Intermittent control models of human standing: similarities and differences

Two architectures of intermittent control are compared and contrasted in the context of the single inverted pendulum model often used for describing standing in humans. The architectures are similar insofar as they use periods of open-loop control punctuated by switching events when crossing a switching surface to keep the system state trajectories close to trajectories leading to equilibrium. The architectures differ in two significant ways. Firstly, in one case, the open-loop control trajectory is generated by a system-matched hold, and in the other case, the open-loop control signal is zero. Secondly, prediction is used in one case but not the other. The former difference is examined in this paper. The zero control alternative leads to periodic oscillations associated with limit cycles; whereas the system-matched control alternative gives trajectories (including homoclinic orbits) which contain the equilibrium point and do not have oscillatory behaviour. Despite this difference in behaviour, it is further shown that behaviour can appear similar when either the system is perturbed by additive noise or the system-matched trajectory generation is perturbed. The purpose of the research is to come to a common approach for understanding the theoretical properties of the two alternatives with the twin aims of choosing which provides the best explanation of current experimental data (which may not, by itself, distinguish beween the two alternatives) and suggesting future experiments to distinguish between the two alternatives

Fully automated image-based estimation of postural point-features in children with cerebral palsy using deep learning

The aim of this study was to provide automated identification of postural point-features required to estimate the location and orientation of the head, multi-segmented trunk and arms from videos of the clinical test ‘Segmental Assessment of Trunk Control’ (SATCo). Three expert operators manually annotated 13 point-features in every fourth image of 177 short (5–10 s) videos (25 Hz) of 12 children with cerebral palsy (aged: 4.52 ± 2.4 years), participating in SATCo testing. Linear interpolation for the remaining images resulted in 30 825 annotated images. Convolutional neural networks were trained with cross-validation, giving held-out test results for all children. The point-features were estimated with error 4.4 ± 3.8 pixels at approximately 100 images per second. Truncal segment angles (head, neck and six thoraco-lumbar–pelvic segments) were estimated with error 6.4 ± 2.8°, allowing accurate classification (F1 > 80%) of deviation from a reference posture at thresholds up to 3°, 3° and 2°, respectively. Contact between arm point-features (elbow and wrist) and supporting surface was classified at F1 = 80.5%. This study demonstrates, for the first time, technical feasibility to automate the identification of (i) a sitting segmental posture including individual trunk segments, (ii) changes away from that posture, and (iii) support from the upper limb, required for the clinical SATCo

Rebuttal from Raymond Reynolds, Callum Osler, Linda Tersteeg and Ian Loram.

This work was supported by BBSRC grant BB/I00579X/

Predictive feedback control and Fitts' law

Fitts’ law is a well established empirical formula, known for encapsulating the “speed-accuracy trade-off”. For discrete, manual movements from a starting location to a target, Fitts’ law relates movement duration to the distance moved and target size. The widespread empirical success of the formula is suggestive of underlying principles of human movement control. There have been previous attempts to relate Fitts’ law to engineering-type control hypotheses and it has been shown that the law is exactly consistent with the closed-loop step-response of a time-delayed, first-order system. Assuming only the operation of closed-loop feedback, either continuous or intermittent, this paper asks whether such feedback should be predictive or not predictive to be consistent with Fitts law. Since Fitts’ law is equivalent to a time delay separated from a first-order system, known control theory implies that the controller must be predictive. A predictive controller moves the time-delay outside the feedback loop such that the closed-loop response can be separated into a time delay and rational function whereas a non- predictive controller retains a state delay within feedback loop which is not consistent with Fitts’ law. Using sufficient parameters, a high-order non-predictive controller could approximately reproduce Fitts’ law. However, such high-order, “non-parametric” controllers are essentially empirical in nature, without physical meaning, and therefore are conceptually inferior to the predictive controller. It is a new insight that using closed-loop feedback, prediction is required to physically explain Fitts’ law. The implication is that prediction is an inherent part of the “speed-accuracy trade-off”

Estimation of Absolute States of Human Skeletal Muscle via Standard B-Mode Ultrasound Imaging and Deep Convolutional Neural Networks

Objective: To test automated in vivo estimation of active and passive skeletal muscle states using ultrasonic imaging. Background: Current technology (electromyography, dynamometry, shear wave imaging) provides no general, non-invasive method for online estimation of skeletal muscle states. Ultrasound (US) allows non-invasive imaging of muscle, yet current computational approaches have never achieved simultaneous extraction nor generalisation of independently varying, active and passive states. We use deep learning to investigate the generalizable content of 2D US muscle images. Method: US data synchronized with electromyography of the calf muscles, with measures of joint moment/angle were recorded from 32 healthy participants (7 female, ages: 27.5, 19-65). We extracted a region of interest of medial gastrocnemius and soleus using our prior developed accurate segmentation algorithm. From the segmented images, a deep convolutional neural network was trained to predict three absolute, driftfree, components of the neurobiomechanical state (activity, joint angle, joint moment) during experimentally designed, simultaneous, independent variation of passive (joint angle) and active (electromyography) inputs. Results: For all 32 held-out participants (16-fold cross-validation) the ankle joint angle, electromyography, and joint moment were estimated to accuracy 55±8%, 57±11%, and 46±9% respectively. Significance: With 2D US imaging, deep neural networks can encode in generalizable form, the activitylength-tension state relationship of these muscles. Observation only, low power, 2D US imaging can provide a new category of technology for non-invasive estimation of neural output, length and tension in skeletal muscle. This proof of principle has value for personalised muscle assessment in pain, injury, neurological conditions, neuropathies, myopathies and ageing

