tissue

Home / Modules / Tissue

Tissue

Core epidermal biology module representing the stratified squamous epithelium of human skin.

Biology

Human epidermis is a self-renewing stratified epithelium organized into four principal strata. At the base, the stratum basale houses proliferative keratinocytes anchored to the basement membrane by integrin adhesion complexes. As cells divide, daughters are displaced upward into the stratum spinosum, where they enlarge and begin expressing differentiation markers. Continued ascent carries cells into the stratum granulosum, where they extrude lipid-filled lamellar bodies and assemble the cornified envelope. Finally, cells in the stratum corneum are terminally differentiated, anucleate corneocytes that form the primary permeability barrier before desquamating from the skin surface.

Extracellular calcium is the master regulator of this vertical program. The epidermis maintains a characteristic calcium gradient, low in the basale and rising sharply through the granulosum, that is sustained by tight junctions and ion pumps rather than by free diffusion. When extracellular calcium rises above successive thresholds, keratinocytes activate differentiation gene programs (involucrin, loricrin, filaggrin) and withdraw from the cell cycle. Below the epidermis, dermal fibroblasts secrete keratinocyte growth factor (KGF/FGF7), a paracrine mitogen that diffuses upward and binds FGFR2b on basal cells, accelerating their transit from G1 into S phase and sustaining the proliferative pool.

The basal layer itself is organized as a stem and transit-amplifying (TA) cell hierarchy. Stem cells divide asymmetrically, producing one daughter that retains stem identity and one that becomes a TA cell committed to a finite number of divisions before exiting the cycle. This architecture ensures long-term tissue renewal while buffering against clonal exhaustion. Oxygen and water, supplied by the dermal vasculature, impose metabolic constraints on proliferation and migration: hypoxia suppresses cell cycle entry, while dehydration from barrier loss impairs both crawling and mitosis.

The UWYN (Use When You Need) hybrid model leverages the observation that healthy epidermis exists in a steady state that can be fully described by continuum PDE fields (calcium, KGF, oxygen, water, stratum identity) without tracking individual cells. Discrete keratinocyte agents are spawned only when an event such as wounding disrupts the continuum equilibrium. After agents have restored local tissue integrity, cornified cells dissolve back into the continuum following a configurable handoff delay. This approach dramatically reduces computational cost in regions of the tissue that are quiescent while preserving single-cell resolution where it matters.

Model

The tissue module maintains five continuum fields and a suite of agent behaviors that together reproduce epidermal homeostasis and wound re-epithelialization. The VolumeManager partitions the simulation domain into horizontal layer profiles using z-height boundaries: basale below 6 um, spinosum from 6 to 15 um, granulosum from 15 to 25 um, and corneum above 25 um. The calcium field is initialized as a sigmoid profile rising from 0.05 mM at the basement membrane to 1.5 mM at the tissue surface, with midpoint and steepness parameters controlling the shape of the curve. KGF is initialized as an exponential decay from 2.0 nM at z=0, reflecting its dermal paracrine origin. Oxygen and water are both initialized as exponential decays from dermal baseline values, with their dermal source voxels pinned proportionally to the local Vascular perfusion field so that vascular damage or recovery directly modulates nutrient supply. The stratum field is a static scalar encoding layer identity at each voxel, used for visualization and gating of calcium recovery.

Each keratinocyte agent carries an explicit four-phase cell cycle (G1, S, G2, M) with literature-derived phase durations. Transition probabilities accumulate over time and are modulated multiplicatively by local field values: KGF boosts G1 to S via Michaelis-Menten kinetics, oxygen gates proliferation linearly below a hypoxia threshold, water gates proliferation below a dehydration threshold, and immune pressure (from the inflammation module) suppresses division through a Hill-function dose response. During S phase the cell grows in volume until it reaches a minimum division diameter. At M phase completion, the cell attempts division subject to contact inhibition: if the neighbor count exceeds max_neighbors, the cell enters quiescence (G0) instead. Successful divisions orient with a lateral scatter randomness and a wound-inward bias when applicable, and crowding in the basal layer triggers vertical extrusion of daughter cells to initiate stratification.

