~~"ZOOM" SEMINAR
SCHOOL OF MECHANICAL ENGINEERING SEMINAR
Wednesday, December 16, 2020 at 14:00

The mechanical response of human humeri

Gal Dahan
Ph.D. student under the supervision of Prof. Zohar Yosibash

Proximal humerus fractures are the 3rd most common fracture in osteoporotic patients. Since osteoporosis is a systemic disease, often clinicians are faced with the question on the risk of fracture of a specific patient and the need for drug prescription. Finite element models based on quantitative computed tomography (QCT-based FE) can serve as a biomechanical-based quantitative tool that can assist in clinical decision-making process. In particular,  the individual intact bone strength or stability assessment of the fractured bone if fracture occurred (should be quantified  to decide whether a surgery is required, or a conservative treatment is sufficient). QCT-based FEs have been shown to provide accurate predictions for femurs and this study is aimed to extend the current capabilities to the humeri.
In the current study we present the enhancement and validation of QCT-based FE models by experiments conducted on fresh frozen humeri. Validation was performed by means of strain gauges (SGs) strain measurements and enhanced using digital image correlation (DIC) enabling full field displacement and strain evaluation.
Following experiments in the elastic regime, the humeri were loaded to obtain a fracture in their proximal part. Two different physiological fractures were realized in the experiments, in both anatomical and surgical neck of the bones. Fracture criteria based on maximum principal strains computed by the QCT-based FE models were checked experimentally both in terms of the load to fracture and the fracture locations. This research opens the door to the novel use of FE analysis in clinical practice in endocrinology and orthopedic treatment of the humeri. 

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https://zoom.us/j/96584758181?pwd=WC9PMXdsYzJ3NFdEN2Q5ZUtOZEVjdz09 The meeting will be recorded and made available on the School’s site.

"ZOOM" SEMINAR

SCHOOL OF MECHANICAL ENGINEERING SEMINAR
Monday, November 30, 2020 at 14:00

Implants in the human proximal femur:

A combined experimental-computational study

Yekutiel Katz

Ph.D. student under the supervision of Prof. Zohar Yosibash

Hip replacement is a common orthopedic surgical procedure. Long-term survival of hip implants is of increasing relevance due to rising life expectancy. The biomechanical effect of strain shielding as a result of implant's presence may lead to bone resorption, thus increasing the risk for implant loosening and periprosthetic hip fractures. Studies on patient-specific finite element (FE) models based on quantitative computed tomography (QCT) showed that the mechanical response of intact femurs can be well predicted. The current study improves these methods and extends their application to femurs inserted with hip implants, focusing mainly on cemented implants.

To enable the use of FE in clinical practice for: femoral fracture risk assessment, pre-operative optimal implant selection and periprosthetic fracture risk prediction, QCT based FEAs must be proven reliable trough a thorough ex-vivo experimental procedure. A combined experimental-computational study on fresh frozen human femurs, in both intact and implanted states with different implants is presented, aiming at validating patient specific QCT based FE models.

The current study incorporates digital image correlation (DIC) full field measurements on human tissues with curved surfaces leading to new insights on the biomechanics of  the femoral neck. This area’s response was misrepresented in previous studies.

The validated FE models were used to develop a systematic algorithm for strain shielding quantification. Different strain measures were examined suggesting the volumetric strain to be the most appropriate for strain shielding quantification, that may assist surgeons to choose the optimal patient specific implant.

Join Zoom Meeting
 

https://zoom.us/j/96584758181?pwd=WC9PMXdsYzJ3NFdEN2Q5ZUtOZEVjdz09 The meeting will be recorded and made available on the School’s site.

https://us02web.zoom.us/j/86785731080?pwd=dk10aVJNM3NXeHE3WFJvZmlUQndadz09
Meeting ID: 867 8573 1080
Passcode: TAUEESYS 

Speaker: Dr.  Nadav Dym

Department of Mathematics of Duke University

Monday, November 9^th, 2020, at 15:00

On the injectivity and (in)stability of invariant encoding

Abstract

            Quotient spaces are a natural mathematical tool to describe a variety of algorithmic problems in computer vision and related fields, where different objects are to be compared while their natural symmetries are to be ignored.

 One popular approach for working in quotient spaces is cancelling out symmetries  by finding a  canonical alignment of the objects at hand. This approach typically involves solving a challenging optimization problem over the symmetry group. We will review the tractability of these problems for sets, their intractability for graphs, and recent advances in the complexity of computing these problems for the intermediate case of rigid point clouds.

An alternative approach for working in quotient spaces avoids the computational challenges of alignment by directly mapping objects to features invariant to the object’s symmetries. The challenge with this approach is devising a sufficiently expressive family of invariant features. We will describe constructive methods for mapping quotient spaces injectively to a finite set of invariants, which lead to proofs of universality of networks for sets and rigid point clouds, and to injectivity of linear phaseless measurements in the context of phase retrieval problems. We will then discuss results in the phase retrieval literature that suggest that though injective, mappings to invariant features can be unstable and suffer from the curse of dimensionality. These results indicate that every system of invariants has `blind spots’, which corresponds to `disconnected signals’ in the measurement domain. We will describe work to quantify the stability via measures of connectivity used in spectral graph theory, and in particular show that real phase retrieval is related to the Cheeger constant, while complex phase retrieval relates to the second eigenvalue of the Laplacian.

Short Bio

I am an applied mathematician and computer scientist, interested in the development and analysis of algorithms, typically targeting 3D problems in computer vision and related fields. I am currently working on problems related to global optimization, phase retrieval, and theoretical and geometric deep learning. I am an Assistant Research Professor at the Department of Mathematics of Duke University, hosted by Prof. Ingrid Daubechies at the Information Initiative at Duke (iiD). In 2018 I completed my PhD in the Department of Computer Science and Applied Mathematics at the Weizmann Institute of Science under the supervision of Prof. Yaron Lipman. I have received a BSc and MSc in mathematics from the Hebrew University.

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