### Abstract

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 ∅. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio D(eff)/D(int) is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. D(eff)/D(int) is found to generally be between (2/3)∅ and ∅ for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on D(eff)/D(int) is examined by varying 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 nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity 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 molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%), This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.

Original language | English (US) |
---|---|

Pages (from-to) | 1638-1646 |

Number of pages | 9 |

Journal | Biophysical Journal |

Volume | 64 |

Issue number | 5 |

State | Published - 1993 |

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### ASJC Scopus subject areas

- Biophysics

### Cite this

*Biophysical Journal*,

*64*(5), 1638-1646.

**Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue.** / Fox, Ardith El-Kareh; Braunstein, S. L.; Secomb, Timothy W.

Research output: Contribution to journal › Article

*Biophysical Journal*, vol. 64, no. 5, pp. 1638-1646.

}

TY - JOUR

T1 - Effect of cell arrangement and interstitial volume fraction on the diffusivity of monoclonal antibodies in tissue

AU - Fox, Ardith El-Kareh

AU - Braunstein, S. L.

AU - Secomb, Timothy W

PY - 1993

Y1 - 1993

N2 - 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 ∅. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio D(eff)/D(int) is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. D(eff)/D(int) is found to generally be between (2/3)∅ and ∅ for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on D(eff)/D(int) is examined by varying 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 nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity 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 molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%), This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.

AB - 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 ∅. Measured diffusivity values are effective values, deduced from concentration profiles with the tissue treated as a continuum. By using homogenization theory, the ratio D(eff)/D(int) is calculated for a range of interstitial volume fractions from 10 to 65%. It is assumed that only diffusion in the interstitial spaces between cells contributes to the effective diffusivity. The geometries considered have cuboidal cells arranged periodically, with uniform gaps between cells. D(eff)/D(int) is found to generally be between (2/3)∅ and ∅ for these geometries. In general, the pathways for diffusion between cells are not straight. The effect of winding pathways on D(eff)/D(int) is examined by varying 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 nonuniformities in the widths of gaps between cells. From our calculations and from published experimental measurements of the effective diffusivity 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 molecular weight) contributes as much as interstitial hindrance to the reduction of effective diffusivity, for small interstitial volume fractions (around 20%), This suggests that the increase in the rate of delivery to tissues resulting from the use of smaller molecular weight molecules (such as antibody fragments or bifunctional antibodies) may be less than expected.

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M3 - Article

C2 - 8324199

AN - SCOPUS:0027315777

VL - 64

SP - 1638

EP - 1646

JO - Biophysical Journal

JF - Biophysical Journal

SN - 0006-3495

IS - 5

ER -