### Abstract

Introduction: Why are cranial sutures the way they are? How do cancers grow? Merging physics and mathematicswith biology, we develop equations describing these complex adaptive systems, to which all biological entities belong, calling them laws of tissue dynamics: lim_{Δt → T}ΣΔ[n_{i}Cell_{i}+Matrix_{j}]/Δt=0, for any stable tissue, n_{i}Cell_{i}=φ (Matrix_{i}), Matrix_{i}=f (Cell_{i}), both φ and f are recursive functions still to be determined, t is unit time and T is greater than t, (1) n is the number of cells k=t × [ΔE] _{max}, or alternatively, using power law: [ΔE] _{max}=Ce^{-at}, and X=X_{0}M^{b}, b=3/4, Ln t+Ln [ΔE] _{max}=constant, the power law format: Ln [ΔE] _{max}=Ln C - at=Constant - at, (2) Ln[ΔE] _{max}+at=Constant Where t is time, E is energy, M is body mass, X is the biological characteristic of interest, C is a constant, a is an exponent. (1) is based on conservation of matter: for any given tissue, materials in must equal to materials out+/- assimilated or degraded. (2) is based on energy conservation. All living systems require energy, without which life becomes impossible. Equation (2) is a power spectrum. Objectives: This study aimed to introduce the laws of tissue dynamics and to illustrate them using observations from craniofacial and cancer growth. Methods:We use cranial sutures as a model system to test Equation (1), we also measure the in vitro growth rate of normal murine liver and spleen cells, comparing them to B16F10 melanoma cells.We show the increase in compound growth rate and energetic requirement ofmalignant versus normal cells as partial proof of Equation (2). Results: The constant width and wavy form of cranial sutures are the inevitable results of repeated iteration from coupling of growth and stress. The compound growth rate of B10F16 melanoma cells exceeds that of normal cells by 1.0 to 1.5%, whereas their glucose uptake is equal to 3.6 billion glucose molecules/cell per minute. Summary: Living things are complex adaptive systems, thus a different way of thinking and investigating, going beyond the current reductive approach, is required.

Original language | English (US) |
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Pages (from-to) | S87-S91 |

Journal | Annals of plastic surgery |

Volume | 77 |

DOIs | |

State | Published - Jan 1 2016 |

### Keywords

- Bioenergetics
- Cancer
- Complex adaptive systems
- Control
- Craniofacial
- Fractal
- Limit
- Morphogenesis
- Power law
- Repeated iteration function
- Tissue dynamics

### ASJC Scopus subject areas

- Surgery

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## Cite this

*Annals of plastic surgery*,

*77*, S87-S91. https://doi.org/10.1097/SAP.0000000000000729