi-asserted-by":"crossref","first-page":"616","DOI":"10.1016\/j.compstruct.2018.06.090","volume":"201","author":"Z Wang","year":"2018","unstructured":"Wang Z, Bai J, Sobey A, Xiong J, Shenoi A (2018) Optimal design of triaxial weave fabric composites under tension. Compos Struct 201(June):616\u2013624","journal-title":"Compos Struct"},{"issue":"3","key":"1258_CR40","first-page":"3077","volume":"13","author":"YG Woldesenbet","year":"2009","unstructured":"Woldesenbet YG, Yen GG, Tessema BG (2009) Constraint handling in multiobjective evolutionary optimization. IEEE Trans Evol Comput 13(3):3077\u20133084","journal-title":"IEEE Trans Evol Comput"},{"issue":"1","key":"1258_CR41","doi-asserted-by":"crossref","first-page":"67","DOI":"10.1109\/4235.585893","volume":"1","author":"DH Wolpert","year":"1997","unstructured":"Wolpert DH, Macready WG (1997) No free lunch theorems for optimization 1 introduction. IEEE Trans Evol Comput 1(1):67\u201382","journal-title":"IEEE Trans Evol Comput"},{"issue":"6","key":"1258_CR42","doi-asserted-by":"crossref","first-page":"712","DOI":"10.1109\/TEVC.2007.892759","volume":"11","author":"Q Zhang","year":"2007","unstructured":"Zhang Q, Li H (2007) MOEA\/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans Evol Comput 11(6):712\u2013731","journal-title":"IEEE Trans Evol Comput"},{"issue":"3","key":"1258_CR43","doi-asserted-by":"crossref","first-page":"188","DOI":"10.1016\/S1350-4533(98)00013-7","volume":"20","author":"M Zhang","year":"1998","unstructured":"Zhang M, Turner-Smith AR, Tanner A, Roberts VC (1998) Clinical investigation of the pressure and shear stress on the trans-tibial stump with a prosthesis. Med Eng Phys 20(3):188\u2013198","journal-title":"Med Eng Phys"}],"container-title":["Biomechanics and Modeling in Mechanobiology"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-019-01258-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10237-019-01258-7\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10237-019-01258-7.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2020,11,16]],"date-time":"2020-11-16T19:31:03Z","timestamp":1605555063000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10237-019-01258-7"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2019,11,18]]},"references-count":43,"journal-issue":{"issue":"4","published-print":{"date-parts":[[2020,8]]}},"alternative-id":["1258"],"URL":"https:\/\/doi.org\/10.1007\/s10237-019-01258-7","relation":{},"ISSN":["1617-7959","1617-7940"],"issn-type":[{"value":"1617-7959","type":"print"},{"value":"1617-7940","type":"electronic"}],"subject":[],"published":{"date-parts":[[2019,11,18]]},"assertion":[{"value":"28 May 2019","order":1,"name":"received","label":"Received","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"8 November 2019","order":2,"name":"accepted","label":"Accepted","group":{"name":"ArticleHistory","label":"Article History"}},{"value":"18 November 2019","order":3,"name":"first_online","label":"First Online","group":{"name":"ArticleHistory","label":"Article History"}}]}}