Programming Branching and Growth in Developing Organs

Definitions and mathematical statement

Scope and terminology. The objects under discussion are growing animals and developing branched organs, including lungs and kidneys. Here branching refers descriptively to the formation and placement of branches during development; epithelial behavior refers to the behavior of the organ's epithelial tissue. The source does not specify mathematical definitions or observables for size, shape, branch points, epithelial behavior, or termination of growth.

Research question. Determine the mechanisms by which size and shape are programmed and executed during development in growing animals and branched organs such as lungs and kidneys. In particular, determine how these mechanisms govern the locations of branch points, epithelial behavior, and the termination of growth.

Unresolved formulation qualifications. This is a qualitative mechanobiological research question. No mathematical state space, governing equations, admissible class of mechanisms, initial or boundary conditions, developmental interval, or criterion for successful prediction is supplied. The source also does not specify whether the intended explanation must apply universally or separately to particular animals and organs. Consequently, the record does not determine a precise quantified mathematical conjecture; choosing such a formulation would require additional hypotheses and biological specifications.

Short English statement

Explain how developing animals and branched organs, including lungs and kidneys, acquire their size and shape, position branches, regulate epithelial behavior, and stop growing. The supplied question lacks the model, measurements, and conditions needed for a precise mathematical conjecture.

Sources

• Local UnsolvedMath registry, data/unsolvedmath/problems.json, permanent ID 30003735, title Programming Branching and Growth in Developing Organs, source problem code catalogue entry; supplied complete source record from the Oberwolfach Reports Open Problems collection. No individual proposer is supplied; the proposed year is recorded as 2018.
• Supplied report citation: The Mathematics of Mechanobiology and Cell Signaling (2019), Oberwolfach Reports, pp. 433--506, DOI 10.4171/owr/2018/8. Supplied source URL: https://doi.org/10.4171/owr/2018/8. The background attributes the question to workshop open-problem discussions documented in Oberwolfach Reports.
• Supplied literature source, labeled "original OWR report": https://doi.org/10.4171/OWR/2018/8.
• Supplied literature source, labeled "Wittwer et al., computational lung organogenesis": https://arxiv.org/abs/1610.09189.
• Supplied literature source, labeled "tissue geometry and lung branching": https://doi.org/10.1016/j.jtbi.2017.12.031.
• Literature assessment dated exactly 2026-08-21: the supplied curation labels the problem partially solved and reports that mechanistic and image-based models reproduce parts of lung and kidney branching and organ growth, while a general predictive account of final organ size and shape remains unresolved. This is supplied dated curation derived from the OWR material, not an independently verified literature assessment. Time-sensitive status and cited claims require independent verification.
• The registry labels the statement corrected_verified and states that mathematical content was preserved while notation, typography, and omitted definitions were repaired for self-contained publication. These are supplied registry assertions, not independent mathematical verification of this draft.