Human balancing of an inverted pendulum with a compliant linkage: neural control by anticipatory intermittent bias

These experiments were prompted by the recent discovery that the intrinsic stiffness of the ankle is inadequate to stabilise passively the body in standing. Our hope was that showing how a large inverted pendulum was manually balanced with low intrinsic stiffness would elucidate the active control of human standing. The results show that the pendulum can be satisfactorily stabilised when intrinsic stiffness is low. Analysis of sway size shows that intrinsic stiffness actually plays little part in stabilisation. The sway duration is also substantially independent of intrinsic stiffness. This suggests that the characteristic sway of the pendulum, rather than being dictated by stiffness and inertia, may result from the control pattern of hand movements. The key points revealed by these experiments are that with low intrinsic stiffness the hand provides pendulum stability by intermittently altering the bias of the spring and, on average, the hand moves in opposition to the load. The results lead to a new and testable hypothesis; namely that in standing, the calf muscle shortens as the body sways forward and lengthens as it sways backwards. These findings are difficult to reconcile with stretch reflex control of the pendulum and are of particular relevance to standing. They may also be relevant to postural maintenance in general whenever the CNS controls muscles which operate through compliant linkages. The results also suggest that in standing, rather than providing passive stability, the intrinsic stiffness acts as an energy efficient buffer which provides decoupling between muscle and body

Use of ultrasound to make noninvasive in vivo measurement of continuous changes in human muscle contractile length

Continuous measurement of contractile length has been traditionally achieved using animal preparations in which the muscle and tendon are exposed. More modern methods, e.g., sonomicroscopy, are still invasive. There is a widely perceived need for a noninvasive, in vivo method of measuring continuous changes of human muscle contractile length. Ultrasonography has been used for several years to measure relatively static, discrete changes in tendon, aponeurosis, and muscle fascicle length. We have recently developed this technique to continuously track changes in muscle contractile length during quiet standing. Here, we present the tracking algorithm and use externally applied perturbations to establish the spatial and temporal resolution of the technique. Subjects maintained a low level of ankle torque while a pneumatic actuator applied rapid, square-pulse ankle rotations of defined magnitude and 0.2-s duration. Tracked changes in gastrocnemius and soleus contractile length follow the temporal profile of the perturbations and scale progressively (5-400 microm) with the size of the ankle rotation (0.03-0.7 degrees ). In a second experiment, we tracked a wire oscillating in water with known peak to peak amplitudes of 1.5 microm to 8 mm. The ultrasound tracking procedure had near 100% accuracy at all amplitudes for frequencies up to 3 Hz and showed attenuation at higher frequencies consistent with an effective sampling frequency of 12 Hz and sampling time of 80 ms. This noninvasive technique is sensitive, without averaging, to changes as small as 1 microm and is suitable for observing neuromotor activity in posture and locomotion

Use of ultrasound to make noninvasive in vivo measurement of continuous changes in human muscle contractile length

Continuous measurement of contractile length has been traditionally achieved using animal preparations in which the muscle and tendon are exposed. More modern methods, e.g., sonomicroscopy, are still invasive. There is a widely perceived need for a noninvasive, in vivo method of measuring continuous changes of human muscle contractile length. Ultrasonography has been used for several years to measure relatively static, discrete changes in tendon, aponeurosis, and muscle fascicle length. We have recently developed this technique to continuously track changes in muscle contractile length during quiet standing. Here, we present the tracking algorithm and use externally applied perturbations to establish the spatial and temporal resolution of the technique. Subjects maintained a low level of ankle torque while a pneumatic actuator applied rapid, square-pulse ankle rotations of defined magnitude and 0.2-s duration. Tracked changes in gastrocnemius and soleus contractile length follow the temporal profile of the perturbations and scale progressively (5-400 microm) with the size of the ankle rotation (0.03-0.7 degrees ). In a second experiment, we tracked a wire oscillating in water with known peak to peak amplitudes of 1.5 microm to 8 mm. The ultrasound tracking procedure had near 100% accuracy at all amplitudes for frequencies up to 3 Hz and showed attenuation at higher frequencies consistent with an effective sampling frequency of 12 Hz and sampling time of 80 ms. This noninvasive technique is sensitive, without averaging, to changes as small as 1 microm and is suitable for observing neuromotor activity in posture and locomotion