### Abstract

INTRODUCTION: Why are cranial sutures the way they are? How do cancers grow? Merging physics and mathematics with biology, we develop equations describing these complex adaptive systems, to which all biological entities belong, calling them laws of tissue dynamics:limΔt→T∑Δ[niCelli + Matrixj]/Δt = 0, for any stable tissue, niCelli = ϕ(Matrixi), Matrixi = f(Celli), both ϕ and f are recursive functions still to be determined, t is unit time and T is greater than t, n is the number of cells (1)k = t × [ΔE]max, or alternatively, using power law: [ΔE]max = Ce, and X = X0M, b = 3/4, Ln t + Ln[ΔE]max = constant, the power law format: Ln[ΔE]max = Ln C − at = Constant − at, Ln[ΔE]max + at = Constant (2)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 of malignant 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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Journal | Annals of Plastic Surgery |

DOIs | |

State | Accepted/In press - Jan 21 2016 |

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### ASJC Scopus subject areas

- Surgery

### Cite this

*Annals of Plastic Surgery*. https://doi.org/10.1097/SAP.0000000000000729

**Tissue Dynamics : Lessons Learned From Sutural Morphogenesis and Cancer Growth.** / Yu, Jack C; Cai, Lei; Wang, Tien Hsiang; Berdel, Henrik O.; Lee, Jun Hoon; Lam, Poh Sang; Hershman, John; Baban, Babak.

Research output: Contribution to journal › Article

*Annals of Plastic Surgery*. https://doi.org/10.1097/SAP.0000000000000729

}

TY - JOUR

T1 - Tissue Dynamics

T2 - Lessons Learned From Sutural Morphogenesis and Cancer Growth

AU - Yu, Jack C

AU - Cai, Lei

AU - Wang, Tien Hsiang

AU - Berdel, Henrik O.

AU - Lee, Jun Hoon

AU - Lam, Poh Sang

AU - Hershman, John

AU - Baban, Babak

PY - 2016/1/21

Y1 - 2016/1/21

N2 - INTRODUCTION: Why are cranial sutures the way they are? How do cancers grow? Merging physics and mathematics with biology, we develop equations describing these complex adaptive systems, to which all biological entities belong, calling them laws of tissue dynamics:limΔt→T∑Δ[niCelli + Matrixj]/Δt = 0, for any stable tissue, niCelli = ϕ(Matrixi), Matrixi = f(Celli), both ϕ and f are recursive functions still to be determined, t is unit time and T is greater than t, n is the number of cells (1)k = t × [ΔE]max, or alternatively, using power law: [ΔE]max = Ce, and X = X0M, b = 3/4, Ln t + Ln[ΔE]max = constant, the power law format: Ln[ΔE]max = Ln C − at = Constant − at, Ln[ΔE]max + at = Constant (2)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 of malignant 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.

AB - INTRODUCTION: Why are cranial sutures the way they are? How do cancers grow? Merging physics and mathematics with biology, we develop equations describing these complex adaptive systems, to which all biological entities belong, calling them laws of tissue dynamics:limΔt→T∑Δ[niCelli + Matrixj]/Δt = 0, for any stable tissue, niCelli = ϕ(Matrixi), Matrixi = f(Celli), both ϕ and f are recursive functions still to be determined, t is unit time and T is greater than t, n is the number of cells (1)k = t × [ΔE]max, or alternatively, using power law: [ΔE]max = Ce, and X = X0M, b = 3/4, Ln t + Ln[ΔE]max = constant, the power law format: Ln[ΔE]max = Ln C − at = Constant − at, Ln[ΔE]max + at = Constant (2)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 of malignant 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.

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U2 - 10.1097/SAP.0000000000000729

DO - 10.1097/SAP.0000000000000729

M3 - Article

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AN - SCOPUS:84955608128

JO - Annals of Plastic Surgery

JF - Annals of Plastic Surgery

SN - 0148-7043

ER -