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Rahman MM, Watton PN, Neu CP, Pierce DM. A chemo-mechano-biological modeling framework for cartilage evolving in health, disease, injury, and treatment. COMPUTER METHODS AND PROGRAMS IN BIOMEDICINE 2023; 231:107419. [PMID: 36842346 DOI: 10.1016/j.cmpb.2023.107419] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Abstract] [Key Words] [MESH Headings] [Track Full Text] [Subscribe] [Scholar Register] [Received: 10/31/2022] [Revised: 02/08/2023] [Accepted: 02/10/2023] [Indexed: 06/18/2023]
Abstract
BACKGROUND AND OBJECTIVE Osteoarthritis (OA) is a pervasive and debilitating disease, wherein degeneration of cartilage features prominently. Despite extensive research, we do not yet understand the cause or progression of OA. Studies show biochemical, mechanical, and biological factors affect cartilage health. Mechanical loads influence synthesis of biochemical constituents which build and/or break down cartilage, and which in turn affect mechanical loads. OA-associated biochemical profiles activate cellular activity that disrupts homeostasis. To understand the complex interplay among mechanical stimuli, biochemical signaling, and cartilage function requires integrating vast research on experimental mechanics and mechanobiology-a task approachable only with computational models. At present, mechanical models of cartilage generally lack chemo-biological effects, and biochemical models lack coupled mechanics, let alone interactions over time. METHODS We establish a first-of-its kind virtual cartilage: a modeling framework that considers time-dependent, chemo-mechano-biologically induced turnover of key constituents resulting from biochemical, mechanical, and/or biological activity. We include the "minimally essential" yet complex chemical and mechanobiological mechanisms. Our 3-D framework integrates a constitutive model for the mechanics of cartilage with a novel model of homeostatic adaptation by chondrocytes to pathological mechanical stimuli, and a new application of anisotropic growth (loss) to simulate degradation clinically observed as cartilage thinning. RESULTS Using a single set of representative parameters, our simulations of immobilizing and overloading successfully captured loss of cartilage quantified experimentally. Simulations of immobilizing, overloading, and injuring cartilage predicted dose-dependent recovery of cartilage when treated with suramin, a proposed therapeutic for OA. The modeling framework prompted us to add growth factors to the suramin treatment, which predicted even better recovery. CONCLUSIONS Our flexible framework is a first step toward computational investigations of how cartilage and chondrocytes mechanically and biochemically evolve in degeneration of OA and respond to pharmacological therapies. Our framework will enable future studies to link physical activity and resulting mechanical stimuli to progression of OA and loss of cartilage function, facilitating new fundamental understanding of the complex progression of OA and elucidating new perspectives on causes, treatments, and possible preventions.
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Affiliation(s)
| | - Paul N Watton
- Department of Computer Science & Insigneo Institute for in silico Medicine, University of Sheffield, Sheffield, UK; Department of Mechanical Engineering and Materials Science, University of Pittsburgh, Pittsburgh, PA, USA
| | - Corey P Neu
- Paul M. Rady Department of Mechanical Engineering, University of Colorado, Boulder, CO, USA
| | - David M Pierce
- Department of Mechanical Engineering, University of Connecticut, Storrs, CT, USA; Department of Biomedical Engineering, University of Connecticut, Storrs, CT, USA.
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Eskelinen ASA, Tanska P, Florea C, Orozco GA, Julkunen P, Grodzinsky AJ, Korhonen RK. Mechanobiological model for simulation of injured cartilage degradation via pro-inflammatory cytokines and mechanical stimulus. PLoS Comput Biol 2020; 16:e1007998. [PMID: 32584809 PMCID: PMC7343184 DOI: 10.1371/journal.pcbi.1007998] [Citation(s) in RCA: 17] [Impact Index Per Article: 4.3] [Reference Citation Analysis] [Abstract] [MESH Headings] [Grants] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/03/2020] [Revised: 07/08/2020] [Accepted: 05/28/2020] [Indexed: 01/12/2023] Open
Abstract
Post-traumatic osteoarthritis (PTOA) is associated with cartilage degradation, ultimately leading to disability and decrease of quality of life. Two key mechanisms have been suggested to occur in PTOA: tissue inflammation and abnormal biomechanical loading. Both mechanisms have been suggested to result in loss of cartilage proteoglycans, the source of tissue fixed charge density (FCD). In order to predict the simultaneous effect of these degrading mechanisms on FCD content, a computational model has been developed. We simulated spatial and temporal changes of FCD content in injured cartilage using a novel finite element model that incorporates (1) diffusion of the pro-inflammatory cytokine interleukin-1 into tissue, and (2) the effect of excessive levels of shear strain near chondral defects during physiologically relevant loading. Cytokine-induced biochemical cartilage explant degradation occurs near the sides, top, and lesion, consistent with the literature. In turn, biomechanically-driven FCD loss is predicted near the lesion, in accordance with experimental findings: regions near lesions showed significantly more FCD depletion compared to regions away from lesions (p<0.01). Combined biochemical and biomechanical degradation is found near the free surfaces and especially near the lesion, and the corresponding bulk FCD loss agrees with experiments. We suggest that the presence of lesions plays a role in cytokine diffusion-driven degradation, and also predisposes cartilage for further biomechanical degradation. Models considering both these cartilage degradation pathways concomitantly are promising in silico tools for predicting disease progression, recognizing lesions at high risk, simulating treatments, and ultimately optimizing treatments to postpone the development of PTOA.
