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A bottom-up approach to model collagen fiber damage and failure in soft biological tissues
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics.
KTH, School of Engineering Sciences (SCI), Engineering Mechanics, Vehicle Engineering and Solid Mechanics, Solid Mechanics. Univ Southern Denmark, Fac Hlth Sci, Odense, Denmark..
2022 (English)In: Journal of the mechanics and physics of solids, ISSN 0022-5096, E-ISSN 1873-4782, Vol. 169, article id 105086Article in journal (Refereed) Published
Abstract [en]

Understanding the damage and failure of load-carrying soft biological tissue is critical in the effectual treatment of injury and disease. The difficulty in experimentally identifying the intrinsic mechanisms by which damage initiates and accumulates, and how this ultimately leads to tissue rupture, has motivated the constitutive modeling of soft tissue failure. We present an extension of our previous microstructural continuum model (Miller and Gasser, 2021) that includes proteoglycan mediated collagen fibril sliding towards capturing the non-linear time dependent properties of collagenous tissue. We now additionally incorporate an interfibrillar failure (fibril pull-out) mechanism and showcase the resulting damage induced mechanical be-havior across several length scales. Importantly, a bottom-up approach is further demonstrated, whereby the microstructural model is employed in a single-element representation of the modes of fracture. A qualitative description of soft tissue rupture is accordingly attained, to which an appropriate cohesive zone model for the equivalent fracture surface is then calibrated. In doing so, a surface-based discontinuous characterization of failure is directly derived from the upscaling of irreversible and dissipative damage mechanisms from the microscale.

Place, publisher, year, edition, pages
Elsevier BV , 2022. Vol. 169, article id 105086
Keywords [en]
Soft biological tissue, Microstructure, Collagen, Constitutive modeling, Damage, Failure, Fracture
National Category
Applied Mechanics
Identifiers
URN: urn:nbn:se:kth:diva-321971DOI: 10.1016/j.jmps.2022.105086ISI: 000876982800002Scopus ID: 2-s2.0-85139875442OAI: oai:DiVA.org:kth-321971DiVA, id: diva2:1713869
Note

QC 20221128

Available from: 2022-11-28 Created: 2022-11-28 Last updated: 2023-04-27Bibliographically approved
In thesis
1. Modelling the time-dependent, damage and fracture mechanical properties of load-bearing soft biological tissues
Open this publication in new window or tab >>Modelling the time-dependent, damage and fracture mechanical properties of load-bearing soft biological tissues
2023 (English)Doctoral thesis, comprehensive summary (Other academic)
Abstract [en]

Load-carrying soft biological tissues exhibit a wide range of complex time-dependent, damage, and fracture mechanical properties. An effective comprehension of such behaviour is advantageous in characterising tolerance to injury and can provide valuable insights regarding the incidence and progression of certain diseases. Improving knowledge in such areas directly benefits the successful integration of engineering concepts within the clinical workflow. Moreover, it can aid in the advancement of preventative measures, patient treatment strategies, and the optimisation of medical device design. The macroscopic material response of soft tissue is inextricably linked to the deformation of mechanically significant extracellular matrix (ECM) components such as fibrous collagen and associated constituents like proteoglycans. There is, however, a fundamental lack of understanding concerning the tensile properties of the collagenous ECM at different length scales. The inherent challenges associated with the experimental discernment of such processes have motivated the deployment of modelling strategies as an effective investigative tool. This thesis has dealt with the design of generalised constitutive descriptions that propose salient microstructural deformation, damage, and failure-related mechanisms.

In Paper A, A multiscale constitutive framework based on a novel description of collagen is introduced. The description accounts for the gradual recruitment of undulated collagen fibrils and introduces proteoglycan-mediated time-dependent fibrillar sliding. Crucially, the proteoglycan deformation allows for the reduction of overstressed fibrils towards a preferential homeostatic stress. An implicit Finite Element implementation of the model uses an interpolation strategy towards collagen fibre stress determination and results in a memory-efficient representation of the model. A number of test cases, including patient-specific geometries, establish the efficiency of the description and demonstrate its ability to explain qualitative properties reported from macroscopic experimental studies of tendon and vascular tissue.

In Paper B, the aforementioned description is extended such that it additionally incorporates an interfibrillar failure (fibril pull-out) mechanism. The resulting damage-induced mechanical behaviour across several length scales is showcased for the microstructurally motivated continuum damage model. Notably, a bottom-up approach is further demonstrated, whereby the model is employed in a single-element representation of the modes of fracture. A qualitative description of soft tissue rupture is accordingly attained, to which an appropriate cohesive zone model for the equivalent fracture surface is then calibrated. In doing so, a surface-based discontinuous characterisation of failure is directly derived from the upscaling of irreversible and dissipative damage mechanisms from the microscale.

