The sample size formula is based on Equation 8.30 on page 335 of Rosner (2006).
$$
n=\frac{2\sigma_d^2 (Z_{1-\alpha/2} + Z_{power})^2}{\delta^2}
$$
where \(\sigma_d = \sigma_1^2+\sigma_2^2-2\rho\sigma_1\sigma_2\), \(\delta=|\mu_1 - \mu_2|\),
\(\mu_1\) is the mean change over time \(t\) in group 1,
\(\mu_2\) is the mean change over time \(t\) in group 2,
\(\sigma_1^2\) is the variance of baseline values within a treatment group,
\(\sigma_2^2\) is the variance of follow-up values within a treatment group,
\(\rho\) is the correlation coefficient between baseline and follow-up values within a treatment group,
and \(Z_u\) is the u-th percentile of the standard normal distribution.
We wish to test \(\mu_1 = \mu_2\).
When \(\sigma_1=\sigma_2=\sigma\), then formula reduces to
$$
n=\frac{4(1-\rho)(Z_{1-\alpha/2}+Z_{\beta})^2}{d^2}
$$
where \(d=\delta/\sigma\).