Pankaj Wahi

Fracture may occur in human lower leg bones considering varying loads acting on them while performing various functions. Implants, commonly used in healing the fractures, must be properly aligned with the bones' anatomical axes for their proper functioning. While attempts to establish tibial anatomical axis have been made previously, combined central anatomical axis of human tibia and fibula remains unexplored. In this study, profiles of individual and combined central anatomical axes of tibia and fibula have been obtained using computed tomography (CT). These profiles are found to be approximately straight with the deviation from straight line for the centroidal axis of the combined system being approximately half of that for the tibia. It is further utilized in assessing the role of fibula in determining the critical stresses in the tibia with the help of static finite element analysis (FEA) of a tibia–fibula model. Even though fibula takes a smaller proportion of the total axial load, its absence increases the compressive stresses in the tibia due to increased bending moments at the critical cross section. Furthermore, FEA has been carried out to understand the clinical significance of the mismatch in the centroidal axis of an implant and its parent bone taking the example of the human tibia alone. FEA suggests that these central anatomical axes are in fact the load bearing axes of the bones and any misalignment of implant with the central anatomical axis may lead to patient discomfort and premature failure of the implant.

The existing techniques solve the rendezvous problem and characterize the final convergence point in the absence or presence of homogeneous input/communication delays. In this article, we analyze the rendezvous problem of double-integrator multi-agent system (MAS) in the presence of heterogeneous input and communication delays. We employ cyclic pursuit strategy to achieve rendezvous of the delayed MAS. It is established in the literature that accommodation of one negative position consensus gain will expand the reachable set beyond the convex hull of the initial position of the agents engaged in cyclic pursuit. Consonantly, we accommodate at most one negative position consensus gain in the system and derive sufficient conditions on the gains for a stable rendezvous. For double-integrator system, damping gains are upper bounded by the input delays while the lower bound of the negative position consensus gain does not depend on the input delays explicitly. The final rendezvous point varies with homogeneous/heterogeneous communication delays as well as with the heterogeneous input delays. The findings are illustrated by numerical simulations.

Temporomandibular joint (TMJ) is a synovial joint that allows for movement of the jaw in relation to the skull. TMJs are located on both sides of the face, one on either side. It aids in performing of activities such as eating. TMJ disorder may sometime require an implant to replace this joint. Excessive stress on certain screws and implants may adversely affect the TMJ implant and may lead to breakage and requirement of replacement. Therefore, to predict stresses in the implant, finite element analysis has been used in this study. We have simulated a human bite by applying force to the teeth and allowing the condyle to rotate and translate over the fossa with the restrictions on the rigid body motions coming from flexible muscles which are modeled as axial connector elements. This method is novel because it eliminates the need to collect data on muscle forces in order to simulate the TMJ as was done conventionally. Each individual mandibular tooth can be loaded in this simulation. Because of the reduced amount of restriction placed on the TMJ implant, it is possible to better understand the true stresses that will be generated under the routine movement of the jaw.

This paper investigates the synchronization problem for generic linear multi-agent systems with known or unknown heterogeneous input and communication delays. We propose two protocols that consist of consensus-based internal controller states and decentralized controllers. This kind of distributed dynamic control methodology is able to circumvent the interactive nature of two delays by translating the synchronization problem of agents into the stability of a set of delay differential equations. We examine the synchronization problem for two distinct cases, namely, known delays and unknown delays. When the delays are known, the stability criteria are satisfied by the feasibility of an input-delay-dependent linear matrix inequality and a communication-delay-dependent coupling strength bound. The margin on the communication delay is dependent not only on the network topology but also on the system matrix, which does not have any eigenvalues with positive real parts. We also develop a distributed dynamic control protocol that can handle unknown input and communication delays, and the stability criteria are realized by using the feasibility of a linear matrix inequality and a positive coupling strength. Synchronization is guaranteed even if the unknown communication delays are arbitrarily large but bounded and the upper bound on the heterogeneous input delays is known. The proposed control methodology guarantees that inaccurate measurements of the actual states of a particular agent will not lead to an irretrievable failure of the mission.