This paper presents a structured analysis of neuro-symbolic design patterns for medical decision-making systems through a graphical notation (the “boxology”) for neuro-symbolic architectures. We formalize and validate five archetypal neuro-symbolic architectures initially defined through textual descriptions and informal diagrams by Kierner et al. We systematically define and refine these archetypes across 68 systems from the literature. Our contributions include: (i) a formalization of these archetypes, (ii) empirical validation of these archetypes via system refinements, (iii) enhanced understanding of neuro-symbolic integration in clinical applications, and (iv) establishing the boxology as a robust tool for comparative architectural analysis. The findings indicate that the elementary patterns within the boxology framework remain consistent across clinical applications, offering new avenues for systematic development and comparison in neuro-symbolic AI for healthcare.