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Affiliation(s)
| | - Petri Tanska
- Department of Applied Physics, University of Eastern Finland, Finland
| | - Cristina Florea
- Department of Applied Physics, University of Eastern Finland, Finland
- Departments of Biological Engineering, Electrical Engineering and Computer Science and Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, United States of America
| | - Gustavo A. Orozco
- Department of Applied Physics, University of Eastern Finland, Finland
| | - Petro Julkunen
- Department of Applied Physics, University of Eastern Finland, Finland
- Department of Clinical Neurophysiology, Kuopio University Hospital, Finland
| | - Alan J. Grodzinsky
- Departments of Biological Engineering, Electrical Engineering and Computer Science and Mechanical Engineering, Massachusetts Institute of Technology, Cambridge, United States of America
| | - Rami K. Korhonen
- Department of Applied Physics, University of Eastern Finland, Finland
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Mukherjee S, Nazemi M, Jonkers I, Geris L. Use of Computational Modeling to Study Joint Degeneration: A Review. Front Bioeng Biotechnol 2020; 8:93. [PMID: 32185167 PMCID: PMC7058554 DOI: 10.3389/fbioe.2020.00093] [Citation(s) in RCA: 25] [Impact Index Per Article: 6.3] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/25/2019] [Accepted: 01/31/2020] [Indexed: 12/13/2022] Open
Abstract
Osteoarthritis (OA), a degenerative joint disease, is the most common chronic condition of the joints, which cannot be prevented effectively. Computational modeling of joint degradation allows to estimate the patient-specific progression of OA, which can aid clinicians to estimate the most suitable time window for surgical intervention in osteoarthritic patients. This paper gives an overview of the different approaches used to model different aspects of joint degeneration, thereby focusing mostly on the knee joint. The paper starts by discussing how OA affects the different components of the joint and how these are accounted for in the models. Subsequently, it discusses the different modeling approaches that can be used to answer questions related to OA etiology, progression and treatment. These models are ordered based on their underlying assumptions and technologies: musculoskeletal models, Finite Element models, (gene) regulatory models, multiscale models and data-driven models (artificial intelligence/machine learning). Finally, it is concluded that in the future, efforts should be made to integrate the different modeling techniques into a more robust computational framework that should not only be efficient to predict OA progression but also easily allow a patient’s individualized risk assessment as screening tool for use in clinical practice.
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Affiliation(s)
- Satanik Mukherjee
- Prometheus, Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium.,Biomechanics Section, KU Leuven, Leuven, Belgium
| | - Majid Nazemi
- GIGA in silico Medicine, University of Liège, Liège, Belgium
| | - Ilse Jonkers
- Human Movement Biomechanics Research Group, Department of Movement Sciences, KU Leuven, Leuven, Belgium
| | - Liesbet Geris
- Prometheus, Division of Skeletal Tissue Engineering, KU Leuven, Leuven, Belgium.,Biomechanics Section, KU Leuven, Leuven, Belgium.,GIGA in silico Medicine, University of Liège, Liège, Belgium
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Maximum shear strain-based algorithm can predict proteoglycan loss in damaged articular cartilage. Biomech Model Mechanobiol 2019; 18:753-778. [PMID: 30631999 DOI: 10.1007/s10237-018-01113-1] [Citation(s) in RCA: 24] [Impact Index Per Article: 4.8] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/09/2018] [Accepted: 12/24/2018] [Indexed: 01/25/2023]
Abstract
Post-traumatic osteoarthritis (PTOA) is a common disease, where the mechanical integrity of articular cartilage is compromised. PTOA can be a result of chondral defects formed due to injurious loading. One of the first changes around defects is proteoglycan depletion. Since there are no methods to restore injured cartilage fully back to its healthy state, preventing the onset and progression of the disease is advisable. However, this is problematic if the disease progression cannot be predicted. Thus, we developed an algorithm to predict proteoglycan loss of injured cartilage by decreasing the fixed charge density (FCD) concentration. We tested several mechanisms based on the local strains or stresses in the tissue for the FCD loss. By choosing the degeneration threshold suggested for inducing chondrocyte apoptosis and cartilage matrix damage, the algorithm driven by the maximum shear strain showed the most substantial FCD losses around the lesion. This is consistent with experimental findings in the literature. We also observed that by using coordinate system-independent strain measures and selecting the degeneration threshold in an ad hoc manner, all the resulting FCD distributions would appear qualitatively similar, i.e., the greatest FCD losses are found at the tissue adjacent to the lesion. The proposed strain-based FCD degeneration algorithm shows a great potential for predicting the progression of PTOA via biomechanical stimuli. This could allow identification of high-risk defects with an increased risk of PTOA progression.
