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PubMed1990

Assessing seasonal leaf area dynamics and vertical leaf area distribution in eastern white pine (Pinus strobus L.) with a portable light meter.

We evaluated the ability of a portable light meter (Sunfleck Ceptometer, Decagon Devices, Pullman, WA, USA) to quantify seasonal photosynthetically active radiation (PAR, 400-700 nm) interception, projected stand leaf area index (LAI), and vertical LAI distribution in a 32-year-old eastern white pine (Pinus strobus L.) plantation. Canopy PAR transmittance measured with the ceptometer was converted to LAI with the Beer-Lambert Equation. The ceptometer was sensitive to changes in PAR transmittance resulting from foliage growth. Predicted stand LAI ranged from 3.5 in the dormant season to a maximum of 5.3 in late July. Predicted LAI values were within 9% of values determined from destructive sampling. Published canopy extinction coefficients (k) were inadequate for converting PAR transmittance data to stand LAI because a significant amount of PAR was intercepted by dead branches and stems below the forest canopy. Because of interception by dead branches and stems, we estimated k = 0.84, which is substantially higher than previously reported values. The ceptometer was also sensitive to seasonal changes in PAR transmittance within the canopy. However, in contrast to predictions based on the Beer-Lambert Law, the relationship between proportional PAR transmittance (Q(i)/Q(o)) and cumulative LAI within the canopy was linear. Thus, vertical LAI distribution was best estimated with a linear model, as opposed to the non-linear model assumed in the Beer-Lambert Equation. We hypothesize that the linear relationship was a result of a gap in the canopy which was not represented by the cumulative leaf area distribution estimation procedure.

Journal Article↗
PubMed2002

[Interfaces in rehabilitation: three models].

Interfaces can cause disruptions in the care provision process. They can, however, also signify a differentiated and specialized division of labour of the care providing system. Three models for the description of interfaces are presented and compared: a linear model oriented towards the continuity of the provision of care for individuals, the Principal Agent (PA) Model from contract theory, and a complex systems model. In all three models coupling and information management are identified as essential interface functions. In regard to optimisation possibilities, the linear model leads to the case-management concept, the PA Model to integrated forms of provision and systems theory to context controlling.

Case Management↗
PubMed1998

A new method to estimate parameters of linear compartmental models using artificial neural networks.

At present, the preferred tool for parameter estimation in compartmental analysis is an iterative procedure; weighted nonlinear regression. For a large number of applications, observed data can be fitted to sums of exponentials whose parameters are directly related to the rate constants/coefficients of the compartmental models. Since weighted nonlinear regression often has to be repeated for many different data sets, the process of fitting data from compartmental systems can be very time consuming. Furthermore the minimization routine often converges to a local (as opposed to global) minimum. In this paper, we examine the possibility of using artificial neural networks instead of weighted nonlinear regression in order to estimate model parameters. We train simple feed-forward neural networks to produce as outputs the parameter values of a given model when kinetic data are fed to the networks' input layer. The artificial neural networks produce unbiased estimates and are orders of magnitude faster than regression algorithms. At noise levels typical of many real applications, the neural networks are found to produce lower variance estimates than weighted nonlinear regression in the estimation of parameters from mono- and biexponential models. These results are primarily due to the inability of weighted nonlinear regression to converge. These results establish that artificial neural networks are powerful tools for estimating parameters for simple compartmental models.

Algorithms↗
PubMed2002

Relation between QT and RR intervals is highly individual among healthy subjects: implications for heart rate correction of the QT interval.

OBJECTIVE: To compare the QT/RR relation in healthy subjects in order to investigate the differences in optimum heart rate correction of the QT interval. METHODS: 50 healthy volunteers (25 women, mean age 33.6 (9.5) years, range 19-59 years) took part. Each subject underwent serial 12 lead electrocardiographic monitoring over 24 hours with a 10 second ECG obtained every two minutes. QT intervals and heart rates were measured automatically. In each subject, the QT/RR relation was modelled using six generic regressions, including a linear model (QT = beta + alpha x RR), a hyperbolic model (QT = beta + alpha/RR), and a parabolic model (QT = beta x RR(alpha)). For each model, the parallelism and identity of the regression lines in separate subjects were statistically tested. RESULTS: The patterns of the QT/RR relation were very different among subjects. Regardless of the generic form of the regression model, highly significant differences were found not only between the regression lines but also between their slopes. For instance, with the linear model, the individual slope (parameter alpha) of any subject differed highly significantly (p < 0.000001) from the linear slope of no fewer than 21 (median 32) other subjects. The linear regression line of 20 subjects differed significantly (p < 0.000001) from the linear regression lines of each other subject. Conversion of the QT/RR regressions to QTc heart rate correction also showed substantial intersubject differences. Optimisation of the formula QTc = QT/RR(alpha) led to individual values of alpha ranging from 0.234 to 0.486. CONCLUSION: The QT/RR relation exhibits a very substantial intersubject variability in healthy volunteers. The hypothesis underlying each prospective heart rate correction formula that a "physiological" QT/RR relation exists that can be mathematically described and applied to all people is incorrect. Any general heart rate correction formula can be used only for very approximate clinical assessment of the QTc interval over a narrow window of resting heart rates. For detailed precise studies of the QTc interval (for example, drug induced QT interval prolongation), the individual QT/RR relation has to be taken into account.

