Table 1.
Variable [Unit] | Description | Normal Value | Tumor Value | |
---|---|---|---|---|
Bioheat Equation,
Eq. (11), (12)
| ||||
ρ [kg/m3] | Tissue densitya | 1050 | 1050 | |
C[J kg−1K−1] | Tissue heat capacitya | 3600 | 3600 | |
k[W m−1K−1] | Thermal conductivitya | 1.0 (0.7) | 1.0 | |
ωb[s−1] | Perfusion ratea | 0.006(0.007) | 0.006 | |
Tb[°C] | Blood temperature | 37 | 37 | |
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Ultrasound Treatment Parameters Eq. (12) | ||||
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Ptap[W] | Acoustic powera | 12 | 12 | |
αz[m−1] | Ultrasound absorptiona | 2.6 | 2.6 | |
σR[mm] | Beam waist half-widtha |
|
1.13 | |
σz[mm] | Focal spot half-lengtha |
|
5.27 | |
| ||||
Fluid Transfer Equation, Eqs. (1) – (3), (6) | ||||
| ||||
Tc[°C] | Transition temperatureb | 49 | 49 | |
λ,μ [mmHg] | Lamé coefficientsc | 684, 15.2 | 684, 15.2 | |
H0[mmHg] | Aggregate modulus | 714 (= λ + 2μ) | 714 | |
f = −ΔH/H0 | Fractional change in H | 0.53 | 0.53 | |
|
Fluid conductivityd | 2.5× 10−7 | 2.5× 10−7 | |
|
Filtration coefficientd | 3.6 × 10−8 | 1.86 × 10−6 | |
S/V[cm−1] | Vascular surface densityd | 100 [50–250] | 100 [50–250] | |
|
Effective filtrationd | 3.6 × 10−6 | 1.86 × 10−4 | |
σ | Osmotic reflection (BSA)d | 0.91 | 8.7× 10−5 | |
πv, πi [mmHg] | Osmotic pressuresd | 20, 10 | 19.8, 17.3 | |
PSS[mmHg] | Steady state IFP | 1.0 | 10 | |
ϕ0 | Volume fraction of fluide | 0.13–0.3 | 0.35–0.55 | |
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Solute Transport Equation, Eqs. (4), (5), (9) | ||||
| ||||
D [cm2/s] | Solute diffusivityf | 4.8 × 10−10 | 1.3 × 10−8 | |
rF | Convection efficiency | 1.0 | 1.0 | |
ζeff [cm/s] | Effective permeabilityf | 7.3 × 10−8 | 5.73 × 10−7 | |
Σ | Effective solute reflection | 0.9 | 0.0001 | |
τp[hr] | Solute plasma half-lifef | 72 | 72 |
Data taken from O’Neill et al (2012)
Data taken from O’Neill et al (2013)
Data taken from Netti et al (1997)
Data taken from Jain et al (2007)
Data taken Jain (1987)
Data taken from Baxter and Jain RK (1989)