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Kapitanov GI, Ayati BP, Martin JA. Modeling the effect of blunt impact on mitochondrial function in cartilage: implications for development of osteoarthritis. PeerJ 2017; 5:e3468. [PMID: 28729949 PMCID: PMC5516774 DOI: 10.7717/peerj.3468] [Citation(s) in RCA: 3] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Download PDF] [Figures] [Journal Information] [Subscribe] [Scholar Register] [Received: 02/10/2017] [Accepted: 05/26/2017] [Indexed: 12/31/2022] Open
Abstract
OBJECTIVE Osteoarthritis (OA) is a disease characterized by degeneration of joint cartilage. It is associated with pain and disability and is the result of either age and activity related joint wear or an injury. Non-invasive treatment options are scarce and prevention and early intervention methods are practically non-existent. The modeling effort presented in this article is constructed based on an emerging biological hypothesis-post-impact oxidative stress leads to cartilage cell apoptosis and hence the degeneration observed with the disease. The objective is to quantitatively describe the loss of cell viability and function in cartilage after an injurious impact and identify the key parameters and variables that contribute to this phenomenon. METHODS We constructed a system of differential equations that tracks cell viability, mitochondrial function, and concentrations of reactive oxygen species (ROS), adenosine triphosphate (ATP), and glycosaminoglycans (GAG). The system was solved using MATLAB and the equations' parameters were fit to existing data using a particle swarm algorithm. RESULTS The model fits well the available data for cell viability, ATP production, and GAG content. Local sensitivity analysis shows that the initial amount of ROS is the most important parameter. DISCUSSION The model we constructed is a viable method for producing in silico studies and with a few modifications, and data calibration and validation, may be a powerful predictive tool in the search for a non-invasive treatment for post-traumatic osteoarthritis.
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Affiliation(s)
- Georgi I Kapitanov
- Department of Mathematics, University of Iowa, Iowa City, IA, United States of America
| | - Bruce P Ayati
- Department of Mathematics, University of Iowa, Iowa City, IA, United States of America.,Program in Applied Mathematical & Computational Sciences, University of Iowa, Iowa City, IA, United States of America.,Department of Orthopedics & Rehabilitation, University of Iowa, Iowa City, IA, United States of America
| | - James A Martin
- Department of Orthopedics & Rehabilitation, University of Iowa, Iowa City, IA, United States of America.,Department of Biomedical Engineering, University of Iowa, Iowa City, IA, United States of America
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Ayati BP, Kapitanov GI, Coleman MC, Anderson DD, Martin JA. Mathematics as a conduit for translational research in post-traumatic osteoarthritis. J Orthop Res 2017; 35:566-572. [PMID: 27653021 PMCID: PMC5352510 DOI: 10.1002/jor.23439] [Citation(s) in RCA: 7] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Received: 03/09/2016] [Accepted: 09/15/2016] [Indexed: 02/04/2023]
Abstract
Biomathematical models offer a powerful method of clarifying complex temporal interactions and the relationships among multiple variables in a system. We present a coupled in silico biomathematical model of articular cartilage degeneration in response to impact and/or aberrant loading such as would be associated with injury to an articular joint. The model incorporates fundamental biological and mechanical information obtained from explant and small animal studies to predict post-traumatic osteoarthritis (PTOA) progression, with an eye toward eventual application in human patients. In this sense, we refer to the mathematics as a "conduit of translation." The new in silico framework presented in this paper involves a biomathematical model for the cellular and biochemical response to strains computed using finite element analysis. The model predicts qualitative responses presently, utilizing system parameter values largely taken from the literature. To contribute to accurate predictions, models need to be accurately parameterized with values that are based on solid science. We discuss a parameter identification protocol that will enable us to make increasingly accurate predictions of PTOA progression using additional data from smaller scale explant and small animal assays as they become available. By distilling the data from the explant and animal assays into parameters for biomathematical models, mathematics can translate experimental data to clinically relevant knowledge. © 2016 Orthopaedic Research Society. Published by Wiley Periodicals, Inc. J Orthop Res 35:566-572, 2017.
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Affiliation(s)
- Bruce P. Ayati
- Departments of Mathematics, Orthopedics & Rehabilitation, and Program in Applied Mathematical and Computational Sciences, University of Iowa
| | | | | | - Donald D. Anderson
- Departments of Orthopedics & Rehabilitation and Biomedical Engineering, University of Iowa
| | - James A. Martin
- Departments of Orthopedics & Rehabilitation and Biomedical Engineering, University of Iowa
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