Current Research 2016 (5)

Neuromuscular Model of Human

neuromuscular

 

Computer simulation of the detailed physical model of human is a long-term study. In the short-range, it will open deeper discussion of sports biomechanics and industrial ergonomics. It may explain change of behavior due to aging. In the middle-range, it will contribute to pathology in medicine and discovery of new drug. In the long-range, it will approach the nature of human perception and intelligence.

In the biomechanical studies at YNL, we learned that robotics and informatics can visualize the physical phenomena and information inside the body from the measurements obtained outside. Dr. Akihiko Murai (AIST) questioned in his Ph.D study if we could go further depth. Dr. Murai’s dissertation in 2009 discussed on mathematical modeling of motor and sensory neurons of skeletal muscles and estimating their activities from motion capturing, wireless EMGs, and force plates. The discussion was greatly simplified and developed assuming a single motor neuron and a single sensory neuron of muscle spindle for each muscle (wire), where continuous models of neurons were adopted. A scientific question was also asked if a recurrent neural network with motor neurons as output and sensory neurons as input could acquire the reflex system like the spinal reflex. The neural network was a model of neuron pools inside the spine, but designed purely mathematically without considering anatomical structure. The neural network was trained to best approximate the signals of motor neurons that generate muscle activities for a set of motion data (motion capturing, wireless EMGs, and force plates) prepared for training. Note that this approach implicitly assumes that the role of voluntary signals from the brain is minimum and the role of spinal reflex is maximum. The assumption is not justified, but made because of the lack of knowledge on the voluntary signals. The trained neural network was tested by simulating muscle activities caused by a sudden external force at patellar tendon. The effects spread over the wholebody, among which the leg movement showed a similarity to what is known as patellar tendon reflex.

The figures above show the recent developments in 2011-2016.3 (a project in HPCI Strategic Program1, MEXT). The project was a joint project among three groups led by Prof. Shu Takagi (University of Tokyo), Prof. Kenji Doya (Okinawa Institute of Science and Technology), Prof. Taishin Nomura (Osaka University), and YNL. The goal of the project was to simulate the symptoms of Parkinson disease. The disease develops symptoms like tremor, slowed movements (bradykinesia), rigid muscles, impaired posture and balance and so on. A cause of the symptoms is explained by reduced activity of dopamine-secreting cells in the substantia nigra of the brain. At OIST a computational model of the basal ganglia (including the substantia nigra) and a column of the cerebral cortex was developed and simulated the neural signals typically observed in Parkinson disease. YNL developed K-BODY, which is the detailed neuro musculoskeletal model of the wholebody. Prof. Takagi’s group developed a fine model of some muscles including microscopic fiber structures and simulated a symptom like tremor at an elbow joint caused by biceps and triceps of the arm.

The figure of the top in the center shows the software tools. The software tools were optimized for the architecture of K-Computer to make best use of its extraordinary performance in parallel computation. The software developments started by connecting four different software tools, namely, NEST, MUSIC, sDIMS, and HI-MUSCLE. NEST was adopted to program neurons. To allow programming by Python, PyNEST was developed from NEST in the project. MUSIC was adopted for NEST and PyNEST to communicate with the external software. sDIMS was optimized to perform in K-Computer and became K-BODY. HI-MUSCLE is a FORTRAN software developed in Riken for Finite Element Method (FEM). We recoded it in C++ in order to use with K-BODY.

YNL developed K-BODY including the wholebody FEM musculoskeletal model, the model of neuron pools in the spine, and the projections of neurons to the muscles. The wire-muscle model of sDIMS was upgraded to the FEM-muscle model with volume, distributed mass, and viscoelasticity. The properties of muscles and tendons are set separately. The muscles, as seen in the right in the above figure, deform by activation. The main development here was to compute many contacts between muscles and bones and the interacting forces at the contacts which in turn cause deformation, where the bones are assumed rigid. The computation was done by developing a new algorithm for parallel computation. Dr. Ko Ayusawa (AIST) and Kensho Hirasawa developed in 2014 the FEM-muscle model and its computational algorithm and software. The computation of contact force and deformation is sensitive, and it is still a problem to make the computation more stable.

Dr. Manish Sreenivasa (Heidelberg University) had developed at YNL using sDIMS a stretch reflex model of the elbow joint driven by biceps and triceps. Although the muscles were modeled by wires, he developed the model of neuron pools of motor neurons, sensory neurons (muscle spindles), and inter neurons. He programmed using PyNEST as many neurons as known for biceps and triceps in the literature. A neuron was described as a point spiking neuron by the leaky-integral-and-fire model, where a neuron fires a spike and discharges when it is charged up to the threshold. Dr. Sreenivasa trained the weights of synaptic connections between neurons using the data of motion capture, wireless EMGs, and force plates obtained by experiments.

Dr. Murai, Yosuke Ikegami, and Kazunari Takeichi in 2015 developed the model of neuron pools of the wholebody. The small colored dots in the spine, in the second figure from the left in the bottom, show the positions of the neurons. They are neuron pools of motor neurons and sensory neurons (muscle spindles). The numbers of motor neurons and sensory neurons are known only for very few (less than 10) muscles. Takeuchi developed a method to make an estimate of the numbers for unknown muscles from those of the known muscles by taking account of the functional similarity of muscles. The neuron pools of inter neurons and their mutual connections are still under development. The neurons in a motor neuron pool transmit activities to the muscle to drive. The neurons arrive at the point known as the motor point of the muscle surface and then enter into the muscles. The motor point is near the middle (or thicken) point of the muscle along the axis.
As seen in the first figure in the left, the projections of motor neurons are randomly spread in a section of the muscle at the motor point. The activity of an element in the section is determined by the projections near the element as the weighted sum of the firing signals of the projections with the distance as the weight. The activity of an element propagates to the other elements along the axis.

In 2016, Ikegami simulated and visualized the activities of the muscles of four limbs by directly connecting the firing signals to the motor neurons from a column of the cerebral cortex, which includes 20 by 20 cells each with 37 neurons on average. The activities of the column were programmed and tuned by OIST group. There was no recurrent connections like reflex system in the simulation. The muscles of limbs showed complex vibrations, which changed their appearance by the change of viscoelastic parameters of muscles. Rohan Budhiraja (LAAS-CNRS) in his MS dissertation modeled the sensory neurons of tactile corpuscle on the sole skin and the sensory neurons of semicircular canals for vestibular sensation.

The development is still underway and there are many tasks to be done. We need to program the neuron pools of inter neurons in the spine and set the network between motor neurons, sensory neurons, and inter neurons. We need to train the neurons to develop the reflex system like the inspiring works by Dr. Murai and Dr. Sreenivasa. The mathematical algorithm for training spiking neurons must be developed, where a preliminary result by Akio Hayakawa in his BS dissertation in 2016 may give us a hint. Although modeling of the brain is a huge problem, OIST showed a model of a column of the cortex with the deeper structure of the basal ganglia. Modeling some columns of the sensory area of cortex with cutaneous sensation, vestibular sensation, and somatic sensation, and combining with a model of some columns of the motor area of cortex, we will be able to start discussions of the posture control problem.

 

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