人工智能在医疗保健中的数学基础：一项系统综述。
完整摘要 · 中文译文
医疗保健中的人工智能（AI）依赖于多种数学框架，但这些框架对模型开发、评估、可解释性和临床转化的贡献仍然分散。本系统综述综合了支撑医疗保健AI的经典与新兴数学基础，并考察了主要的方法学和应用趋势。遵循PRISMA 2020指南，通过系统检索Scopus、Google Scholar和PubMed/MEDLINE，确定了2016年1月至2026年6月30日期间发表的研究，适用时使用Harzing的Publish or Perish v8进行检索。使用VOSviewer进行文献计量分析，同时使用改编的基于JBI的框架评估方法学质量，并使用AMSTAR-2评估系统综述。在确定的653条记录中，147项研究符合纳入标准。非互斥的数学领域编码在100/147项研究（68.0%）中识别出线性代数，在91/147项（61.9%）中识别出微积分与优化，在79/147项（53.7%）中识别出概率与统计，凸显了它们在数据表示、学习、优化、推断、不确定性量化和验证中的作用。对主导方法学主题进行的单独互斥分类在24/147项研究（16.3%）中识别出可解释与可信AI，在23/147项（15.6%）中识别出统计与学习理论，在23/147项（15.6%）中识别出概率与贝叶斯方法，在19/147项（12.9%）中识别出微积分与优化，在15/147项（10.2%）中识别出线性代数。放射学与医学成像是领先的医疗保健应用 ication（24.3%），而分类与诊断是最常见的临床任务（17.1%）。总体而言，医疗人工智能由一个相互关联的数学生态系统支撑。新兴方法，包括图神经网络、Transformer 和量子机器学习，需要更强的外部验证、标准化的基准测试以及严格评估，才能实现可靠的临床转化。
完整摘要 · 英文原文
Artificial intelligence (AI) in healthcare relies on diverse mathematical frameworks, yet their contributions to model development, evaluation, interpretability, and clinical translation remain fragmented. This systematic review synthesized the classical and emerging mathematical foundations underpinning healthcare AI and examined major methodological and application trends. Following PRISMA 2020 guidelines, studies published between January 2016 and June 30, 2026, were identified through systematic searches of Scopus, Google Scholar, and PubMed/MEDLINE, with searches conducted using Harzing's Publish or Perish v8 where applicable. Bibliometric analysis was performed using VOSviewer, while methodological quality was assessed using an adapted JBI-based framework and AMSTAR-2 for systematic reviews. Of 653 records identified, 147 studies met the eligibility criteria. Non-mutually exclusive mathematical-domain coding identified linear algebra in 100/147 studies (68.0%), calculus and optimization in 91/147 (61.9%), and probability and statistics in 79/147 (53.7%), highlighting their roles in data representation, learning, optimization, inference, uncertainty quantification, and validation. A separate mutually exclusive classification of dominant methodological themes identified explainable and trustworthy AI in 24/147 studies (16.3%), statistics and learning theory in 23/147 (15.6%), probability and Bayesian methods in 23/147 (15.6%), calculus and optimization in 19/147 (12.9%), and linear algebra in 15/147 (10.2%). Radiology and medical imaging were the leading healthcare application (24.3%), while classification and diagnosis were the most frequent clinical task (17.1%). Overall, healthcare AI is supported by an interconnected mathematical ecosystem. Emerging approaches, including graph neural networks, Transformers, and quantum machine learning, require stronger external validation, standardized benchmarking, and rigorous evaluation for reliable clinical translation.