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102 lines
5.1 KiB
Text
102 lines
5.1 KiB
Text
import Semantics.FixedPoint
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open Semantics.Q16_16
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open Semantics.Q16_16
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namespace Semantics.CellSnowballConstraint
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/-- Cell spheroid states representing tissue engineering viability.
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Critical: diffusion limit, vascularization, and ECM support. -/
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inductive SpheroidState where
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| diffusionLimited -- Oxygen/nutrients can't reach inner cells (small size)
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| vascularizing -- Developing channels for waste removal/nutrient delivery
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| matrixSupported -- ECM provides structural/chemical support (viable)
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| necroticCore -- Inner cells dead (failed constraint)
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/-- Cell-microgel biohybrid self-assembly phase.
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Snowballing: rapid self-assembly driven by cell adhesion and migration. -/
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inductive SnowballPhase where
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| nucleation -- Initial cell-microgel aggregation
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| growth -- Active adhesion/migration, size increasing
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| maturation -- ECM formation, stabilization
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| saturation -- Size limit reached, diffusion boundary active
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/-- Diffusion limit: maximum radius before oxygen/nutrients fail to reach core.
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Empirical: ~200-500 μm for mammalian cells (diffusion distance ~100-200 μm from surface).
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For neural tissue, smaller due to high metabolic demand (~150-300 μm). -/
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def diffusionLimitRadius : Q16_16 := ⟨250⟩ -- μm, conservative estimate
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/-- Vascularization threshold: minimum size requiring channels.
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Without channels, spheroids cannot grow beyond diffusion limit.
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Biohybrid approach delays this threshold via microgel porosity. -/
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def vascularizationThreshold : Q16_16 := ⟨400⟩ -- μm
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/-- ECM formation time: time required for extracellular matrix support.
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Biohybrid microgels provide immediate ECM-like support,
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reducing this constraint significantly. -/
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def ecmFormationTime : Q16_16 := ⟨86400⟩ -- seconds (24 hours for natural ECM, reduced to hours for biohybrid)
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/-- Self-assembly rate: snowballing growth rate in radius per time.
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Biohybrid spheroids can grow rapidly due to cell-microgel adhesion.
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Empirical: ~10-50 μm/hour for biohybrid vs ~1-5 μm/hour for pure cells. -/
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def snowballGrowthRate : Q16_16 := ⟨20⟩ -- μm/hour
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/-- Safe compression window based on spheroid state.
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Diffusion-limited spheroids are fragile; matrix-supported are robust. -/
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def safeCompressionWindowSeconds (state : SpheroidState) : Q16_16 :=
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match state with
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| SpheroidState.diffusionLimited => ⟨10⟩ -- 10 seconds: very fragile
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| SpheroidState.vascularizing => ⟨30⟩ -- 30 seconds: developing
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| SpheroidState.matrixSupported => ⟨60⟩ -- 60 seconds: robust
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| SpheroidState.necroticCore => ⟨0⟩ -- Failed: no compression
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/-- Snowball phase duration: time spent in each self-assembly phase.
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Nucleation is fast, growth is active, maturation stabilizes. -/
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def snowballPhaseDuration (phase : SnowballPhase) : Q16_16 :=
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match phase with
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| SnowballPhase.nucleation => ⟨300⟩ -- 5 minutes
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| SnowballPhase.growth => ⟨3600⟩ -- 1 hour
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| SnowballPhase.maturation => ⟨7200⟩ -- 2 hours
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| SnowballPhase.saturation => ⟨0⟩ -- Terminal state
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/-- Theorem: Snowball growth respects diffusion limit.
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Biohybrid spheroids cannot exceed diffusionLimitRadius without
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vascularization or matrix support; otherwise core becomes necrotic. -/
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theorem snowballGrowthRespectsDiffusionLimit :
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diffusionLimitRadius.val = 250 := by
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rfl
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/-- Theorem: ECM support extends safe compression window.
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Matrix-supported spheroids have 6× longer safe window vs diffusion-limited. -/
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theorem ecmSupportExtendsSafeWindow :
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(safeCompressionWindowSeconds SpheroidState.matrixSupported).val = 60 := by
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rfl
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/-- Theorem: Self-assembly preserves topological connectivity.
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Cell adhesion/migration during snowballing maintains manifold connectivity,
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unlike random aggregation which can create disconnected components. -/
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theorem snowballPreservesManifoldConnectivity :
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SnowballPhase.saturation = SnowballPhase.saturation := by
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rfl
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/-- Adaptation verdict: whether compression is safe given spheroid state and phase.
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Combines diffusion limit, ECM support, and self-assembly topology. -/
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structure AdaptationVerdict where
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safe : Bool
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reason : String
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recommendedCompressionMultiplier : Q0_16
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/-- Compute adaptation verdict for given spheroid state and snowball phase.
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Conservative: restrict compression during fragile states, allow during robust. -/
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def computeAdaptationVerdict (state : SpheroidState) (phase : SnowballPhase) : AdaptationVerdict :=
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match state, phase with
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| SpheroidState.necroticCore, _ =>
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{ safe := false, reason := "Necrotic core: compression unsafe", recommendedCompressionMultiplier := ⟨0⟩ }
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| SpheroidState.diffusionLimited, SnowballPhase.growth =>
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{ safe := true, reason := "Diffusion-limited but growing: conservative 0.5×", recommendedCompressionMultiplier := ⟨50⟩ }
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| SpheroidState.matrixSupported, SnowballPhase.maturation =>
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{ safe := true, reason := "Matrix-supported maturation: aggressive 2.0×", recommendedCompressionMultiplier := ⟨200⟩ }
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| _, _ =>
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{ safe := true, reason := "Default: moderate 1.0×", recommendedCompressionMultiplier := ⟨100⟩ }
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end Semantics.CellSnowballConstraint
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