Adult↗
PubMed1982

A computer linear regression model to determine ventilatory anaerobic threshold.

The anaerobic threshold has generally been determined by simple visual inspection of ventilation or other gas-exchange data obtained during incremental exercise. To establish objective criteria for the determination of anaerobic threshold, a computer algorithm has been developed that models the ventilatory response to exercise using multisegment linear regression. The best-fit regression model is chosen by minimizing the pooled residual sum of squares . The anaerobic threshold is reported as the first break point in that model. The computer-determined anaerobic threshold values for 37 subjects were compared with subjectively determined values as chosen by four independent observers. The observers' estimates, when pooled to yield a single a single value for each subject, gave a mean value for the gas-exchange anaerobic threshold of 2.26 +/- 0.69 l/min. The estimates by the computer method averaged 2.21 +/- 0.65 l/min. The correlation coefficient for these two methods was 0.94.

Adult↗
PubMed2006

A multivariate model for ordinal trait analysis.

Many economically important characteristics of agricultural crops are measured as ordinal traits. Statistical analysis of the genetic basis of ordinal traits appears to be quite different from regular quantitative traits. The generalized linear model methodology implemented via the Newton-Raphson algorithm offers improved efficiency in the analysis of such data, but does not take full advantage of the extensive theory developed in the linear model arena. Instead, we develop a multivariate model for ordinal trait analysis and implement an EM algorithm for parameter estimation. We also propose a method for calculating the variance-covariance matrix of the estimated parameters. The EM equations turn out to be extremely similar to formulae seen in standard linear model analysis. Computer simulations are performed to validate the EM algorithm. A real data set is analyzed to demonstrate the application of the method. The advantages of the EM algorithm over other methods are addressed. Application of the method to QTL mapping for ordinal traits is demonstrated using a simulated baclcross (BC) population.

Algorithms↗
PubMedDate not supplied

Arrhenius analysis of the thermal response of human colonic adenocarcinoma cells in vitro using the multi-target, single-hit and the linear-quadratic model.

In order to compare the intrinsic thermal sensitivity of different malignant cell lines the multi-target, single-hit model has been widely accepted. It is even applied in clinical hyperthermia by the so-called thermal isoeffect dose (TID) concept originated from this model. The second model which is preferentially used to describe radiation survival curves is the linear-quadratic (LQ) model which can be also applied to thermal response. Interestingly, no breaking point and different activation energies are obtained with this model. In the present paper we demonstrate this discrepancy with the two human colonic adenocarcinoma cell lines WiDr and SW620. Our results further validate the already earlier published persuasion, that neither the multi-target, single-hit model, nor the LQ model are adequate to describe hyperthermic survival. Since both models give completely different results, further data aquisition of isoeffect factors, breaking points and activation enthalpies based on the multi-target, single-hit model only, is unprofitable until advanced models of thermal inactivation have been developed.

Adenocarcinoma↗
PubMed2004

Highly scalable video compression with scalable motion coding.

A scalable video coder cannot be equally efficient over a wide range of bit rates unless both the video data and the motion information are scalable. We propose a wavelet-based, highly scalable video compression scheme with rate-scalable motion coding. The proposed method involves the construction of quality layers for the coded sample data and a separate set of quality layers for the coded motion parameters. When the motion layers are truncated, the decoder receives a quantized version of the motion parameters used to code the sample data. The effect of motion parameter quantization on the reconstructed video distortion is described by a linear model. The optimal tradeoff between the motion and subband bit rates is determined after compression. We propose two methods to determine the optimal tradeoff, one of which explicitly utilizes the linear model. This method performs comparably to a brute force search method, reinforcing the validity of the linear model itself. Experimental results indicate that the cost of scalability is small. In addition, considerable performance improvements are observed at low bit rates, relative to lossless coding of the motion information.

Algorithms↗
PubMed1987

Estimating the size of closed populations using inverse multiple-recapture sampling.

A log-linear model for estimating the size of a closed population is defined for inverse multiple-recapture sampling with dependent samples. Efficient estimators of the log-linear model parameters and the population size are obtained by the method of minimum chi-square. A chi-square test of the general linear hypothesis regarding the log-linear model parameters is defined.

