EFFECT OF CELL ARRANGEMENT AND INTERSTITIAL VOLUME FRACTION ON THE DIFFUSIVITY OF MONOCLONAL-ANTIBODIES IN TISSUE

We present theoretical calculations relating the effective diffusivity of monoclonal antibodies in tissue (D(eff)) to the actual diffusivity in the interstitium (D(int)) and the interstitial volume fraction phi . Measured diffusivity values are effective values, deduced from conce ntration profiles with the tissue treated as a continuum. By using hom ogenization theory, the ratio D(eff)/D(int) is calculated for a range of interstitial volume tractions from 1 0 to 65%. It is assumed that o nly diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cel ls arranged periodically, with uniform gaps between cells. D(eff)/D(in t) is found to generally be betWeen(2/3)phi and phi for these geometri es. In general, the pathways for diffusion between cells are not strai ght. The effect of winding pathways on D(eff)/D(int) is examined by va rying the arrangement of the cells, and found to be slight. Also, the estimates of D(eff)/D(int) are shown to be insensitive to typical nonu niformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusi vity of an IgG polyclonal antibody both in water and in tumor tissue, we deduce that the diffusivity of this molecule in the interstitium is one-tenth to one-twentieth its diffusivity in water. We also conclude that exclusion of molecules from cells (an effect independent of mole cular weight) contributes as much as interstitial hindrance to the red uction of effective diffusivity, for small interstitial volume fractio ns (around 20%). This suggests that the increase in the rate of delive ry to tissues resulting from the use of smaller molecular-weight molec ules (such as antibody fragments or bifunctional antibodies) may be le ss than expected.