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PubMed1987

LILLY--a linear least squares curve fitting program for one independent variable.

A program was written to perform a linear least squares curve fitting on data. It includes facilities to report the usual statistics and digital plotter output. Seven types of curves are available for fitting the data. Other features of LILLY include provision of facilities for the selection of subsets in different symbols and separate curve fitting for these subsets. The program also provides a confidence region about the fitted line and the prediction interval for data points. Examples of the use of the program are described.

Mathematical Computing↗

PubMedDate not supplied

ESB Research Award 1992. The mechanism of bone remodeling and resorption around press-fitted THA stems.

A major problem threatening the long-term integrity of total hip replacement is the loss of proximal bone often found around noncemented stems in the long term. It is generally accepted that 'stress shielding' is the cause for this problem: after implantation of the prosthesis the surrounding bone is partially 'shielding' from load carrying and starts to resorb. One of the proposed answers to this problem is the application of press-fitted stems. These smooth-surfaced implants are thought to provoke higher proximal bone loading, and, hence, less stress shielding than bonded implants, because they are wedged into the femur every time when loaded. However, in a two-year experiment in dogs, similar amounts of resorption of the proximal cortex were found around press-fitted and bonded implants. The question arises how similar resorption patterns can develop under completely different stress conditions, and whether this phenomenon can be explained by adaptive bone remodeling theories based on Wolff's law. In the present study an answer was sought for this question. An advanced iterative computer simulation model was used to analyze the remodeling process in the animal experiment. Three-dimensional finite element models were constructed from the animal experimental configuration, in which smooth, press-fitted stems were applied unilaterally in the canine. The FE model was integrated with iterative remodeling procedures, validated in earlier studies. In the model an appropriate non-linear representation of the loose bone-implant interface was realized, also capable of simulating the proximal interface gap that was found around the uncoated implants. The simulation models predicted similar amounts of proximal bone loss and distal bone densification as found in the animal model. Hence, the cortical bone loss could indeed be predicted by the strain-adaptive bone remodeling theory. By unraveling the simulation process, the question stated above could be answered. Densification of the distal bone bed during the initial remodeling process was found to cause reduced axial stem displacement (elastic subsidence), decreasing the wedging effect of the stem and, hence, decreasing the loading of the proximal bone, resulting in proximal bone loss. Hence, whereas in the case of bonded stems the proximal resorption process develops monotonously to a new equilibrium, the process around smooth, press-fitted stems develops nonmonotonously. This is due primarily to the unbonded interface conditions and the development of a proximal fibrous membrane. The remodeling process then gradually causes the stem to be jammed in the distal diaphyses (proximal 'stress bypass').

Alloys↗

PubMed1992

A comparative study of the fit and retention of interocclusal splints constructed from heat-cured and autopolymerized polymethylmethacrylate.

Fifty-three subjects each had a single Michigan splint constructed of either heat-cured or autopolymerized polymethylmethacrylate. The choice of material was decided randomly. A blind assessment for fit and retention was used on a three-point scale. Fit and retention were apparently unaffected by the material used. Thirteen percent of splints were unsatisfactory for clinical use (poor fit or retention) and this was also independent of material. A small number of splints contained structural faults (voids, porosity, or cracks) that may shorten the clinical life of these restorations; 9 of 12 such faults occurred in the autopolymerized group. Previous research has shown that conventional heat-cured polymethyl-methacrylate has superior properties compared with autopolymerized resin. In the absence of differences in accuracy of fit or retention, a heat-cured material is therefore advised where splints are intended for long-term clinical use.

Adult↗

PubMed1987

Transcervical sperm transport in the rat: the roles of pre-ejaculatory behavior and copulatory plug fit.