In Paper C, we present the novel coupling of the above continuum damage model with an embedded phenomenological representation of the fracture surface. Tissue separation is therefore accounted for through the integration of the cohesive crack concept within the partition of unity finite element method. A transversely isotropic cohesive potential per unit undeformed area is introduced that comprises rate-dependent damage evolution and accounts for mixed-mode failure. Furthermore, a novel crack initialisation procedure is detailed that identifies the occurrence of localised deformations in the continuum material and the orientation of the inserted discontinuity. Proof of principle is demonstrated via the application of the computational framework to two representative numerical simulations, illustrating the robustness and versatility of the formulation.

Abstract [sv]

Mjuk biologisk vävnad som belastas mekaniskt uppvisar en myriad av komplexa tidsberoenden samt skade- och brottmekaniska egenskaper. Fördjupad kunskap om dessa beteenden bidrar väsentligt till att karakterisera tåligheten mot skador och kan ge värdefulla insikter om förekomst och utveckling av vissa sjukdomar. Förbättrad kunskap inom detta område är till stor fördel för att framgångsrikt kunna tillämpa ingenjörskoncept i klinisk praktik. Dessutom kan det hjälpa till att främja förebyggande åtgärder, strategier för patientbehandling och optimal utformning av medicinsk utrustning. Det makroskopiska materialbeteendet hos mjuk vävnad är oupplösligt kopplat till deformationen av mekaniskt signifikanta extracellulära matriskomponenter (ECM, ExtraCellular Matrix) som fibrös kollagen och associerade beståndsdelar som proteoglykaner. Kunskap saknas om egenskaperna i dragning för kollagenös ECM på olika längdskalor. Det finns inneboende utmaningar förknippade med experimentell bestämning av dessa, vilket motiverat användningen av modelleringsstrategier som ett effektivt undersökningsverktyg. Denna avhandling behandlar utformningen av generaliserade konstitutiva beskrivningar som pekar på framträdande mikrostrukturell deformation och skaderelaterade mekanismer.

I artikel A introduceras ett multipel-skala konstitutivt ramverk som baseras på en ny beskrivning av kollagen. Beskrivningen innefattar gradvis aktivering av vågformade kollagenfibriller och introducerar proteoglykanmedierad tidsberoende fibrillär glidning. Avgörande är att deformationen av proteoglykan möjliggör en minskning av överbelastade fibriller mot en preferentiell homeostatisk spänning. En implicit Finita Element-implementering av modellen använder en interpolationsstrategi för bestämning av kollagenfiberspänning och resulterar i en minneseffektiv representation av modellen. Ett antal testfall, inklusive patientspecifika geometrier, påvisar beskrivningens effektivitet och visar också dess förmåga att förklara kvalitativa egenskaper som rapporterats från makroskopiska experimentella studier av senor och kärlvävnad.

I artikel B utökas beskrivningen så att den även innefattar en mekanism för interfibrillärt brott (fibrill-utdragning). Det resulterande skadeinducerade mekaniska beteendet över flera längdskalor påvisas för denna mikrostrukturellt motiverade kontinuumskademodell. Ett angreppssätt av typen "nerifrån-och-upp" demonstreras, där en en-elements modell används för att representera de olika brottmoderna. Det resulterar i en kvalitativ beskrivning av brott i mjuk vävnad, till vilken en lämplig kohesiv zon-modell för den ekvivalenta brottytan sedan kalibreras. Genom detta härleds en ytbaserad diskontinuerlig karakterisering av brott direkt från irreversibla och dissipativa skademekanismer från mikroskalan.

I artikel C presenteras en koppling mellan ovanstående kontinuumskademodell och en inbyggd fenomenologisk representation av brottytan. Vävnadsseparation (brott) redovisas där genom att inkorporera sprickan, med sin kohesiva zon, som en byggsten i finita element-metoden. En potentialfunktion för transversellt isotrop kohesiv spricka (per enhet odeformerad area) introduceras som omfattar tidsberoende skadeutveckling och beskriver brott vid blandat modus. Dessutom beskrivs en ny sprickinitieringsmodell som utgår från förekomsten av lokaliserad deformation i kontinuumet och orienteringen för en tänkt diskontinuitet. Metodiken demonstreras genom att den tillämpas på två representativa numeriska simuleringar. Den visar sig vara både robust och mångsidig.

Place, publisher, year, edition, pages
Stockholm, Sweden: KTH Royal Institute of Technology, 2023
Series
TRITA-SCI-FOU ; 2023:21
National Category
Applied Mechanics
Research subject
Solid Mechanics
Identifiers
urn:nbn:se:kth:diva-326231 (URN)978-91-8040-566-9 (ISBN)
Public defence
2023-05-26, D3, Lindstedtsvägen 9, Stockholm, 10:00 (English)
Opponent
Supervisors
Funder
Swedish Research Council, 2015-04476
Available from: 2023-04-28 Created: 2023-04-27 Last updated: 2023-05-16Bibliographically approved

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Miller, ChristopherGasser, T. Christian

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