Implementation of Discrete Element Analysis for Subject-Specific, Population-Wide Investigations of Habitual Contact Stress Exposure

Abstract

There exist no large-series human data linking contact stress exposure to an articular joint's propensity for developing osteoarthritis because contact stress analysis for large numbers of subjects remains impractical. The speed and simplicity of discrete element analysis (DEA) for estimating contact stresses makes its application to this problem highly attractive, but to date DEA has been used to study only a small numbers of cases. This is because substantial issues regarding its use in population-wide studies have not been addressed. Chief among them are developing fast and robust methods for model derivation and the selection of boundary conditions, establishing accuracy of computed contact stresses, and including capabilities for modeling in-series structural elements (e.g., a meniscus). This article describes an implementation of DEA that makes it feasible to perform subject-specific modeling in articular joints in large population-based studies. Keywords computational joint modeling; osteoarthritis; contact stressThe development of expeditious methods suitable for determining in vivo articular contact stress distributions is critical to understanding normal articular function and the mechanopathology of osteoarthritis (OA). Excessive functional loads habitually applied to at-risk joints (shoulder, wrist, hip, knee, ankle) can negatively impact the health of articular cartilage, eventually leading to degeneration (Buckwalter & Brown, 2004). Many computational models have been developed to determine contact stresses in a variety of joints, mostly using finite element analysis (FEA) . For the most part, however, these studies have involved lengthy and concerted efforts in well-controlled research settings, and have yielded articular contact stresses for only small numbers of cases. The high logistical cost of performing 3-D contact FEA on a subject-or patient-specific basis makes FEA of limited attraction for stress analysis in large epidemiologic studies (Englund et al., 2007;Felson & Nevitt, 2004;Lester, 2008). Advancement of expeditious methods for determining in vivo articular contact stress distributions will enhance the understanding of normal articular function, and of the mechano-pathology of OA. Chao and colleagues popularized the use of rigid body spring modeling (now commonly known as discrete element analysis, or DEA) in biomechanics, as a simple numerical framework to model articular contact (An et al., 1990;Genda et al., 2001;Iwasaki et al., 1998;Li et al., 1994;Volokh et al., 2007). The DEA formulation involves treating bones as rigid bodies, and the cartilage at a given joint as an array of compressive-only springs distributed over the articulating bone surfaces. This modeling approach has been used to study contact mechanics in various diarthrodial joints, most recently progressing to fully 3D subject-specific geometry (Elias & Cosgarea, 2007;Elias et al., 2004;Iwasaki et al., 1998). However, it has rarely been used to study large numbers of cases. To our knowledge, the largest 3-D ...

Subject-Specific Analysis of Joint Contact Mechanics: Application to the Study of Osteoarthritis and Surgical Planning

“…There are several continued veins of further development and future work in this area: more efficient computational methods for predicting contact pressure and area (as started by Refs. [73], [84], [85], and [344]), more efficient methods that provide accurate predictions of results other than contact stress and area, and sharing data sets for model inputs (e.g., Osteoarthritis Initiative, which provides MR and other data for the knee, http://oai.epi-ucsf.org/datarelease/, and the Musculoskeletal Research Laboratories dataset, which provides CT arthrography image data for the hip, http://mrl.sci.utah.edu/ software/hip-image-data). As an alternative to subject-specific analysis to capture the effects of geometry in large cohorts, the use of parameterized or statistical shape modeling should be explored further.…”

“…For example, in a hip model, the analysis with DEA took less than 1% of the time required for analysis with FEA [83]. This has led to the development and deployment of DEA methods to study large populations [73,84,85]. The main disadvantages of DEA are that results are not available at every point in the continuum, and the assumptions of linear elasticity and unidirectional deformation limit its utility to the prediction of only contact stress.…”

“…Similarly, changes in cartilage Young's modulus and Poisson's ratio in the knee changed surface contact pressure more than von Mises stress [332]. Idealized and subject-specific comparisons between FEA and DEA demonstrated that DEA can be used to predict accurate contact mechanics, again reiterating the relative insensitivity to cartilage constitutive description [81,84,334] (Fig. 11).…”

“…Because computational efficiency is an important consideration for modeling large groups, researchers have developed several efficient analysis methods. Anderson et al developed DEA methods explicitly for the purpose of modeling large populations [84]. Rigid contact has been used to predict subject-specific contact mechanics in the patellofemoral joint, which were in reasonable agreement with defonnable contact at a lower computational cost [344].…”

Toward patient-specific articular contact mechanics

“…Ultimately, patient-specific modeling offers the potential for use in surgical planning and for large scale studies of treatment efficacy. Such approaches have already seen some application in the hip, knee and ankle (Adouni and Shirazi-Adl, 2014; Anderson et al, 2010b; Fitzpatrick et al, 2012; Henak et al, 2014; Henak et al, 2013a; Li et al, 2008a; Wang et al, 2014). The following section focuses on our own research related to patient-specific modeling of the hip.…”