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Abstract
The step-temperature technique is a thermal technique that uses a small thermistor probe for measuring blood perfusion of tissue. The blood perfusion is derived from temperature and power measurements using equations that describe heat transfer in the integrated probe/tissue system. A numerical experiment is used to analyse the theoretical error caused by the assumptions used in the technique. The effects of the bead parameters, tissue parameters and measurement parameters are investigated. The study results are in accordance with experimental phenomena described previously. An optimal measurement time window is found to be 4 – 10 s, dependent mainly on the thermal conductivity and blood perfusion of tissue measured. This research will lead to reduce perfusion measurement errors.
| Nomenclature | ||
| a | = | probe bead radius (m) |
| C | = | specific heat (J kg−1 °C−1) |
| f(t) | = | transient power function (s−1/2) |
| k | = | thermal conductivity (W m−1 °C−1) |
| q(t) | = | transient power (W) |
| r | = | radial distance in spherical coordinates (m) |
| T | = | temperature (°C) |
| t | = | time (s) |
| ΔT | = | volume average temperature increment of bead (°C) |
| Wb | = | tissue blood perfusion (kg m−3 s−1) |
| z | = | CbWba2/kt |
| α | = | thermal diffusivity (m2 s−1) |
| Γ | = | steady state power (W m−3) |
| β | = | slope of transient power (W s1/2 m−3) |
| θ | = | temperature increment, T(r, t) –T0(r, t) (°C) |
| ρ | = | density (kg m−3) |
| Subscripts | ||
| a | = | arterial |
| b | = | blood |
| p | = | probe bead |
| t | = | tissue |
| eff | = | effective |
| 0 | = | initial |
| Nomenclature | ||
| a | = | probe bead radius (m) |
| C | = | specific heat (J kg−1 °C−1) |
| f(t) | = | transient power function (s−1/2) |
| k | = | thermal conductivity (W m−1 °C−1) |
| q(t) | = | transient power (W) |
| r | = | radial distance in spherical coordinates (m) |
| T | = | temperature (°C) |
| t | = | time (s) |
| ΔT | = | volume average temperature increment of bead (°C) |
| Wb | = | tissue blood perfusion (kg m−3 s−1) |
| z | = | CbWba2/kt |
| α | = | thermal diffusivity (m2 s−1) |
| Γ | = | steady state power (W m−3) |
| β | = | slope of transient power (W s1/2 m−3) |
| θ | = | temperature increment, T(r, t) –T0(r, t) (°C) |
| ρ | = | density (kg m−3) |
| Subscripts | ||
| a | = | arterial |
| b | = | blood |
| p | = | probe bead |
| t | = | tissue |
| eff | = | effective |
| 0 | = | initial |