Diagrammatic Monte Carlo study of the Fermi polaron in two dimensions

We study the properties of the two-dimensional Fermi polaron model in which an impurity attractively interacts with a Fermi sea of particles in the zero-range limit. We use a diagrammatic Monte Carlo (DiagMC) method which allows us to sample a Feynman diagrammatic series to very high order. The convergence properties of the series and the role of multiple particle-hole excitations are discussed. We study the polaron and molecule energy as a function of the coupling strength, revealing a transition from a polaron to a molecule in the ground state. We find a value for the critical interaction strength which complies with the experimentally measured one and predictions from variational methods. For all considered interaction strengths, the polaron $Z$ factor from the full diagrammatic series almost coincides with the one-particle-hole result. We also formally link the DiagMC and the variational approaches for the polaron problem at hand.Comment: 7 pages, 5 figure

Quasiparticle properties of an impurity in a Fermi gas

We report on a study of a spin-down impurity strongly coupled to a spin-up Fermi sea (a so-called Fermi polaron) with the diagrammatic Monte-Carlo (DiagMC) technique. Conditions of zero temperature and three dimensions are considered for an ultracold atomic gas with resonant interactions in the zero-range limit. A Feynman diagrammatic series is developed for the one-body and two-body propagators providing information about the polaron and molecule channel respectively. The DiagMC technique allows us to reach diagram orders that are high enough for extrapolation to infinite order. The robustness of the extracted results is examined by checking various resummation techniques and by running the simulations with various choices for the propagators and vertex functions. It turns out that dressing the lines in the diagrams as much as possible is not always the optimal choice. We also identify classes of dominant diagrams for the one-body and two-body self-energy in the region of strong interaction. These dominant diagrams turn out to be the leading processes of the strong-coupling limit. The quasiparticle energies and $Z$-factor are obtained as a function of the interaction strength. We find that the DiagMC results for the molecule and polaron properties are very similar to those obtained with a variational ansatz. Surprisingly, this variational ansatz gives very good predictions for the quasiparticle residue even when this residue is significantly smaller than one.Comment: 11 pages, 15 figure

Diagrammatic Monte Carlo study of the acoustic and the BEC polaron

We consider two large polaron systems that are described by a Fr\"{o}hlich type of Hamiltonian, namely the Bose-Einstein condensate (BEC) polaron in the continuum and the acoustic polaron in a solid. We present ground-state energies of these two systems calculated with the Diagrammatic Monte Carlo (DiagMC) method and with a Feynman all-coupling approach. The DiagMC method evaluates up to very high order a diagrammatic series for the polaron Green's function. The Feynman all-coupling approach is a variational method that has been used for a wide range of polaronic problems. For the acoustic and BEC polaron both methods provide remarkably similar non-renormalized ground-state energies that are obtained after introducing a finite momentum cutoff. For the renormalized ground-state energies of the BEC polaron, there are relatively large discrepancies between the DiagMC and the Feynman predictions. These differences can be attributed to the renormalization procedure for the contact interaction.Comment: 9 pages, 10 figure

A Combined Geometric Morphometric and Discrete Element Modeling Approach for Hip Cartilage Contact Mechanics.

Finite element analysis (FEA) provides the current reference standard for numerical simulation of hip cartilage contact mechanics. Unfortunately, the development of subject-specific FEA models is a laborious process. Owed to its simplicity, Discrete Element Analysis (DEA) provides an attractive alternative to FEA. Advancements in computational morphometrics, specifically statistical shape modeling (SSM), provide the opportunity to predict cartilage anatomy without image segmentation, which could be integrated with DEA to provide an efficient platform to predict cartilage contact stresses in large populations. The objective of this study was, first, to validate linear and non-linear DEA against a previously validated FEA model and, second, to present and evaluate the applicability of a novel population-averaged cartilage geometry prediction method against previously used methods to estimate cartilage anatomy. The population-averaged method is based on average cartilage thickness maps and therefore allows for a more accurate and individualized cartilage geometry estimation when combined with SSM. The root mean squared error of the population-averaged cartilage geometry predicted by SSM as compared to the manually segmented cartilage geometry was 0.31 ± 0.08 mm. Identical boundary and loading conditions were applied to the DEA and FEA models. Predicted DEA stress distribution patterns and magnitude of peak stresses were in better agreement with FEA for the novel cartilage anatomy prediction method as compared to commonly used parametric methods based on the estimation of acetabular and femoral head radius. Still, contact stress was overestimated and contact area was underestimated for all cartilage anatomy prediction methods. Linear and non-linear DEA methods differed mainly in peak stress results with the non-linear definition being more sensitive to detection of high peak stresses. In conclusion, DEA in combination with the novel population-averaged cartilage anatomy prediction method provided accurate predictions while offering an efficient platform to conduct population-wide analyses of hip contact mechanics