The stem and TA hierarchy governs clonal dynamics. Stem cells (identified by divisions_left = -1) divide indefinitely and are anchored to the basement membrane by simulated integrin adhesion. On division, a stem cell produces a TA daughter (with probability p_asymmetric) that inherits a finite division budget of max_ta_divisions. TA daughters decrement their count at each division and enter G0 when exhausted. The stem_fraction parameter controls the initial ratio of stem to TA cells when agents are seeded at the wound margin, with low-calcium voxels biased toward stem identity to reflect the basal niche environment.

Migration is implemented as a tractor force directed toward the wound center, composing naturally with BioDynaMo's mechanical repulsion. Speed scales with radial distance (leader cells at the wound edge move fastest, with a 30% floor to prevent convergence stall) and is gated by water availability, fibronectin concentration (integrin-mediated crawling enhancement), and immune pressure (Hill-function suppression). The differentiation behavior reads local calcium and z-height to assign stratum identity, with calcium able to override volume boundaries near layer transitions. Cornified cells that exceed the handoff_delay residence time dissolve back into the continuum, completing the per-cell UWYN lifecycle. The shedding behavior removes cornified cells after a configurable desquamation delay and clears exhausted TA cells that linger in the basale past the apoptosis timeout.

Parameters

Core tissue parameters live in bdm.core.toml under [skin]. The modules/tissue/config.toml file is minimal, serving as a placeholder for the merge script.

Cell cycle

Parameter	Default	Units	Description	Source
g1_duration	7.0	hours	G1 phase duration	Grabe & Bhatt-Neuber 2005
s_duration	6.0	hours	S phase duration	Grabe & Bhatt-Neuber 2005
g2_duration	3.0	hours	G2 phase duration	Grabe & Bhatt-Neuber 2005
m_duration	1.0	hours	M phase duration	Grabe & Bhatt-Neuber 2005

Division mechanics

Parameter	Default	Units	Description	Source
growth_rate	5	-	Volume growth rate during S phase	Calibrated
max_neighbors	14	count	Contact inhibition threshold	Eisenhoffer et al. 2012
lateral_scatter	0.3	-	Lateral randomness in division axis	Calibrated
max_ta_divisions	4	count	Max TA divisions before G0	Jones et al. 1993
division_diameter	5.0	um	Minimum diameter to divide	Calibrated
p_asymmetric	0.7	probability	Asymmetric stem division probability	Clayton et al. 2007
stem_fraction	0.50	fraction	Fraction of seeded basal cells that are stem	Safferling et al. 2013

Calcium gradient

Parameter	Default	Units	Description	Source
calcium_diffusion	0	-	Diffusion coefficient (0 = static prescribed)	Convention
calcium_decay	0	-	Decay rate (0 = persistent gradient)	Convention
calcium_basal	0.05	mM	Concentration at basement membrane	Menon et al. 1985
calcium_peak	1.5	mM	Concentration at tissue surface	Menon et al. 1985
calcium_midpoint_z	15.0	um	Z-height where sigmoid reaches 50%	Calibrated
calcium_steepness	2.0	-	Sigmoid steepness	Calibrated

Differentiation thresholds

Parameter	Default	Units	Description	Source
ca_spinous_threshold	0.1	mM	Ca2+ for spinous transition	Bikle et al. 2012
ca_granular_threshold	0.5	mM	Ca2+ for granular transition	Bikle et al. 2012
ca_cornified_threshold	1.0	mM	Ca2+ for cornified transition	Bikle et al. 2012
spinous_threshold	6.0	um	Z-height reinforcement for basal identity	Calibrated

Volume boundaries

Parameter	Default	Units	Description	Source
volume_z_spinous	6.0	um	Basal/spinous boundary	Calibrated
volume_z_granular	15.0	um	Spinous/granular boundary	Calibrated
volume_z_cornified	25.0	um	Granular/cornified boundary	Calibrated

KGF

Parameter	Default	Units	Description	Source
kgf_diffusion	0	-	Diffusion (0 = static)	Convention
kgf_decay	0	-	Decay (0 = persistent)	Convention
kgf_basal_conc	2.0	nM	Concentration at basement membrane	Calibrated
kgf_half_maximal	0.5	nM	Michaelis-Menten Km	Calibrated
kgf_max_boost	1.0	fold	Max fold-increase in G1 to S rate	Calibrated
kgf_decay_length	5.0	um	Z-scale for exponential decay	Calibrated

