Efforts on modeling and analysis of various biological processes have been significantly increased in recent years, with diverse pursuits from mechanical, electrical, biomedical, and computational engineering. Various analytical and numerical techniques have been developed to qualitatively and quantitatively study dynamics associated with design, diagnosis, and control in these problems. However, there is a lack of integrated approaches to biomedical research from a dynamical systems point of view. The main focus of this special issue is to present several studies of nonlinear phenomena, computational modeling, dynamic analysis, and control for clinical diagnosis, patient health monitoring, drug administration, and biosignal-assisted rehabilitation. The guest editors collect latest innovative and integrated approaches to further understanding of the dynamics of biological and biomedical systems by using techniques from nonlinear dynamics and computational fields.

This special issue includes ten high quality articles on computational and nonlinear dynamics in biomedical applications. Here, we provide a summary of these articles. The sequence of the articles is in no particular order.

In the article titled “A Third Order Model of Hip and Ankle Joints During Balance Recovery: Modeling and Parameter Estimation,” the authors proposed a third-order, double-inverted-pendulum model to describe human standing dynamics. A torque is applied at each joint to represent the muscle actuation using Poynting–Thomson muscle-tendon systems. The coefficients are nonlinear functions of the joint angles and their derivatives. The authors adopted both a regression technique and an Kalman filter to estimate the muscle-tendon parameters of the model. The model may be used to study fall recovery using a hip-ankle strategy, which is of tremendous importance for improving postural stability and reducing risk of injuries.

In the article titled “Semi-Adaptive Closed-Loop Control for Infusion of Medications With Transport Delay in Clinical Effects” the authors present a semi-adaptive closed-loop control approach to autonomous infusion of medications exhibiting significant transport delay in clinical effects. The model incorporates transport delay explicitly into control design by the way of a Padé approximation, and facilitates linear parameterization of control design model by desensitization of a nonlinearly parameterized cooperativity constant associated with pharmacodynamics. The paper presents an investigation on the impact of nontrivial transport delay on the performance of closed-loop medication infusion and studies the control design incorporating nontrivial transport delay on the performance and robustness of closed-loop medication infusion. The current work is an extension of semi-adaptive closed-loop control idea for medication infusion problems to the problems involving large transport delay.

In the article titled “Simulating Ultrasound Tissue Deformation Using Inverse Mapping,” the authors present mathematical methods for simulating tissue deformation in ultrasound images. The developed methodology can characterize the magnitude of the motion as a Gaussian distribution. The methodology is flexible and can include any tissue motion through additions in the deformation vector field. The approach presented here can be used as a training system for ultrasound-needle insertion techniques. Additionally, this methodology outlined allows for an increase or decrease in complexity by altering the number of zones of motion to be simulated.

In the article titled “Variable Impedance Control of Powered Knee Prostheses Using Human-Inspired Algebraic Curves,” the authors propose to fit nominal human walking data using an algebraic curve to achieve coordinated motion between transfemoral amputee patients and powered prosthetic joints. The authors demonstrate the approach using an impedance model of the knee-joint motion. A variable impedance-based control law, based on the parameter-dependent Lyapunov function, is able to produce a family of spring and damper behaviors to achieve coordinated hip–knee motions. The proposed methodology may be used to overcome existing limitations for powered prostheses and to achieve real-time implementation on an embedded system.

In the article titled “Numerical Nonlinear Analysis for Dynamic Stability of an Ankle‐Hip Model of Balance on a Balance Board,” the authors conducted numerical analyses of a human balance-board model to study stability properties and to explore nonlinear dynamic phenomena of the model. The human balance-board model is a nonlinear delay differential equation. The model may be used to study human upright posture stability, which is of important relevance to rehabilitation and fall prevention. The results of this article may have significant impacts on understanding human upright posture trajectories. The authors also suggested important directions for future research, including improvements on the model, investigations on parameter variation, and experimental validation.

In the article titled “Model Predictive Control of a Feedback-Linearized Hybrid Neuroprosthetic System With a Barrier Penalty,” the authors studied a hybrid neuroprosthesis platform, which integrates an electric motor assist and functional electrical stimulation. A model predictive control method is used to optimally allocate control inputs between the two mechanisms. The authors adopted linearized feedback inside the model predictive control method to reduce computational time. A barrier cost function is used to overcome nonlinear and state-dependent constraints. Numerical simulations demonstrate a satisfactory control performance.

In the article titled “Bipedal Model and Hybrid Zero Dynamics of Human Walking With Foot Slip,” the authors presented a new bipedal model to capture and predict human walking locomotion under a foot-slip assumption, and includes control strategies for slip-induced fall prevention. The authors validated the proposed slip-walking dynamic model by tuning and optimizing the model parameters to match the experimental results, and demonstrated that the model successfully predicts both the human walking and recovery gaits with slip. Then they extend the hybrid zero dynamics model and properties to capture human walking with slip, and discussed the transition between the nonslip and slip states through slip recovery control design.

In the article titled “Human Knee Inverse Dynamics Model of Vertical Jump Exercise,” the authors developed a two-dimensional sagittal plane, inverse-dynamics knee model, which uses data from a motion capture system and force plates in order to predict knee-joint forces during the vertical jump exercise. The knee model consists of three bony structures femur, tibia, and patella, ligament structures to include both cruciate and collateral ligaments, and knee-joint muscles. The inverse dynamics model was solved using optimization in order to predict knee-joint forces during this exercise, and the results were compared with data available in the literature.

In the article titled “Computational Modeling of Inertial Effects on Electromechanics of the Heart,” the authors investigated the role of inertia in cardiac dynamics, and modeled electromechanical activity of the heart with inertia terms for computing the pressure–volume relation and action potentials over a complete cardiac cycle. To this end, they used the continuum balance laws to capture physiological function of the human left ventricle on an idealized geometry and solved the resulting equations using a Python-based finite element platform. The authors demonstrated that for the same set of pressure boundary conditions, the finite element models for quasi-static (less inertia) and dynamic (with inertia terms) formulations yielded a difference of 4.2% end diastolic volume, 3.1% ejection fraction, and variations in fiber strain patterns. The mechano-electric transduction channels sensitive to small mechanical perturbations in combination with changes in electrical conductivity due to deformation caused quantitative variations over cardiac electrical activity up to 2.75–5% reduction in APD50 and 3.5–5.75% reduction in APD90.

In the article titled “A Rigid Multibody Model to Study the Translational Motion of Guidewires Based on Their Mechanical Properties,” the authors developed a two-dimensional guidewire model, which consists of a set of small rigid segments connected to each other via revolute joints. Elastic properties of two commercial guidewires are measured and used in the model. The model was validated using guidewires in a simple phantom model. The authors demonstrated that the behavior of a guidewire is influenced by its mechanical properties and the friction forces. The developed model may be used to predict the performance of a guidewire in a vasculature prior to the procedure.