Accuracy of navigated cam resection in femoroacetabular impingement: A randomised controlled trial.

BACKGROUND: The main cause for revision hip arthroscopy surgery is incomplete bony resection of femoroacetabular impingement (FAI). This study aimed to compare the cam resection accuracy via the conventional hip arthroscopy technique with the navigation technique. METHODS: Two prospectively randomized groups were recruited: navigated (n = 15) and conventional (n = 14). A pre-operative CT and post-operative MRI scan were obtained in all cases to compare alpha angle, range of motion simulation and determine a pre-operative 3D surgical resection plan. RESULTS: Post-operatively, the mean maximal alpha angle improved significantly in the navigated group compared with the conventional group (55°vs.66°; P = 0.023), especially in the 12 o' clock position (45°vs.60°; P = 0.041). However, positioning time and radiation exposure were significantly longer in the navigated group. CONCLUSION: Navigated surgery is effective for patients with cam type FAI in helping restore normal anatomy, however, not without drawbacks. Larger studies will be required to validate our results.Jan Van Houcke was supported by a doctoral grant of the Research Foundation‐Flanders

Personalized hip joint kinetics during deep squatting in young, athletic adults

The goal of this study was to report deep squat hip kinetics in young, athletic adults using a personalized numerical model solution based on inverse dynamics. Thirty-five healthy subjects underwent deep squat motion capture acquisitions and MRI scans of the lower extremities. Musculoskeletal models were personalized using each subject's lower limb anatomy. The average peak hip joint reaction force was 274 percent bodyweight. Average peak hip and knee flexion angles were 107 degrees and 112 degrees respectively. These new findings show that deep squatting kinetics in the younger population differ substantially from the previously reported in vivo data in older subjects

Statistical-Shape Prediction of Lower Limb Kinematics During Cycling, Squatting, Lunging, and Stepping-Are Bone Geometry Predictors Helpful?

Purpose: Statistical shape methods have proven to be useful tools in providing statistical predications of several clinical and biomechanical features as to analyze and describe the possible link with them. In the present study, we aimed to explore and quantify the relationship between biometric features derived from imaging data and model-derived kinematics. Methods: Fifty-seven healthy males were gathered under strict exclusion criteria to ensure a sample representative of normal physiological conditions. MRI-based bone geometry was established and subject-specific musculoskeletal simulations in the Anybody Modeling System enabled us to derive personalized kinematics. Kinematic and shape findings were parameterized using principal component analysis. Partial least squares regression and canonical correlation analysis were then performed with the goal of predicting motion and exploring the possible association, respectively, with the given bone geometry. The relationship of hip flexion, abduction, and rotation, knee flexion, and ankle flexion with a subset of biometric features (age, length, and weight) was also investigated. Results: In the statistical kinematic models, mean accuracy errors ranged from 1.60° (race cycling) up to 3.10° (lunge). When imposing averaged kinematic waveforms, the reconstruction errors varied between 4.59° (step up) and 6.61° (lunge). A weak, yet clinical irrelevant, correlation between the modes describing bone geometry and kinematics was observed. Partial least square regression led to a minimal error reduction up to 0.42° compared to imposing gender-specific reference curves. The relationship between motion and the subject characteristics was even less pronounced with an error reduction up to 0.21°. Conclusion: The contribution of bone shape to model-derived joint kinematics appears to be relatively small and lack in clinical relevance

