Mathematical Modeling and Algorithm Development

Ahmadian, Amir Sharif

doi:10.1016/b978-0-12-802413-3.00005-5

Cited by 2 publications

(6 citation statements)

References 18 publications

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“…Our SSM‐based first variation mode confirms uniform scapula scaling observed in prior studies 11,18,22,36 . However, the second and third modes showed variabilities that appear to be specifically associated with B glenoid pathologies.…”

Section: Discussionsupporting

confidence: 85%

“…To achieve the first goal, significant modes of variability were found for the SSM and SDM, representing 86% and 57% of their corresponding variability, respectively. The relatively high compactness of the SSM as well as the lower compactness of the SDMs are in agreement with the previous literature 11,18,36 . We evaluated the accuracy of the SSM and SDM in reconstructing the left‐out subject by measuring RMSE, which were in line with previous studies, albeit they were typically performed on an assumed less‐challenging population of healthy scapula 11,18,22,36 …”

Section: Discussionsupporting

confidence: 82%

“…The correlation between these first and fourth SDM modes and patients' BMI and gender showed that females and patients with higher BMI have more asymmetrical BMDD. Bone density variability in the posterior and inferior part of the glenoid was observed in the previous study of B glenoids (B2 and B3), however, it is important to note that not all modes corresponded to each other as we examined more localized regions and a broader group of B glenoids, including B1, B2, and B3 subtypes 36 . Identification of these asymmetrical BMDD and the following asymmetrical distribution of bone stress after glenoid component implantation 14 can be considered as one of the possible reasons behind glenoid component loosening in B glenoids.…”

Section: Discussionmentioning

confidence: 75%

“…Consequently, the findings of our study hold considerable importance in the context of glenoid component fixation and failure. Finally, the low compactness of the resulting SDM, already observed in previous studies, can be related to the high 3D BMDD variability across specimens different imaging protocols, the lack of a calibration phantom, or difficulties related to the interior elements registrations in the volumetric mesh morphing due to the absence of unique features to drive the mesh morphing 18,36 . However, the developed SDM has a comparable compactness with other studies and effectively identifies the main pattern of variations.…”

Section: Discussionmentioning

confidence: 76%

“…The first limitation pertains to the size and distribution of B glenoid subtypes. While the training set of 62 subjects was in the range of previous scapula studies (53–75 subjects 11,18,36 ), it may not be fully representative of the entire population. Nonetheless, we are of the opinion that expanding the study population improves the chances of identifying new variations and covariation patterns without limiting the patterns already found in this study.…”

Section: Discussionmentioning

confidence: 99%

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Covariations between scapular shape and bone density in B‐glenoids: A statistical shape and density modeling‐approach

Daneshvarhashjin,

Debeer,

Innocenti

et al. 2023

Journal Orthopaedic Research

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B‐type glenoids are characterized by posterior humeral head migration and/or bony‐erosion‐induced glenoid retroversion. Patients with this type of osteoarthritic glenoids are known to be at increased risk of glenoid component loosening after anatomic total shoulder arthroplasty (aTSA). One of the main challenges in B glenoid surgical planning is to find a balance between correcting the bony shape and maintaining the quality of the bone support. This study aims to systematically quantify variabilities in terms of scapular morphology and bone mineral density in patients with B glenoids and to identify patterns of covariation between these two features. Using computed tomography scan images of 62 patients, three‐dimensional scapular surface models were constructed. Rigid and nonrigid surface registration of the scapular surfaces, followed by volumetric registration and material mapping, enabled us to develop statistical shape model (SSM) and statistical density model (SDM). Partial least square correlation (PLSC) was used to identify patterns of covariation. The developed SSM and SDM represented 85.9% and 56.6% of variabilities in terms of scapular morphology and bone density, respectively. PLSC identified four modes of covariation, explaining 66.0% of the correlation between these two variations. Covariation of posterior–inferior glenoid erosion with posterior sclerotic bone formation in association with reduction of bone density in the anterior and central part of the glenoid was detected as the primary mode of covariation. Identification of these asymmetrical distribution of bone density can inform us about possible reasons behind glenoid component loosening in B glenoids and surgical guidelines in terms of the compromise between bony shape correction and bone support quality.

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Section: Discussionsupporting

confidence: 85%

Section: Discussionsupporting

confidence: 82%

Section: Discussionmentioning

confidence: 75%

Section: Discussionmentioning

confidence: 76%

Section: Discussionmentioning

confidence: 99%

See 3 more Smart Citations

Covariations between scapular shape and bone density in B‐glenoids: A statistical shape and density modeling‐approach

Daneshvarhashjin,

Debeer,

Innocenti

et al. 2023

Journal Orthopaedic Research

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Roadmap of the Multiplier Method for Partial Differential Equations

Alvarez-Valdez,

Fernandez-Anaya

2023

Mathematics

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This review paper gives an overview of the method of multipliers for partial differential equations (PDEs). This method has made possible a lot of solutions to PDEs that are of interest in many areas such as applied mathematics, mathematical physics, engineering, etc. Looking at the history of the method and synthesizing the newest developments, we hope to give it the attention that it deserves to help develop the vast amount of work still needed to understand it and make the best use of it. It is also an interesting and a relevant method in itself that could possibly give interesting results in areas of mathematics such as modern algebra, group theory, topology, etc. The paper will be structured in such a manner that the last review known for this method will be presented to understand the theoretical framework of the method and then later work done will be presented. The information of four recent papers further developing the method will be synthesized and presented in such a manner that anyone interested in learning this method will have the most relevant information available and have all details cited for checking.

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Mathematical Modeling and Algorithm Development

Cited by 2 publications

References 18 publications

Covariations between scapular shape and bone density in B‐glenoids: A statistical shape and density modeling‐approach

Covariations between scapular shape and bone density in B‐glenoids: A statistical shape and density modeling‐approach

Roadmap of the Multiplier Method for Partial Differential Equations

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