What Is the Krogh Cylinder Microvascular Oxygen Diffusion Calculator?
The Krogh cylinder models oxygen diffusion from a central capillary cylinder through a concentric sheath of consuming tissue.
How Does the Krogh Cylinder Microvascular Oxygen Diffusion Calculator Work?
Combines Ficks law of diffusion in cylindrical coordinates with constant zero-order metabolic oxygen consumption.
Krogh Cylinder Microvascular Oxygen Diffusion Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
P(r) = P_c - rac{M_0}{4K} left[ r^2 left(2 lnleft( rac{r}{r_c}
ight) - 1
ight) + r_c^2
ight]
Krogh-Erlang analytical solution for radial steady-state oxygen diffusion with zero-order consumption.
How to Use the Krogh Cylinder Microvascular Oxygen Diffusion Calculator
- Input capillary radius, outer tissue radius, blood PO2, metabolic consumption rate, and Krogh permeation coefficient.
Step-by-Step Example Calculation
Skeletal Muscle Tissue Cylinder
Input Values:
capillaryRadiusMicrons:4
tissueRadiusMicrons:28
capillaryPo2MmHg:42
oxygenConsumptionM0:0.045
diffusionKroghK:2.4
Worked Steps: PO2 at outer tissue boundary = 26.8 mmHg (adequately oxygenated, no peripheral anoxia).
Understanding Your Result
Shows PO2 at outer perimeter; if PO2 drops to zero, computes the critical anoxic radius.
Factors That Affect the Result
- Increased inter-capillary distance exponentially worsens tissue hypoxia; angiogenesis restores perfusion.
When Should You Use This Calculator?
- Physiological modeling, tumor hypoxia studies, ischemic tissue research, and artificial organ oxygenator design.
Assumptions & Limitations
- Assumes zero-order metabolic consumption and cylindrical symmetry without axial longitudinal diffusion.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Classical analytical solution in microvascular physiological transport.