MEASUREMENT AND SIMULATION OF WATER TRANSPORT DURING FREEZING IN MAMMALIAN LIVER-TISSUE

Optimization of cryosurgical procedures on deep tissues such as liver requires an increased understanding of the fundamental mechanisms of i ce formation and water transport in tissues during freezing. In order to further investigate and quantify the amount of water transport that occurs during freezing in tissue, this study reports quantitative and dynamic experimental data and theoretical modeling of rat liver freez ing under controlled conditions. The rat liver was frozen by one of fo ur methods of cooling: Method 1-ultrarapid ''slam cooling'' (greater t han or equal to 1000 degrees C/min) for control samples; Method 2-equi librium freezing achieved by equilibrating tissue at different subzero temperatures (-4, -6, -8, -10 degrees C); Method 3-two-step freezing, which involves cooling at 5 degrees C/min. to -4, -6, -8, -10 or -20 degrees C followed immediately by slain cooling; or Method 4-constant and controlled freezing at rates from 5-400 degrees C/Ni in. on a dire ctional cooling stage. After freezing, the tissue was freeze substitut ed, embedded in resin, sectioned, stained, and imaged under a light mi croscope fitted with a digitizing system. Image analysis techniques we re then used to determine the relative cellular to extracellular volum es of the tissue. The osmotically inactive cell volume was determined to be 0.35 by constructing a Boyle van't Hoff plot using cellular volu mes from Method 2. The dynamic volume of the rat liver cells during co oling was obtained using cellular volumes from Method 3 (two-step free zing at 5 degrees C/min). A nonlinear regression fit of a Krogh cylind er model to the volumetric shrinkage data in Method 3 yielded the biop hysical parameters of water transport in rat liver tissue of: L-pg = 3 .1 X 10(-13) m(3)/Ns (1.86 mu m/min-atm) and E-Lp = 290 kJ/mole (69.3 kcal/mole), with chi-squared variance of 0.00124. These parameters wer e then incorporated into the Krogh cylinder model and used to simulate water transport in rat liver tissue during constant cooling at rates between 5-100 degrees C/min. Reasonable agreement between these simula tions and the constant cooling rate freezing experiments in Method 4 w ere obtained The model predicts that the water transport ceases at a r elatively, high subzero temperature (-10 degrees C), such that the amo unt of intracellular ice forming in the tissue cells rises from almost none (=extensive dehydration and vascular expansion) at less than or equal to 5 degrees C/min to over 88 percent of the original cellular w ater at greater than or equal to 50 degrees C/min. The theoretical sim ulations based on these experimental methods may be of use in visualiz ing and predicting freezing response, and thus can assist in the plann ing and implementing of cryosurgical protocols.