Assessing the behavior of a hybrid model of the knee with contact surrogate under parameter uncertainties.

Modeling the knee is an important factor in increasing the quality of life of both healthy individuals and patients. Nevertheless, the intricate nature of the knee makes this problem complicated. In this study, an extension to an established planar knee joint model with Hertzian contact pairs is proposed with contact mechanics based on polynomial chaos expansion surrogate. Firstly, the finite element (FE) model is made representing a contact pair of sphere-to-plane type with two layers on both bodies, corresponding to the cartilage and the bone. Five variables corresponding to both geometry and material parameters are used to parametrize this model. Then, 128 distinct variants of the FE model are created based on a quasi-Monte Carlo sequence. This dataset is used to train and validate the surrogate. The trained surrogate is proven to have predictive capabilities with an average nRMSE of 0.2% in randomized test/train splits. When included in a model of the knee and tested under parameter uncertainties in Monte Carlo simulations, it results in nRMSE of 58% for angular coordinate compared to the original model with Hertzian pair. This signifies the high influence of contact formulation on the model output and the need for more physically based models in knee contact modeling.

Analyzing ligament prestrain in a multibody model of an ankle joint with random sampling.

Purpose: Modeling an ankle joint is a challenge, especially when considering complex phenomena such as prestrain. In the literature two main approaches to ligament prestrain can be found in ankle modeling. The first one assumes a strain-free configuration, effectively omitting the prestrain, while in the second one the slack lengths are obtained by shortening the ligament lengths in the rest configuration by 2%. These approaches were not compared directly in a controlled environment. Methods: The aim of the study to compare the two common approaches to ligament prestrain in ankle joint modeling. The approaches are compared on a collection of models generated by random sampling from a 6-link, 2-contact pair multibody model of the ankle. Random sampling includes perturbation of slack lengths, which makes the generated models prestrained and with known output characteristics. Their resemblance to the original model and the ankle joint makes them viable for using in a prestrain comparison. Each generated model is prestrain with the two approaches, then the outputs are compared to determine, which approach returns results closer to reality. Results: The comparison was performed on 592 generated models. On average, the strain-free approach significantly outperformed the 2% shortening. Conclusions: The method for testing prestrain proposed in the paper is an effectively tool for exploring the solution space of the model. The obtained results were interesting, but should be taken with caution as they are connected to the test condition. However, the method is general and could used with any other biomechanical model.

Differential evolution and cost-maps for needle path planning in Baker's cyst aspiration.

PURPOSE: The Baker's cysts appear within the popliteal fossa along with the progression of degenerative changes. Removal of its contents through aspiration is often a necessary complement to treatment at various stages of the development of gonarthritis. METHODS: The paper presented a procedure for needle automatic needle path planning in cyst aspiration in transverse plane. The method was based on optimization and used a custom objective function, which utilized cost maps obtained from preprocessed, segmented images of the knee. The optimization was carried out with Differential Evolution. Furthermore, a preliminary sensitivity analysis was carried out. The obtained paths were compared to the reference paths proposed by an experienced surgeon. RESULTS: The procedure was tested on 165 numerical simulations. In all of the obtained paths, the needle successfully avoided crucial objects, such as veins, arteries and nerves. Furthermore, the overall travel distance in the joint was also minimized. When compared to the reference from the surgeon, 90% of the paths were almost the same or only slightly different. Furthermore, the remaining 10% of the generated paths were viable but different. CONCLUSION: Based on the obtained results, the proposed solution could be a viable solution for planning the aspiration of Baker's cyst.

Selected aspects of the application of the hybrid circulatory system in the analysis of heart insufficiency.

PURPOSE: There are many causes of heart failure, one of them being valvular heart disease. In this case, the stage and type of the disease can significantly affect the hemodynamic parameters of the left ventricle of the heart. In turn, these parameters can significantly influence the mode, type and strategy of clinical treatment. The aim of the study was to analyze and map the hydrodynamic conditions of the heart using a hybrid-digital model of the circulatory system. METHODS: The tests performed using the circulatory system model allowed for the simulation of the failure of both heart's left ventricle and a set of arteries in the systemic circulation. Furthermore, the changes in hemodynamic parameters for valvular anomalies at various heartbeats were obtained. RESULTS: The results suggested that a higher heartbeat should be sustained in such cases of complex mitral-aortic anomalies in the clinical practice. When observing low aortic pressures, heartbeat should be increased to compensate for the valvular insufficiencies. CONCLUSIONS: Extending the already conducted research could result in constituting a wide database for clinicians who are treating the insufficiency of the left ventricle of the heart. Moreover, the information included in this paper may be used for a comparison of the clinical anomalies, which facilitates a correct diagnosis. The test-stand used in the research can be applied to predict the anomalies of the circulation system for a quick and precise analysis of a clinical anomaly of a patient without physical presence.

Analyzing Uncertainty of an Ankle Joint Model with Genetic Algorithm.

Recent studies in biomechanical modeling suggest a paradigm shift, in which the parameters of biomechanical models would no longer treated as fixed values but as random variables with, often unknown, distributions. In turn, novel and efficient numerical methods will be required to handle such complicated modeling problems. The main aim of this study was to introduce and verify genetic algorithm for analyzing uncertainty in biomechanical modeling. The idea of the method was to encode two adversarial models within one decision variable vector. These structures would then be concurrently optimized with the objective being the maximization of the difference between their outputs. The approach, albeit expensive numerically, offered a general formulation of the uncertainty analysis, which did not constrain the search space. The second aim of the study was to apply the proposed procedure to analyze the uncertainty of an ankle joint model with 43 parameters and flexible links. The bounds on geometrical and material parameters of the model were set to 0.50 mm and 5.00% respectively. The results obtained from the analysis were unexpected. The two obtained adversarial structures were almost visually indistinguishable and differed up to 38.52% in their angular displacements.

