Equation (22) is obtained by replacing λ with ˜ λ$_{k}$ in Eq. (13). The parameter V$_{1}$ in Eq. (22) is the total volume of the cell (the core and the shells). In the limit of a dilute suspension of identical shelled particles, with a low volume fraction f , the effective permittivity (1) is In general, the effective permittivity ϵ$_{sus}$ of a suspension of objects with m shells will have m +1 Debye relaxation terms for each dipole active eigenmode. The proof is recursive and is based on partial fraction expansion with respect to variable iω of equations (22) and (23), provided that the complex permittivity of various dielectric phases is ϵ = ε − i σ/ ( ωε$_{vac}$ ) where i = √ − 1 and ε$_{vac}$ is the permittivity of the free space (8 . 85 × 10 − 12 F/m). Thus the first Debye term comes out from (23) and the remaining m Debye terms result from (21) by the homogenization process described for shelled particles. Hence, a suspension of cells with m shells (and m +1 interfaces) has a dielectric spectrum containing a number of Debye terms equal to m + 1 times the number of dipole-active eigenvalues. The suspension effective permittivity ϵ$_{sus}$ has the expansion where ϵ$_{f}$ = ε$_{hf}$ − i σ$_{lf}$/ ( ωε$_{vac}$ ), ε$_{hf}$ is the high-frequency permittivity, and σ$_{lf}$ is the low- frequency conductivity; Δ ε$_{kj}$ and T$_{kj}$ are the dielectric decrement and the relaxation time of the kj Debye term, respectively; index k enumerates the dipole-active eigenmodes and index j enumerates interfaces. Although the measurable bulk quantities in equation (24) are directly correlated with the microscopic (electric and shape) parameters, a solution of the inverse problem, which aims at obtaining the microscopic information non-intrusively, from the effective permittivity, is in general difficult, if not impossible for the general multi-shell structure. However, biolog- ical cell has a thin and almost non-conductive membrane, and several simplifications and approximations can be made. Two Debye relaxation terms in the effective permittivity ϵ$_{sus}$ are expected for each dipole-active eigenmode, corresponding to the two interfaces which define the membrane. 9 ϵ$_{sus}$ = ϵ$_{f}$ + ∑ k,j Δ ε$_{kj}$/ (1 + i ω T$_{kj}$) (24) ε sus = ε$_{0}$ ( 1 + f ∑ k p$_{k}$ ˜ ε$_{k}$ − ε$_{0}$ (1 / 2 + χ$_{k}$ ) ε$_{0}$ + (1 / 2 − χ$_{k}$ )˜ ε$_{k}$ ) . (23) C. The Debye relaxation expansion