Partial identification of underdetermined compartmental models: a method based on positive linear Lyapunov functions.

A class of models is considered in which the number of unknown parameters exceeds the number of independent equations that are derived from the input/observation configuration. It is shown that, under certain circumstances, if the number of unknown parameters is sufficiently decreased by setting some of the exit parameters to zero, then the fallaciously derived model has the following interesting properties. The functions of time that give the amounts in the compartments are constant multiples of their counterparts in the fallacious model. A subset of the fallacious fractional transfer coefficients have the same values as their counterparts in the true model whereas others yield interval bounds. These and related results are obtained from a method based on positive linear Lyapunov functions.

Constrained optimization and protein structure determination.

Energy minimization is one of the main approaches to the computational determination of macromolecular structure. Due to the approximations in the empirical free-energy functions and due to the computational difficulties in locating their global minima, the problem is at present intractable when the only information available is the sequence of subunits forming the molecule. A less-demanding problem in terms of both physics and mathematics is constrained optimization, which uses additional but incomplete experimental information such as distances between certain atoms. This paper reviews methods for generating molecular structure using bond lengths and angles as variables and shows how the structure can be fully specified in terms of local geometry. The analysis permits precise statements to be made about the minimum set of distances that specify a unique structure without recourse to energy minimization. We then discuss the complementary situation, i.e., structure prediction with energy minimization based only on sequence information. Finally, we show how distance constraints can be incorporated into energy minimization methods.

Estimation of tissue blood perfusion rate from diffusible indicator measurements: a sensitivity analysis.

Recording the washout of indicator (for example, heat, radio-labeled dissolved gas, etc.) transiently introduced into tissue allows the estimation of tissue blood perfusion rate. Analysis of the washout data requires a material balance which appropriately accounts for all transport mechanisms and sources and sinks of the given indicator. From that balance one may perform a sensitivity analysis which specifies the susceptibility of the perfusion estimate to experimental errors in any of the pertinent parameters and variables. The sensitivity analysis is based on the normalized partial derivatives of tissue indicator concentration with respect to the experimental variables. The results indicate that the estimation of the tissue blood perfusion rate is highly sensitive to errors in the concentration of the diffusible indicator which dominate, by two orders of magnitude or more, the errors attributed to other parameters. For typical experimental conditions, the errors in the perfusion estimate due to the various parameters are shown to vary considerably, according to the sensor position and time of measurement. Based on this type of analysis, one may specify optimal temporal and spatial domains for the parameter estimation in order to minimize error propagation. The optimal time domains are shown to differ from those used in typical indicator washout analyses for estimating tissue perfusion rate.

A systems-theory approach to the analysis of multiexponential fluorescence decay.

A mathematical model of the fluorescence decay experiment based on linear systems theory is presented. The model suggests an experimental technique that increases the probability of correctly determining the decay constants of a multicomponent system. The use of moment methods for data analysis improves accuracy by combining information obtained from several discrete experiments. Examples are presented to show that the analysis of a three component system composed of known standards is improved as the number of experimental determinations is increased from one to four. The discrete measurements are made by changing the excitation and emission wavelengths.

Comparative study between the SFS and LFS rotation as a possible morphogenic mechanism.

Cephalometric tracings of twenty-seven untreated adult Caucasians, selected on a clinical impression of reduced lower facial height were studied and compared with tracings of nine untreated adult Caucasians with increased lower facial height. Various linear and angular measurements for both groups were analyzed and compared. As has been previously described for the SFS, the LFS group can be subdivided into at least two subtypes. Subtype I is characterized by a long ramus, increased OP-PP, an increased SN:MP-angle, and excessive lower anterior facial height. These persons manifest the most typical clinical characteristics of the long face syndrome and have excessively long faces. In Subtype II, however, extreme backward and downward rotation of the mandible, combined with a short or extremely short ramus, is associated with an increase in lower anterior facial height. The increase in posterior maxillary height was not striking in this subtype. It was demonstrated that many of the characteristics of the LFS group and the SFS group can be explained by clockwise or counterclockwise rotation of the mandible "in concert" with the hyoid, tongue, pharynx, and cervical spine. The LFS group was characterized by a clockwise rotation of the mandible "in concert" with the hyoid, tongue, pharynx, and cervical spine. The mandible of the SFS group rotated similarly, but in the opposite counterclockwise direction. The vital need to maintain patency of the upper airway at the level of the base of the tongue may account for rotation in the LFS.

Superior repositioning of the maxilla: stability and soft tissue osseous relations.

The skeletal stability and soft-tissue changes associated with superior repositioning of the maxilla by Le Fort I osteotomy or simultaneous anterior and posterior maxillary osteotomies was studied in thirty patients by means of a computerized craniofacial model. Excellent skeletal stability was demonstrated 14 months postoperatively. Postsurgically, the reduction in lower face height and amount of maxillary incisor exposure resulted in improved facial balance. The use of a computerized osseous and soft-tissue craniofacial model has added a new dimension to evaluation of surgical changes associated with correction of dentofacial and craniofacial deformities.

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.

Soft-hard tissue correlations and computer drawings for the frontal view.

Hard and soft tissue measurements were obtained for nine Caucasian women. Based on these measurements, regression formulas were derived to approximate the soft tissue covering based on hard tissue data. The results are presented iconically by computer drawings. The preliminary data presented would suggest a definite predictable influence exerted by the facial skeleton on the position of landmarks in the overlying soft tissue.