Structural and Material Optimization for Automatic Synthesis of Spine-Segment Mechanisms for Humanoid Robots with Custom Stiffness Profiles.

Typical artificial joints for humanoid robots use actual human body joints only as an inspiration. The load responses of these structures rarely match those of the corresponding joints, which is important when applying the robots in environments tailored to humans. In this study, we proposed a novel, automated method for designing substitutes for a human intervertebral joint. The substitutes were considered as two platforms, connected by a set of flexible links. Their structural and material parameters were obtained through optimization with a structured Genetic Algorithm, based on the reference angular stiffnesses. The proposed approach was tested in three numerical scenarios. In the first test, a mechanism with angular stiffnesses corresponded to the actual L4-L5 intervertebral joint. Scenarios 2 and 3 featured mechanisms with geometry and structure comparable to the joint, but with custom stiffness profiles. The obtained results proved the effectiveness of the proposed method. It could be employed in the design of artificial joints for humanoid robots and orthotic structures for the human spine. As the approach is general, it could also be extended to different body joints.

A Planar Model of an Ankle Joint with Optimized Material Parameters and Hertzian Contact Pairs.

The ankle is one of the most complicated joints in the human body. Its features a plethora of elements with complex behavior. Their functions could be better understood using a planar model of the joint with low parameter count and low numerical complexity. In this study, an accurate planar model of the ankle with optimized material parameters was presented. In order to obtain the model, we proposed an optimizational approach, which fine-tuned the material parameters of two-dimensional links substituting three-dimensional ligaments of the ankle. Furthermore, the cartilage in the model was replaced with Hertzian contact pairs. The model was solved in statics under moment loads up to 5 Nm. The obtained results showed that the structure exhibited angular displacements in the range of the ankle joint and that their range was higher in dorsiflexion than plantarflexion. The structure also displayed a characteristic ramp up of the angular stiffness. The results obtained from the optimized model were in accordance with the experimental results for the ankle. Therefore, the proposed method for fine-tuning the material parameters of its links could be considered viable.

Path planning for minimally-invasive knee surgery using a hybrid optimization procedure.

The aim of this study was to develop a procedure for medical tool path planning in minimally-invasive knee surgery. The collision-free paths for the tool were obtained using the control locations method with a hybrid optimization strategy. The tool and knee elements were described with surface meshes. The knee model allowed for bones displacement and variable incision size and location. The proposed procedure was proven to be effective in path planning for minimally-invasive surgery. It can serve as a valuable aid in surgery planning and may also be used in systems for autonomous or semi-autonomous knee surgery.

A novel planning solution for semi-autonomous aspiration of Baker's cysts.

BACKGROUND: A Baker's cyst is a pathological structure located near a kneepit, which causes discomfort and reduces mobility of the knee. It is commonly treated with aspiration, which often requires MRI scanning and US guidance. The aim of this study was to propose a novel planning solution for semi-autonomous aspiration of the Baker's cyst using only MRI imaging. METHODS: The proposed method requires minimal user input and offers automatic cyst segmentation with collision-free path planning for the assumed robotic structure with four degrees of freedom. RESULTS: The prepared software was tested on four image sets obtained from patients eligible for cyst aspiration. It was possible to accurately segment the cyst in the considered cases. The collision-free path planning method was investigated in numerical scenarios. CONCLUSIONS: The simulations verified the proposed software solution. Future work will be devoted to experimental verification of the path planning procedure.

Load analysis of a patellofemoral joint by a quadriceps muscle.

PURPOSE: The aim of this paper is to develop a model of the patellofemoral joint by considering the linear displacement along axis of cylindrical joint and to use this model in the analysis of the femur spatial displacements caused by the quadriceps muscle force. METHOD: The linear displacement along the axis of cylindrical joint of the patellofemoral joint is computed using optimization methods - minimization of the difference between the modeled and measured spatial displacements of the femur with respect to the tibia over the full range of the knee flexion. Then, the instantaneous screw displacements of the femur with regard to the tibia and corresponding muscle forces are computed for the model developed. The moment of the force arm with respect to the vector of screw displacement is used to evaluate the effectiveness of the acting force. RESULTS: The simulation results for the model developed show significant improvement of the modeled linear coordinates of the femur reference system with respect to tibia reference system. The displacement analysis of the femur loaded by quadriceps muscle force can be used to describe the patellofemoral dislocation problem. CONCLUSIONS: The model of the patella- femur joint where the linear displacement along axis of the cylindrical joint is considered can reproduce the actual patella displacements more accurately. It seems expedient to study elasto-statics problem of this mechanism. The model can be used to study some medical conditions such as patellofemoral dislocation.

A novel kinematic model for a functional spinal unit and a lumbar spine.

PURPOSE: The aim of this paper is to present the novel model for the functional spinal unit and spine designed as a rigid mechanism and solve it with methods commonly used in robotics. METHOD: The structure of the intervertebral joint is analyzed with special attention paid to elements defining the displacements in the joint. The obtained mechanism is then numerically solved using a constraint equations method. RESULTS: The input data set for the simulation is prepared using the 3D scan of the lumbar spine. The simulation results show that the intervertebral joint mechanism can satisfy the ranges of flexion, lateral bending and axial rotation as compared with literature data. It is also possible to study complex, coupled displacements of the lumbar spine segment. CONCLUSIONS: Structural analysis of the functional spinal unit with methods common in robotics can eventually lead to better understanding of stabilizing and guiding mechanisms. The proposed mechanism can be used as a reference in the study of spine guidance. It can reproduce the angular displacements of the actual functional spine unit. It is also possible to expand the model to facilitate the analysis of a lumbar spine segment.