In the rat, the transport of sperm from the vagina, where they are deposited at ejaculation, into the uterus is not automatic. Various behavioral and physiological factors influence this transport process: the number of pre-ejaculatory intromissions, the duration of immobility at ejaculation, and the fit of the copulatory plug. The interplay of these three factors in producing adequate sperm transport, and their relations with each other, were examined in 52 female rats that received various numbers of pre-ejaculatory intromissions (from 0 to more than 15). The number of intromissions was strongly related to all other measures. Ejaculatory immobility was associated with better fitting copulatory plugs when females received few intromissions. Sperm transport was most strongly predicted by plug fit. Intromissions were a major predictor of good fitting copulatory plugs and transcervical sperm transport; immobility did not mediate intromission's influence and did not have a major independent role.

Animals↗

PubMed1988

Inclusive fitness models with two sexes.

Much recent work has focused on the transition from G. R. Price's (1970, Nature 227, 520-521) formula for allele frequency change to an inclusive fitness condition for the selective advantage of a certain behaviour. In case there is any kind of asymmetry between the sexes, the analysis must keep track of the two sexes separately, and this leads to a number of different forms of the expression for inclusive fitness. In this paper I gather these forms together and note the assumptions needed to make each valid. I also show how inclusive fitness should be formulated when the behaviour of the actor is controlled by another individual. I illustrate the inclusive fitness approach with a sex allocation example in a haplodiploid population with a local breeding structure.

Animals↗

PubMed1993

Effects of 'rogue' points on non-linear fitting.

Computers make it possible to fit data directly to curves such as a hyperbola or the Hill equation (sometimes called logistic equation), and remove the requirement of previously used methods to convert the data so as they fit a straight line (as in Scatchard or Hill plots). There are good reasons for abandoning these older procedures, but what are the problems with the new ones? Errors in points at either end of straight line have more effect on the slope and intercept than errors in the middle range, but what is to be expected with a direct fit to curves? In this article, Dick Barlow describes the effects of errors at particular points ('rogue' points) on the results of the analysis for the fit of data by equally-weighted least-squares to: (1) a single line that may represent the results obtained in ligand-binding experiments or the relationship between dose and pharmacological response; (2) two dose-response curves that may represent the results obtained with a competitive antagonist and are used to calculate dose ratios; and (3) two dose-response curves in which the second curve is flattened that may represent the results obtained with an irreversible antagonist and are used to calculate the EC50 (apparent equilibrium constant) for the interaction between an agonist and a receptor. The method used involves making the repeated analysis of theoretical data and can be extended to other relations, including those describing pharmacokinetics.

Analysis of Variance↗

PubMed1996

Analysis of kinetic data of antibody-antigen interaction from an optical biosensor by exponential curve fitting.

An optical biosensor system employing a resonant mirror (RM), with a stirred cuvette has been used to follow the interaction of a recombinant antibody fragment with its antigen, hen egg lysozyme. The data generated by the biosensor were analysed in order to determine the kinetic constants for the interaction using a linear transform (derivative analysis). For comparison the data were also analysed using an exponential curve fitting routine. It was demonstrated that the exponential curve fitting method produced results which were in agreement with the existing linear transform method. It was also shown that early fitting of the association phase response, using the exponential curve fitting routine between 0 and 70 s after sample addition, yielded sufficient information to provide a prediction of Kon. The potential use of the optical biosensor for the rapid monitoring of protein production and purification is discussed.

Animals↗

PubMed1989

BASIC program for non-parametric fitting of user-defined functions to experimental data with plotting of results.

Graphic displays of experimental results facilitate decisions regarding mathematical models which relate experimental results to controlled parameters. Experiments frequently produce response variables which are non-linearly related to the controlled variable. Computer programs can be useful to fit model functions to experimental data. SIMPLOT7, written in Microsoft QuickBASIC, provides graphic display of experimental data and non-parametric fitting of user-defined functions to experimental data. The algorithm utilizes simplex-based non-parametric minimization of residuals, and the user-defined function may contain up to seven parameters to be determined for best fit. Once optimum fit values have been determined, both function and data can be graphed for visual inspection of the result.

Computer Simulation↗

PubMed1993

A Macintosh BASIC program for fitting linear additive models to data by weighted least squares methods, with automatic elimination of redundant parameters from the model.

