Jerome Eisenfeld

The long face syndrome: Vertical maxillary excess☆

There is a clinically recognizable facial morphology, the long face syndrome, which has been incompletely described in the literature. On the basis of the clinical summary in thirty-one adults with this syndrome, an analysis of esthetics, skeletal morphology, and occlusion was undertaken. Herein we report on these findings, which confirm that this basic dentofacial deformity is associated with excessive vertical growth of the maxilla. Dental open and closed bite are two variants of the syndrome. An increased mandibular ramus height is associated with the closed-bite group.

On identifiability of impulse-response in compartmental systems

Abstract Structural identifiability in compartmental systems deals with the map fromimpulse-response parameters to model parameters. If the data are analyzed in terms of integral transforms s k (Fourier, moments, etc.), then we may study also the map from the s k to impulse-response parameters. This paper is mainly concerned with the latter correspondence. In other words, we discuss the possibility of removing (inadvertently or intentionally) decay terms in the process of forming integral transforms.

Relationship between stochastic and differential models of compartmental systems

Abstract This paper shows that the differential-equation model for compartmental systems is consistent with a stochastic description. Consequently, we may employ either a differential-equation or a stochastic formulation, either for parameter identification or for physical interpretation, as best suits the purpose. The differential-equation parameters, the so-called fractional transfer coefficients, may be determined from the corresponding set of stochastic parameters and vice versa.

On mean residence times in compartments

Abstract This paper is concerned with a set of parameters which measure the mean time a random particle resides in individual compartments in response to a given load distribution. These parameters are related to other time parameters and to each other.

Some surface characteristics of articular cartilage—II. On the stability of articular surface and a possible biomechanical factor in etiology of chondrodegeneration

Abstract A biomechanical model is proposed for the study of the dynamic interaction of synovial fluid and articular cartilage. This model incorporates some of the salient SEM observed ultrastructural features of articular cartilage. The tissue is considered as a two-layer system with the superficial tangential zone considered as a mechanical plate and the middle and deep zone considered as an isotropic elastic medium. This model is a generalization of previously proposed ‘protective membrane’ models of other investigators. A normal mode stability analysis shows that a streaming fluid over such a two-layer system may create an instability at the fluid-solid interface. Quantitative results show that the critical speed is governed by the elastic modulus of the middle and deep zones. The band of unstable wavelengths is governed by the stiffness of the plate. Clearly, the present model for the dynamic interaction of synovial fluid and articular cartilage is a simple model. Even so the solution demonstrates a complex mechanical interaction phenomenon between the superficial tangential zone and the middle and deep zones. The limiting membrane solution of a surface tension effect (where the thickness of the superficial tangential zone becomes vanishingly small) has also been obtained. Based upon these solutions a possible mechanism is suggested as a factor in the etiology of chondrodegeneration.

On Washout in Nonlinear Compartmental Systems

Abstract Let x ( t ) be a solution of a compartmental system. If, for some compartment j , x j ( t )→0 as t →∞, then we say that the compartment j washes out. We show that a compartment washes out if it always reaches (along a fixed path) either the environment or another compartment for which there is no return path. Additional criteria, particularly regarding exponential convergence, are also presented. Examples are drawn from tracer kinetics, enzyme reactions, and epidemic models.

Stochastic parameters in compartmental systems

Abstract Let r ij denote the probability that a particle in compartment j will reach (or enter) compartment i . We present several formulas for obtaining the r ij in terms of the fractional transfer coefficients. The parameters are interesting for their own sake, and they are also useful for obtaining qualitative properties of compartmental systems and for interpreting results already obtained. The reachability parameters also play a role in structural identification, since they give us a new method for expressing the transfer function.

A simple solution to the compartmental structural-indentifiability problem

Abstract The problem of structural identifiability has been considered difficult because it requires the inversion of a highly nonlinear system of equations. The problem can be formulated in terms of the Jacobian matrix J ( θ ) of the transformation from the vector of unknown parameters θ to the vector of observable parameters. A necessary and sufficient condition for structural identifiability is that the function det[ J T ( θ ) J ( θ )] is different from zero almost everywhere in the parameter domain. It is not possible to verify this criterion numerically, because the domain of θ is uncountably infinite. This paper points out an important fact which reduces the difficulty of the problem enormously, viz., if the function (given above) is different from zero at one value of θ , then it is different from zero almost everywhere.

System Identification Problems and the Method of Moments

Abstract The method of moments is developed and applied to the identification problem arising in biosciences. In particular, we are concerned with computing the elements of an N × N matrix A such that X ′( t )= AX ( t )+ W ( t ), t > 0. Here the data for X ( t ) and W ( t ) is obtained from experiments. Using the moments, mom n ( X ) = ∫ ∞ 0 t n X ( t ) dt , of X ( t ) and W ( t ), we obtain a linear system of equations for the elements of A . An application to a four compartmental model for studying liver disorders is given. Numerical examples of our results are discussed in detail for flourescence decay experiments.

The role of nonreal eigenvalues in the identification of cycles in a compartmental system

Abstract The paper concerns the relationship between the cycles in the graph of a compartmental system and the modes of the impulse response function associated with an input-output experiment. Suppose that there is at least one oscillatory mode, e μt cos( vt - α ). Let e ϱt be the slowest mode. The main result is that the system contains a cycle of length 3 or longer and that the length of the longest cycle is at least π /tan -1 [¦ v ¦/( ϱ - μ )]. The paper also deals with the problem of estimating the cycle length from discrete data.