Computational Geometry: Advancing Biomedical and Medical Field

Jonas Eriksson^*
*Correspondence: Jonas Eriksson, Department of Theoretical and Applied Mathematics, University of Stockholm South, Stockholm, Sweden, Email:

Introduction

This paper delves into how computational geometry provides the foundational tools for building and refining meshes used in simulations of complex biological systems. It highlights the importance of accurate mesh generation and optimization techniques to ensure the fidelity and efficiency of these simulations, enabling deeper understanding of biological phenomena [1].

This systematic review investigates the role of computational geometry in assessing radiotherapy dose distributions. It highlights various geometric algorithms and techniques employed to analyze and optimize treatment plans, emphasizing their crucial contribution to improving the precision and efficacy of cancer radiation therapy [2].

This research introduces a deep learning and computational geometry framework designed for real-time 3D reconstruction and path planning in robot-assisted surgery. The method aims to enhance surgical precision and safety by providing accurate spatial awareness and optimized robot trajectories within complex anatomical environments [3].

This research introduces a novel computational geometry method for creating micro-architectural models of human trabecular bone. This approach enables detailed analysis of bone structure, crucial for understanding mechanical properties and disease progression, by accurately replicating the complex geometric features of trabecular bone [4].

This overview explores the application of computational geometry in medical image reconstruction. It details various geometric algorithms and their role in transforming raw data into meaningful diagnostic images, highlighting how these methods contribute to enhanced image quality and clinical utility across different imaging modalities [5].

This chapter focuses on using computational geometry for efficient and scalable feature extraction in bioimage analysis. It details how geometric algorithms can precisely quantify complex biological structures and patterns, crucial for extracting meaningful data from large-scale microscopic images, accelerating discoveries in biological research [6].

This study utilizes computational geometry to characterize complex morphologies found in biological tissues. By applying advanced geometric algorithms, researchers can quantify intricate cellular and tissue structures, providing new insights into tissue development, disease progression, and therapeutic responses with high precision [7].

This review examines recent advancements in the application of computational geometry within biomedical engineering. It covers various geometric algorithms and their impact on areas like medical imaging, surgical planning, and prosthetics design, highlighting the ongoing innovation and diverse utility of these techniques [8].

This paper presents a computational geometry-based framework for the automated detection of carotid artery dissection. The approach leverages geometric algorithms to analyze medical imaging data, aiming to provide a robust and efficient tool for early diagnosis and improved patient outcomes by precisely identifying arterial abnormalities [9].

This study focuses on applying computational geometry to analyze cardiac motion and deformation. It explores how geometric models and algorithms can accurately quantify complex heart movements, providing critical insights for diagnosing cardiovascular diseases and evaluating therapeutic interventions with high precision [10].

Description

Computational geometry provides foundational tools for building and refining meshes used in simulations of complex biological systems, ensuring the fidelity and efficiency of these simulations, enabling deeper understanding of biological phenomena [1]. This field also investigates the role of computational geometry in assessing radiotherapy dose distributions, highlighting various geometric algorithms and techniques employed to analyze and optimize treatment plans, emphasizing their crucial contribution to improving the precision and efficacy of cancer radiation therapy [2].

This research introduces a deep learning and computational geometry framework designed for real-time 3D reconstruction and path planning in robot-assisted surgery. The method aims to enhance surgical precision and safety by providing accurate spatial awareness and optimized robot trajectories within complex anatomical environments [3]. Another aspect involves a novel computational geometry method for creating micro-architectural models of human trabecular bone, an approach enabling detailed analysis of bone structure, crucial for understanding mechanical properties and disease progression [4].

Furthermore, this discipline focuses on efficient and scalable feature extraction in bioimage analysis, detailing how geometric algorithms can precisely quantify complex biological structures and patterns, crucial for extracting meaningful data from large-scale microscopic images [6]. This overview also explores the application of computational geometry in medical image reconstruction. It details various geometric algorithms and their role in transforming raw data into meaningful diagnostic images, highlighting how these methods contribute to enhanced image quality and clinical utility across different imaging modalities [5].

In biological contexts, computational geometry is utilized to characterize complex morphologies found in biological tissues, providing new insights into tissue development, disease progression, and therapeutic responses with high precision [7]. A broader review examines recent advancements of computational geometry within biomedical engineering, covering various geometric algorithms and their impact on areas like medical imaging, surgical planning, and prosthetics design [8].

A specific application presents a computational geometry-based framework for the automated detection of carotid artery dissection, aiming to provide a robust and efficient tool for early diagnosis and improved patient outcomes [9]. The field also applies to analyzing cardiac motion and deformation, exploring how geometric models and algorithms accurately quantify complex heart movements, providing critical insights for diagnosing cardiovascular diseases and evaluating therapeutic interventions [10].

Conclusion

Computational geometry serves as a fundamental discipline, offering essential tools for diverse applications within biological and medical sciences. This field is instrumental in refining meshes for complex biological system simulations, ensuring both fidelity and efficiency for understanding biological phenomena. It significantly contributes to assessing radiotherapy dose distributions by optimizing treatment plans and improving precision in cancer therapy. In surgical contexts, computational geometry, often combined with deep learning, facilitates real-time 3D reconstruction and path planning for robot-assisted procedures, thereby enhancing surgical accuracy and patient safety. Researchers also use these methods to create detailed micro-architectural models of human trabecular bone, which allows for crucial analysis of bone structure and disease progression. Furthermore, computational geometry is vital in medical image reconstruction, transforming raw data into meaningful diagnostic images, and in bioimage analysis for scalable feature extraction, accelerating discoveries. Its algorithms are key to characterizing complex morphologies in biological tissues, offering insights into development and disease. The broader scope in biomedical engineering includes advances in medical imaging, surgical planning, and prosthetics design. Specific applications extend to automated detection of carotid artery dissection and precise analysis of cardiac motion and deformation, all aimed at improving diagnosis, treatment, and our understanding of biological phenomena.

Acknowledgement

None

Conflict of Interest

None

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