A BASIC program for fitting linear additive models to data with weighted or unweighted least squares methods and matrix procedures is described. Written and compiled to run on Macintosh II type machines (68020/68030/68040) with coprocessor (68881/68882), the program fits the model supplied by the user as an X or design matrix and provides the option of making the model's parameters orthogonal. Predicted values plus regression and residual terms are calculated. For the weighted fit, the significance of the residual term is evaluated and redundant parameters sequentially and automatically removed until a minimum adequate model is achieved. An appropriate design matrix allows weighted fitting of models for multiway analyses of variance (e.g. factorial, nested and split plot), simple or multiple linear or curvilinear regression, combinations of these in covariance analyses, and genetic analyses (including diallel cross analyses). Sums of squares for individual parameters and orthogonal comparisons can be calculated by the program.

Least-Squares Analysis↗

PubMed1995

Comparison of diastolic filling models and their fit to transmitral Doppler contours.

Anatomic/physiologic and kinematic mathematical models of diastolic filling which employ (lumped) parameters of diastolic function have been used to predict or characterize transmitral flow. The ability to determine model parameters from clinical transmitral flow, the Doppler velocity profile (DVP), is equivalent to solving the "inverse problem" of diastole. Systematic model-to-model and model-to-data comparison has never been carried out, in part due to the requirement that DVPs be digitized by hand. We developed, tested and verified a computerized method of DVP acquisition and reproduction, and carried out numerical determination of model-to-model and model-to-data goodness-of-fit. The transmitral flow velocity of two anatomic/physiologic models and one kinematic model were compared. Each model's ability to fit computer-acquired and reproduced transmitral DVPs was assessed. Results indicate that transmitral flow velocities generated by the three models are 'graphically indistinguishable and are able to fit the E-wave of clinical DVPs with comparable mean-square errors. Nonunique invertibility of the anatomic/physiologic models was verified, i.e., multiple sets of model parameters could be found that fit a single DVP with comparable mean-square error. The kinematic formulation permitted automated, unique, model-parameter determination, solving the "inverse problem" for the Doppler E-wave. We conclude that automated, quantitative characterization of clinical Doppler E-wave contours using this method is feasible. The relation of kinematic parameters to physiologic variables is a subject of current investigation.

Algorithms↗

PubMed1990

Fit of underwear and male spermatogenesis: a pilot investigation.

We evaluated the effect fit of underwear had on sperm production in two healthy adult males in their early thirties. The subjects alternated from wearing tight fitting bikini type briefs to loose fitting boxer type briefs in an ABAB withdrawal design. Conditions lasted three months and were alternated twice resulting in a one year study. The initial condition for each subject was randomly determined with the laboratory technologist blind to the conditions. Four semen parameters were analyzed in this study: sperm density, total number of sperm, total number of motile sperm, and total number of motile sperm per hour of abstinence. The results showed the semen parameters gradually decreased in tight conditions and gradually increased during loose conditions. Although preliminary, the results support the commonly held but undocumented belief that the fit of men's underwear can influence sperm production.

Adult↗

PubMed1994

Improved fit by asymmetric tibial prosthesis for total knee arthroplasty.

The adequacy of the fit of the prosthesis to the tibia is an important variable in the outcome of total knee arthroplasty. A good fit covers the cancellous bone of both condyles, involves the denser bone of the tibial shell, but does not overhang beyond the bone at any point. In this research, an anatomically shaped tibial prosthetic base plate was developed from tibial measurements. A series of five template sizes, chosen to fit our patient database, was then evaluated for fit in the operating room by one surgeon. The assessment included bone exposure and the overhang of the prosthesis beyond the bone perimeter. The measurements of overhang or bone exposure were analysed. A commercial prosthesis was used as a control. An asymmetrical tibial plate conformed well to the anatomical shape of the resected upper tibia resulting in very little exposed bone and very few cases of overhang. The absence of such overhang provides better function in the surrounding stabilizing soft tissues, and so permits recovery of the maximum range of motion post-operatively.

Anthropometry↗

PubMed2005

Fitness of drug-resistant malaria parasites.