Oxygen

Parameter	Default	Units	Description	Source
oxygen_diffusion	0.1	-	Diffusion coefficient	Calibrated
oxygen_decay	0.01	-	Consumption rate	Calibrated
oxygen_basal_conc	1.0	normalized	Arterial pO2 at z=0	Convention
oxygen_decay_length	8.0	um	Z-scale for initial profile	Calibrated
oxygen_prolif_threshold	0.3	normalized	O2 below this suppresses proliferation	Calibrated
oxygen_recovery_enabled	true	bool	Vasculature regenerates with healing	Convention

Water

Parameter	Default	Units	Description	Source
water_diffusion	1e-4	-	Lateral diffusion	Calibrated
water_decay	0.002	-	Background TEWL	Calibrated
water_basal_conc	1.0	normalized	Hydration at dermis	Convention
water_decay_length	12.0	um	Z-scale for initial profile	Calibrated
water_recovery_rate	0.02	per step	Serum hydration rate	Sakai et al. 2005
water_surface_loss_rate	0.03	per step	Evaporation at exposed surface	Calibrated
water_migration_threshold	0.3	normalized	Min moisture for full migration	Calibrated
water_prolif_threshold	0.4	normalized	Min moisture for full proliferation	Calibrated

Mechanics

Parameter	Default	Units	Description	Source
repulsion_coeff	5.0	-	Hertz-like steric repulsion	Van Liedekerke et al. 2015
attraction_coeff	0.0	-	Desmosome/E-cadherin adhesion	Calibrated

Shedding

Parameter	Default	Units	Description	Source
shedding_delay	99999	steps	Steps before cornified cells shed	Convention
apoptosis_delay	99999	steps	Steps before exhausted TA cells die	Convention

Dynamic coupling

Parameter	Default	Units	Description	Source
calcium_recovery_rate	0.002	per step	Sigmoid recovery rate in healed voxels	Calibrated
migration_enabled	true	bool	Active crawling toward wound center	Convention
migration_speed	2.0	-	Tractor force magnitude	Calibrated
handoff_delay	500	steps	Steps in stable stratum before dissolving	Calibrated

Coupling

Reads

Field	Source module	How used
Vascular	perfusion	O2 and Water dermal pinning proportional to local perfusion
ImmunePressure	inflammation	Hill-function gating of migration speed and G1 to S probability
Fibronectin	fibronectin	Migration speed boost via integrin-FN binding
Hyaluronan	hyaluronan	Water retention modulation

Writes

Field	Consumer modules	What is written
Calcium	(self)	Sigmoid gradient, wound recovery
KGF	(self)	Exponential decay from dermis
O2	(self), fibroblast	Perfusion-gated dermal source
Water	(self)	Perfusion-gated dermal source, TEWL evaporation
Stratum	wound, scar, tumor	Layer identity from differentiating agents

Validation

Dataset	Observable	Sources	Notes
core_tissue_parameters	Cell cycle, calcium, KGF, stem hierarchy	Grabe 2005, Menon 1985, Bikle 2012, Adra 2010, Jones 1993, Clayton 2007, Safferling 2013	Parameter derivation
normal_skin_profile	Turnover time, stem fraction	Dover & Potten 1988, Potten 1988	Healthy adult epidermis

Metrics

Column	Units	Description
n_agents	count	Active keratinocyte agents
n_stem	count	Stem cell agents
n_ta	count	Transit-amplifying agents
n_g0	count	Quiescent (G0) agents
n_basal	count	Agents in stratum basale
n_spinous	count	Agents in stratum spinosum
n_granular	count	Agents in stratum granulosum
n_cornified	count	Agents in stratum corneum
mean_o2_wound	normalized	Mean O2 in wound cylinder
mean_ca_wound	mM	Mean Ca2+ in wound cylinder

Source files

File	Purpose
keratinocyte.h	Keratinocyte agent with stratum, cell cycle, stem/TA identity
basal_division.h	G1/S/G2/M cell cycle with O2, water, KGF, inflammation gating
migration.h	Tractor force toward wound center with inflammation, water, fibronectin gating
differentiation.h	Calcium-driven stratum transitions
shedding.h	Desquamation and UWYN continuum handoff
stratum.h	Stratum continuum field PDE
calcium.h	Calcium gradient field with wound recovery
kgf.h	KGF growth factor field
oxygen.h	Oxygen diffusion with vascular source
water.h	Water diffusion, evaporation, and dermal pinning
config.toml	Module configuration (placeholder; params in bdm.core.toml)