EPITAXIAL RELATIONSHIPS OF CUPROIYS OXIDEatomic scale (111) facets which make up the structure of the (012) plane. The electron microscope pictures, in addition to confirming the orientations determined by electron diffraction, gave specific data on the shapes of the oxide growth and the particular faces present. 0nly the three most densely packed faces occurred on the oxide.The authors would like to thank Dr A. T. Gwathmey and Dr N. Cabrera for many helpful discussions. This work was sponsored by the Office of Naval Research.References BRADLEY, D. E. (1954). J. Inst. Met. 83, 35. DONY-HENAVLT, O. (1910). Bull. Soc. Chem. Belg. The fitting of a plane or a line to a set of points by least squares is discussed, and a convenient numerical method is given.In the description of a crystal structure, it is sometimes desired to fit a least-squares plane to the positions found for some approximately coplanar set of atoms.Because it seems that an incorrect method is often used for doing this, we would like to discuss the problem and recommend an alternative method that is both correct in principle and convenient in computation. It becomes evident that the problem of the plane is essentially equivalent to the problem of finding the principal plane of least inertia for a set of point masses and that the problem of the best line is similarly equivalent to the very closely related problem of the least axis of inertia. The discussion therefore naturally covers line as well as plane and essentially recapitulates parts of a classical mechanical theory in deriving what is special to the present application. We first formulate the problem of the plane and present the recommended alternative method of solution, including a detailed numerical example, then discuss the prevalent incorrect method as well as various special cases, and finally consider the problem of the line and give a convenient method for handling it. * Contribution No. 2287 from the Gates and Crellin Laboratories.We find it convenient to use both ordinary vector notation, as in equations (1), (2), and (3), and matrix notation, as in equation (11), sometimes side by side. We also use two summation conventions: the Gaussian bracket [ ], to express summation over a set of points (cf., e.g., Whittaker & Robinson, 1940), and the convention of dropping the operator Z whenever it applies to repeated alphabetic indices. Definitions we often express as identities. The least-squares planeWhat is desired is to find the plane that minimizes , the weighted sum of squares of distances D~ of points k from the plane sought. These points are defined by the vectors r -xlal +x2a2+xSas -= x'a,.(The plane is defined by its unit normal and by the origin-to-plane distance d, whereupon the distance from the plane to a point is

We explore the ramifications of the fractal geometry of the key organ for drug elimination, the liver, on pharmacokinetic data analysis. A formalism is developed for the use of a combination of well-stirred Euclidean and fractal compartments in the body. Perturbation analysis is carried out to obtain analytical solutions for the drug concentration time evolution. These results are then fitted to experimental data collected from clinically instrumented dogs [see, A. Skerjanec et al., J. Pharm. Sci. 85, 189 (1995)] using the drug mibefradil. The thus obtained spectral fractal dimension has a range of values that is consistent with the value found in independently performed ultrasound experiments on the liver.

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We develop a physiologically-based lattice model for the transport and metabolism of drugs in the functional unit of the liver, called the lobule. In contrast to earlier studies, we have emphasized the dominant role of convection in well-vascularized tissue with a given structure. Estimates of convective, diffusive and reaction contributions are given. We have compared drug concentration levels observed exiting the lobule with their predicted detailed distribution inside the lobule, assuming that most often the former is accessible information while the latter is not.