Drug-resistant mutant forms of an organism are likely to be less fit than their wild-type strains in the absence of selection. Experimental work on prokaryotic organisms suggests that this is the case, but that compensatory mutations may occur which restore the fitness of mutants to that of sensitive forms. Here, we review experimental and field studies on this subject in malaria. In the rodent model Plasmodium chabaudi, a pyrimethamine-resistant mutant has been found to grow more slowly in mice than its drug-sensitive progenitor; however, following passage in the absence of the drug it grew faster, suggesting the occurrence of compensatory mutations. Similar findings were made with a chloroquine-resistant mutant. Field studies on Plasmodium falciparum have provided circumstantial evidence of a loss of fitness of chloroquine-resistant mutants, which appear to become less frequent in the parasite population following withdrawal of the drug. However, the occurrence of frequent recombination in the life-cycle of this parasite means that in natural conditions, a gene conferring resistance, once it has arisen, can then spread into a diversity of genetically distinct backgrounds which will influence its fitness and capacity to survive in the parasite population.

Animals↗

PubMed2006

Relationships at school and stage-environment fit as resources for adolescent engagement and achievement.

Guided by Self-Determination and associated theories, we examined whether adolescent (N=324, Mage=15, 52% female) competence (academic engagement and achievement) were supported by relationships at school and school fit. Aspects of relationships and school fit that were measured included adolescents' perceptions of each context as promoting autonomy, relatedness and competence. Within a latent-variable structural equation model, direct and indirect path estimates, standard errors and confidence intervals were produced using maximum likelihood and bootstrapping. Results supported the hypothesized model. As predicted, school fit partially mediated the association between teacher-student relationships and engagement, but fully mediated the association between peer relationships and engagement. Engagement fully mediated the path from school fit to achievement. The use of SEM and bootstrapping are encouraged as the combination of these techniques can increase power to detect direct and indirect effects, and can be a better choice for data that do not conform to normal theory assumptions. Overall, these techniques allowed for more firm conclusions about the importance of a hierarchy of multidimensional contextual experiences for adolescent competence.

Adaptation, Psychological↗

PubMed2006

Identification and analysis of fitness of resistance mutations against the HCV protease inhibitor SCH 503034.

HCV NS3 protease variants resistant to the protease inhibitor SCH 503034 were selected. Three mutations, T54A, V170A and A156S mutations conferred low to moderate levels of resistance (<20-fold). Longer exposure (>10 passages) or selection with higher levels of compound led to the selection of a more resistant variant, A156T (>100-fold). [Lin, C., Lin, K., Luong, Y.P., Rao, B.G., Wei, Y.Y., Brennan, D.L., Fulghum, J.R., Hsiao, H.M., Ma, S., Maxwell, J.P., Cottrell, K.M., Perni, R.B., Gates, C.A., Kwong, A.D., 2004. In vitro resistance studies of hepatitis C virus serine protease inhibitors, VX-950 and BILN 2061: structural analysis indicates different resistance mechanisms. J. Biol. Chem. 279(17), 17508-17514; Lu, L., Pilot-Matias, T.J., Stewart, K.D., Randolph, J.T., Pithawalla, R., He, W., Huang, P.P., Klein, L.L., Mo, H., Molla, A., 2004. Mutations conferring resistance to a potent hepatitis C virus serine protease inhibitor in vitro. Antimicrob. Agents Chemother. 48(6), 2260-2266.] Combination with IFN-alpha drastically reduced the number of emergent colonies. Resistant colonies showed no change in sensitivity to IFN-alpha. Although the A156T mutation conferred the highest level of resistance to SCH 503034, it significantly reduced the colony formation efficiency (CFE) of the mutant replicon RNA, and rendered replicon cells less fit than those bearing wild-type replicons. Replicon cells bearing mutation A156S were less fit than wild-type in co-culture growth competition assays but showed no impact on CFE. The V170A mutation, on the other hand, did not affect replicon fitness in either assay, which was consistent with its emergence as the dominant mutant after 12 months of continuous selection. The reduced fitness of the most resistant variant suggests that it may be rare in naïve patients and that development of high-level resistance may be slow. Combination therapy with IFN-alpha should also greatly reduce the potential emergence of resistance.

