Cells seeded on a porous biomaterial scaffold proliferate to fill the available space while nutrients and oxygen are delivered by perfusion flow through the bioreactor. Growth follows a logistic model bounded by a carrying capacity set by the scaffold's pore volume (porosity), and the effective growth rate depends on how well-perfused the construct is.
dN/dt = r_eff · N · (1 − N/K)
r_eff = r_base · (0.4 + 0.6 · Q/Q_max)
K = K_max · (φ / 100)
I(t) = 100 · e^(−k_d · t)
N = live cell number, K = carrying capacity, r_eff = perfusion-adjusted proliferation rate, Q = perfusion flow rate, φ = scaffold porosity (%), I(t) = scaffold structural integrity as the bioresorbable polymer degrades at rate k_d.
- Seeding density sets the initial fraction of the carrying capacity occupied by cells at t = 0.
- Proliferation rate r is the intrinsic per-cell division rate of the logistic model.
- Scaffold porosity sets the carrying capacity K — more open pore space, more room for tissue to form.
- Perfusion flow rate scales oxygen/nutrient delivery, directly multiplying the effective growth rate.
- Scaffold degradation controls how fast the bioresorbable scaffold loses structural integrity as it is replaced by extracellular matrix.
This mirrors real regenerative-medicine practice: seeding stem or progenitor cells onto resorbable scaffolds inside perfusion bioreactors to grow functional replacement tissue for skin, cartilage, bone, or vascular grafts.