Understanding the mechanical environment of the hip

The hip functions as a ball and socket joint, with cartilage layers that cover the joint surfaces on both sides protecting it from impacts and permitting smooth movements. When the cartilage is impaired by mechanical, infectious or inflammatory causes, the joint might eventually wear down - a disabling condition known as osteoarthritis. Recent literature indicates that up to 80\% of all osteoarthritis cases are potentially caused by subtle hip variations: the round shape of the ball (femur head) that is disturbed by a bump or/and the socket (acetabulum) that overcovers the femur head. These abnormal variants can give rise to conflicts and altered load distribution in the hip joint. When the load on the joint is no longer evenly distributed, peak stresses can arise in certain areas of the hip posing a risk of developing focal cartilage damage. Since the apparent prevalence of these morphological hip abnormalities is reported to be much higher than the number of actual patients, the question remains how to differentiate potential patients from incidental findings.The aim of this thesis was to describe and explore the impact of shape variation in the hip joint and by doing so improve the understanding of the mechanical environment of the hip joint. First differences in hip anatomy between white and Chinese subjects were mapped using a cross sectional design. Pelvic computed tomography scans of 201 subjects (99 white Belgians and 102 Chinese; 105 men and 96 women; 18-40 years old) were assessed. Ten radiographic parameters predisposing to femoroacetabular impingement were evaluated. The white subjects had a less spherical femoral head than the Chinese subjects. The Chinese subjects had less lateral acetabular coverage than the white subjects. A shallower acetabular configuration was predominantly present in Chinese women. Static and dynamic variation in hip joint reaction forces was evaluated using an experimental computational modeling design. We therefore calculated the hip joint reaction force and hip flexion angle in a virtual representative male Caucasian population by means of musculoskeletal modeling of three distinct sitting configurations: a simple chair, a car seat and a kneeling chair configuration. The observed median hip joint reaction force in relation to body weight and hip flexion angle, respectively, was 22.3$\%$ body weight and 63° for the simple chair, 22.5$\%$ body weight and 79° for the car seat and 8.7$\%$ body weight and 50° for the kneeling chair. The kneeling chair appears to hold the greatest potential as an ergonomic sitting configuration for the hip joint since it requires the lowest hip flexion angle and hip joint reaction force of these 3 distinct sitting configurations. Dynamic mapping of deep squat hip kinetics was performed in young, athletic adults using a personalized numerical model solution based on inverse dynamics. Thirty-five healthy subjects underwent deep squat motion capture acquisitions and MRI scans of the lower extremities. Musculoskeletal models were personalized using each subject’s lower limb anatomy. The average peak hip joint reaction force was found to be 274$\%$ body weight. Average peak hip and knee flexion angles were 107° and 112° respectively. Deep squatting kinetics in the younger population differ substantially from the previously reported in vivo data in older subjects. In order to map variation in cartilage stress, a numerical discrete element analysis algorithm was developed. A validation study with hip joint contact stress data from 10 healthy subjects calculated by means of subject-specific finite element analysis was performed. Furthermore an efficient cartilage anatomy prediction tool was defined that does not require manual cartilage image segmentation. We showed that this novel population-averaged cartilage anatomy prediction method, integrated with the discrete element analysis algorithm could provide an efficient platform to predict cartilage contact stresses in large populations compared to subject specific finite element analysis. The mechanical effect of arthroscopic cam resection in femoroacetabular impingement was explored with a case-control study design. For this purpose, patient-specific discrete element models from 10 cam type femoroacetabular patients (all male, aged 18-40 years old) were defined based on preoperative CT and postoperative MRI scans. Complete cam resection postoperatively on MRI was confirmed with alpha angles $<$ 55°. The preoperative and postoperative peak contact stress findings during impingement testing were compared against a matched virtual control group. Peak contact stress was significantly elevated in patients with cam type femoroacetabular impingement during impingement testing with increasing amount of internal rotation. This effect was however normalized following arthroscopic cam resection and loading patterns matched those of the control group. Using multidimensional statistics and personalized load and stress predictions, we were able to demonstrate that the important population variation in shape and joint mechanics adds to differences in the onset and progression of cartilage lesions of the hip joint. Further, our work contributes to an improved identification and classification of patients who are truly at risk for developing cartilage damage. The final step of this thesis was to gradually transfer these findings into practice at the operating theater. We demonstrated that an accurate surgical treatment of cam lesions has the potential to effectively restore the normal mechanical environment of the hip