Blotting, Western↗

PubMed2004

Combination of nonlinear function and mixing method for fitting HPGe efficiency curve in the 59-2754 kev energy range.

A nonlinear function in combination with the method of mixing activity-calibrated and uncalibrated gamma-ray sources is applied for fitting the experimental peak efficiency of HPGe spectrometers in the 59-2754 keV energy range. In addition, a step function was developed for fitting the gamma-ray background under the peak. Calibrated 241Am, 133Ba, 137Cs, 152Eu, 60Co and 88Y sources, as well as one 24Na source (treated as uncalibrated) were used for obtaining the experimental peak efficiency curve. The results were compared to the conventional linear polynomial fitting. From the fitted parameters, the 24Na activity was determined and compared with the result obtained from absolute measurements in a 4pibeta-gamma coincidence system.

Journal Article↗

PubMed2005

Clinical applicability of using spherical fitting to find hip joint centers.

The functional or sphere-fitting method has been proposed as an alternative to the traditional predictive approach to locating hip centers based on inter-ASIS breadth. In the functional approach, the movement of a marker on the thigh is fit to a sphere whose center coincides with the hip joint center. The first objective of this study was to determine the required parameters that allow an accurate application of a sphere-fitting method. The parameters examined in this study included: (1) the range of motion in flexion-extension and abduction-adduction, (2) the specific algorithm used to fit a sphere to the data, (3) the method of placing markers on the thigh, and (4) the type of motion used to generate points, either walking or a standing leg motion (SLM) trial. This objective was addressed with a computer simulation and clinical data. The second objective was to compare the accuracy of the functional method to the traditional predictive approach in a group of nine human subjects. The location of the hip center estimates from both methods were compared to an ultrasound-determined hip center standard, and linear errors and errors along each axis were compared. Results from the computer simulation indicated that an iterative algorithm is needed, with a method using the derivative yielding slightly more accurate results. Clinical results indicated that the functional method with a standing leg motion trial produced significantly smaller errors in hip joint center estimates (1.34 cm) versus the predictive method (2.16 cm). In addition, the range of error across hips was smaller for the functional method. If high joint center accuracy is needed or in populations characterized by obesity or pelvic asymmetries, the subject specificity and independence from anatomical landmarks characteristic of the functional method would likely provide more accurate results.

Adult↗

PubMed2005

Virulence and fitness of the fungal pathogen Entomophaga maimaiga in its host Lymantria dispar, for pathogen and host strains originating from Asia, Europe, and North America.

In this study, we tested (1) whether non-North American gypsy moth strains are susceptible to North American isolates of Entomophaga maimaiga and (2) the potential for erosion in the efficacy of E. maimaiga in controlling gypsy moth. We used bioassays to assess the variability in virulence (measured as time to death) as well as fitness of the pathogen (measured as spore production) in four gypsy strains challenged with six E. maimaiga isolates, using host and pathogen strains originating from Asia, Europe, and North America. We found that all E. maimaiga isolates tested were pathogenic to all strains of Lymantria dispar, regardless of the geographical origin of the fungal isolate, with at least 86% mortality for all combinations of fungal isolate and gypsy moth strain. We therefore conclude that Asian gypsy moths are susceptible to North American strains of E. maimaiga. No significant interactions between fungal isolates and gypsy moth strains with regard to time to death were found, indicating that each fungal isolate had the same overall effect on all the gypsy moth strains tested. However, fungal isolates differed significantly with regard to virulence, with a Russian isolate being the slowest to kill gypsy moth (5.1+/-0.1 days) and a Japanese isolate being the overall fastest to kill its host (4.0+/-0.1 days). Fungal isolates also differed in fitness, with variability in types of spores produced. These differences in virulence and fitness were, however, not correlated with geographical origin of the fungal isolate. Gypsy moth strains had no or only little effect on fungal virulence and fitness. Based on our studies with laboratory-reared gypsy moth strains, erosion of successful control of gypsy moth by E. maimaiga seems unlikely.

Animals↗