Active spring muscle model - a new phenomenological model of skeletal muscle mechanics

Understanding Machina Carnis, how our muscles mechanically generate movement, is one of the fundamental research questions in human movement science and also has significant implications in many application areas including, to name a few, physiotherapy, sport/exercise science and humanoid robotics. Notwithstanding the scientific achievements over the centuries in elucidating the molecular mechanism of the muscle contraction in micro/nanoscopic levels, one would be surprised to find that our understanding of the muscle becomes substantially elusive when it comes to the actual force production. As a highlighting example, we do not yet have any model that fully explains muscle's behaviour when it is being stretched against an external force (called eccentric contraction). A well-known fact is that the muscle works as an efficient "brake" during eccentric contraction, actively stabilising itself against a stretch consuming a just minimal amount of metabolic energy. Eccentric contraction is known to make a critical contribution to the muscle's mechanical efficiency, but currently existing muscle models offer very limited explanations on eccentric contraction and little effort has been put forward to rationally recognize this issue and to develop an alternative model that has a wider explanatory scope.

This "inconvenient truth" in muscle mechanics has been particularly overlooked in the upper-layer, musculoskeletal modelling studies, where simple muscle models are highly preferred in order to efficiently simulate the behaviour a large group of muscles. Despite numerous problems of the conventional muscle models in predicting dynamic contractile behaviour of the muscle, including eccentric contraction, the eighty years old Hill-type muscle model is predominantly used as a standard phenomenological model of the musculoskeletal simulation studies. This is not because the researchers in this area are unaware of its weaknesses, but because there is no alternative model that can yet replace the Hill-type muscle model.

For these reasons, the proposed study aims to build and validate an effective alternative to the Hill-type muscle model. The key insight is on the recently proposed titin-based muscle contraction theories, collectively called the active spring model that shows great potential for elucidating many unexplained dynamic muscle behaviours. In addition to the traditional sliding-filament mechanism between the actin and the myosin filament, the active spring model highlights the mechanical role of titin, an additional spring-like filament that connects those filaments, in regulating the stiffness of the active muscle. It is important, however, that the proposed study does not aim to develop a purely explanatory, microscopic model of which the mechanical and parametric simplicity is often sacrificed, but aims to develop a simple and reliable phenomenological model that can be readily used by upper-layer musculoskeletal researchers. By developing such a model, the study is expected to bridge an eighty-years standing gap between muscle and musculoskeletal studies.

The proposed study will take an integrative approach to achieve this goal. The study will first focus on building a model of single fiber/muscle under a controlled in vitro setup. To ensure the reliability as a general-purpose muscle mechanics model, rigorous validations will be conducted under various dynamic contractile situations, including eccentric contraction and naturalistic locomotion-like stimulation patterns. After that, the model will be further validated in the in vivo human experiment, focusing on predicting the mechanics of leg muscle during locomotion, by incorporating novel non-invasive techniques that estimate the architectural and mechanical changes of the working muscle. As a pathway to impact, the model and the simulation code will be open to general musculoskeletal modellers/researchers via OpenMuscle.org, an open-source muscle project website.

HMM has been the predominant muscle mechanics model in biomechanical studies due to its relatively simple and clear mechanical structure. However, it is well-known that the HMM suffers many problems that seriously undermine its reliability, such as its lack of explanation on eccentric contractions and dynamic force patterns during sub-maximal contractions. The proposed study aims to develop a new "active-spring" muscle model (ASMM) that can effectively replace the HMM. The ASMM highlights an active, spring-like property of the titin filament in regulating the stiffness of the muscle, and provides a novel insight of interpreting the muscle's dynamic contractile behaviour, including eccentric contractions, as a mechanical interaction between the cross-bridges and titin. The succinct mechanical structure of the ASMM finally opens up the possibility of developing a reliable phenomenological muscle model, whose complexity is as low as the HMM.

To develop this model, the proposed study will take a two-stage approach of developing and validating the model. In the first stage, the study will focus on in vitro experiments on electrically stimulated mouse muscles. The model development procedure will be focused on predicting 1) dynamic and residual force enhancements during eccentric contractions, 2) activation-dependent force production, and 3) a realistic force pattern under locomotion-like length and activation profile. The second stage of the development will be focused on a human in vivo study to ensure the model's applicability to human biomechanics studies. In this stage, the study will first focus on developing novel methods of non-invasively and reliably estimating the activation level and the force output of individual muscle in vivo, using high-density EMG, ultrasound tomography and tensiomyography. Ultimately, the performance of the developed muscle model in predicting the mechanics of the tibialis anterior during locomotion will be tested and validated.

Regarding the significant impact of Hill-type muscle model on biology/biomedical sciences, education and industry over eighty years, the impact of the new phenomenological muscle mechanics model is expected to be broad-reaching and substantial and also is not limited to fundamental research. The applicant will make sure that the developed model and its simulation code will be open to anyone who uses muscle models either in academia or industry. Specifically, the applicant will develop an "OpenMuscle" project web-site as a part of "SimTK.org", a free project-hosting platform for open-source biomedical computational models for education, research and industrial development. In addition, the applicant aims to facilitate the interaction between the developers (muscle/musculoskeletal mechanics researchers) and the existing or the potential users (clinicians, physiotherapists, roboticians and industrial product developers) via an "OpenMuscle workshop", designed to introduce the state-of-the-art of the muscle modelling research and to identify major demands from the application domain of musculoskeletal simulation models. In addition, the applicant will participate in the "Meet the Expert" event in Birmingham Science Museum in order to increase the public awareness on what is the the state-of-the-art models and techniques in muscle and musculoskeletal mechanics, how they helps us to better understand human movement, and how these techniques can be potentially utilized to cure various motor diseases.