  We consider optical response induced by bound states in the continuum (BICs)
in arrays of dielectric spheres. By combining quasi-mode expansion technique
with coupled mode theory (CMT) we put forward a theory of the optical response
by high-Q resonance surrounding BICs in momentum space. The central result are
analytical expressions for the CMT parameters, which can be easily calculated
from the eigenfrequencies and eigenvectors of the interaction matrix of the
scattering systems. The results obtained are verified in comparison against
exact numerical solutions to demonstrate that the CMT approximation is capable
of reproducing Fano features in the spectral vicinity of the BIC. Based on the
quasi-mode expansion technique we derived the asymptotic scaling law for the
CMT parameters in the vicinity of the $\Gamma$-point. It is rigorously
demonstrated that the line width in the CMT approximation exhibits different
asymptotic behaviour depending on the symmetry of the BIC.
