Equation describing critical radius What are the coefficients α, β, and κ in this equation for decompression-induced gas bubble growth in human tissue?

I am reading a text about gas nuclei I encountered the following formula:

$r = \alpha + \beta \left( \frac{T}{P} \right)^\frac{1}{3} + \kappa \left( \frac{T}{P} \right)^\frac{2}{3}$$$r = \alpha + \beta \left( \frac{T}{P} \right)^\frac{1}{3} + \kappa \left( \frac{T}{P} \right)^\frac{2}{3}$$

$r$ is the critical radius of the nucleus, while $T$ and $P$ are the current temperature and pressure respectively.

I have no idea what $\alpha$, $\beta$ or $\kappa$ are. Also, I don't even known the name of such formula and the principle behind it.

Can anybody explain what $\alpha$, $\beta$ or $\kappa$ are and what the underlying principle is?

The text is REDUCED GRADIENT BUBBLE MODEL, page 12 equation 61.

UPDATE:

The problem is that I'm not able to find the values of the three constants. If I use the values from the first three rows of the table below the equation:

$T = 293 K, P = 13 fsw, r = 2.10$
$T = 293 K, P = 33 fsw, r = 1.36$
$T = 293 K, P = 53 fsw, r = 1.34$

I get (approximately) $\alpha = 4.395, \beta = -3.260, \kappa = 0.866$. However such values do not work for e.g. $P = 273 fsw$. If I use my constants, I get $r = 1.966$, while the table reports $r = 0.80$.

Also, the table shows that $r$ decreases for $P \in [13, 273]$, my function increases approximately at $P = 73$ (where my $r$ is 1.403 against 1.32).

I think $\alpha$, $\beta$ and $\kappa$ must be functions of pressure. The Wikipedia page about Equation of State shows $\alpha$ and $\kappa$ as functions of pressure and temperature, but there are no traces of $\beta$.

Equation describing critical radius for decompression-induced gas bubble growth in human tissue

I am reading a text about gas nuclei I encountered the following formula:

$r = \alpha + \beta \left( \frac{T}{P} \right)^\frac{1}{3} + \kappa \left( \frac{T}{P} \right)^\frac{2}{3}$

$r$ is the critical radius of the nucleus, while $T$ and $P$ are the current temperature and pressure respectively.

I have no idea what $\alpha$, $\beta$ or $\kappa$ are. Also, I don't even known the name of such formula and the principle behind it.

Can anybody explain what $\alpha$, $\beta$ or $\kappa$ are and what the underlying principle is?

The text is REDUCED GRADIENT BUBBLE MODEL, page 12 equation 61.

UPDATE:

The problem is that I'm not able to find the values of the three constants. If I use the values from the first three rows of the table below the equation:

$T = 293 K, P = 13 fsw, r = 2.10$
$T = 293 K, P = 33 fsw, r = 1.36$
$T = 293 K, P = 53 fsw, r = 1.34$

I get (approximately) $\alpha = 4.395, \beta = -3.260, \kappa = 0.866$. However such values do not work for e.g. $P = 273 fsw$. If I use my constants, I get $r = 1.966$, while the table reports $r = 0.80$.

Also, the table shows that $r$ decreases for $P \in [13, 273]$, my function increases approximately at $P = 73$ (where my $r$ is 1.403 against 1.32).

I think $\alpha$, $\beta$ and $\kappa$ must be functions of pressure. The Wikipedia page about Equation of State shows $\alpha$ and $\kappa$ as functions of pressure and temperature, but there are no traces of $\beta$.

What are the coefficients α, β, and κ in this equation for decompression-induced gas bubble growth?

I am reading a text about gas nuclei I encountered the following formula:

$$r = \alpha + \beta \left( \frac{T}{P} \right)^\frac{1}{3} + \kappa \left( \frac{T}{P} \right)^\frac{2}{3}$$

$r$ is the critical radius of the nucleus, while $T$ and $P$ are the current temperature and pressure respectively.

I have no idea what $\alpha$, $\beta$ or $\kappa$ are. Also, I don't even known the name of such formula and the principle behind it.

Can anybody explain what $\alpha$, $\beta$ or $\kappa$ are and what the underlying principle is?

The text is REDUCED GRADIENT BUBBLE MODEL, page 12 equation 61.

UPDATE:

The problem is that I'm not able to find the values of the three constants. If I use the values from the first three rows of the table below the equation:

$T = 293 K, P = 13 fsw, r = 2.10$
$T = 293 K, P = 33 fsw, r = 1.36$
$T = 293 K, P = 53 fsw, r = 1.34$

I get (approximately) $\alpha = 4.395, \beta = -3.260, \kappa = 0.866$. However such values do not work for e.g. $P = 273 fsw$. If I use my constants, I get $r = 1.966$, while the table reports $r = 0.80$.

Also, the table shows that $r$ decreases for $P \in [13, 273]$, my function increases approximately at $P = 73$ (where my $r$ is 1.403 against 1.32).

I think $\alpha$, $\beta$ and $\kappa$ must be functions of pressure. The Wikipedia page about Equation of State shows $\alpha$ and $\kappa$ as functions of pressure and temperature, but there are no traces of $\beta$.