Animals↗
PubMed1999

A multivariate linear regression model for predicting children's blood lead levels based on soil lead levels: A study at four superfund sites.

For the purpose of examining the association between blood lead levels and household-specific soil lead levels, we used a multivariate linear regression model to find a slope factor relating soil lead levels to blood lead levels. We used previously collected data from the Agency for Toxic Substances and Disease Registry's (ATSDR's) multisite lead and cadmium study. The data included the blood lead measurements (0.5 to 40.2 microg/dL) of 1015 children aged 6-71 months, and corresponding household-specific environmental samples. The environmental samples included lead in soil (18.1-9980 mg/kg), house dust (5.2-71,000 mg/kg), interior paint (0-16.5 mg/cm2), and tap water (0.3-103 microg/L). After adjusting for income, education of the parents, presence of a smoker in the household, sex, and dust lead, and using a double log transformation, we found a slope factor of 0.1388 with a 95% confidence interval of 0.09-0.19 for the dose-response relationship between the natural log of the soil lead level and the natural log of the blood lead level. The predicted blood lead level corresponding to a soil lead level of 500 mg/kg was 5.99 microg/kg with a 95% prediction interval of 2. 08-17.29. Predicted values and their corresponding prediction intervals varied by covariate level. The model shows that increased soil lead level is associated with elevated blood leads in children, but that predictions based on this regression model are subject to high levels of uncertainty and variability.

Child↗
PubMed2000

Counteraction of aortic baroreflex to carotid sinus baroreflex in a neck suction model.

Although neck suction has been widely used in the evaluation of carotid sinus baroreflex function in humans, counteraction of the aortic baroreflex tends to complicate any interpretation of observed arterial pressure (AP) response. To determine whether a simple linear model can account for the AP response during neck suction, we developed an animal model of the neck suction procedure in which changes in carotid distension pressure during neck suction were directly imposed on the isolated carotid sinus. In six anesthetized rabbits, a 50-mmHg pressure perturbation on the carotid sinus decreased AP by -27.4+/-4.8 mmHg when the aortic baroreflex was disabled. Enabling the aortic baroreflex significantly attenuated the AP response (-21.5+/-3.8 mmHg, P<0.01). The observed closed-loop gain during simulated neck suction was well predicted by the open-loop gains of the carotid sinus and aortic baroreflexes using the linear model (-0.43+/-0.13 predicted vs. -0.41 +/-0.10 measured). We conclude that the linear model can be used as the first approximation to interpret AP response during neck suction.

Animals↗
PubMed1992

Linear quadratic model of radiocurability on multicellular spheroids of human lung adenocarcinoma LCT1 and mouse fibrosarcoma FSA.

The LCT1 cells derived from a human lung adenocarcinoma and the FSA cells from a mouse fibrosarcoma were found to form spheroids. The cure-dose relationship of spheroids and the survival curves of their component cells were analysed by using a linear-quadratic model for cell survival and a Poisson distribution for cure. The analysis resulted in three conclusions: (1) the double minus logarithm of cure probability was linearly related to radiation dose, (2) the critical cell number was constant at any given cure probability, and (3) cellular radiosensitivity was also constant. The experiments seem to meet these conditions for each of two kinds of spheroids. Control doses (50%) were 20 Gy for LCT1 spheroids and 21 Gy for FSA spheroids, both 400 microns in diameter. The analysis showed that the lower cellular radiosensitivity and the higher number of clonogenic cells made LCT1 spheroids more radioresistant than FSA spheroids and that the higher critical number of 130 cells made the LCT1 spheroids more sensitive than the FSA spheroids with 18 such cells. The overall radiocurability of spheroids was a result of these three opposing effects, indicating that the critical cell number can be one important factor in determining the radiocurability of multicellular systems.

Adenocarcinoma↗
PubMedDate not supplied

The accurate estimation of meteorological profiles employing ANNs.

The lack of meteorological measurements at a location of interest (target location) constitutes a problem that is crucial for the purposes of both weather forecasting and energy system design/validation. This paper constitutes a pilot study for the accurate estimation of meteorological values at a target location employing the meteorological measurements collected at a nearby (reference) location. Artificial neural networks are investigated and compared with traditional estimation methods such as linear models of first and higher orders and the non-linear model. The significance of the improvement obtained via the estimation--and especially the artificial neural network approach--over simply considering the measurements at the reference location is demonstrated in a number of energy applications.

Algorithms↗
PubMedDate not supplied

High-dose-rate brachytherapy at 14 Gy per hour to point A: preliminary results of a prospectively designed schedule for cancer of the cervix based on the linear-quadratic model.

The objective of this study was to describe the results and complications of a prospectively designed high-dose-rate (HDR) brachytherapy schedule for early-stage cancer of the cervix, at 14 Gy/h to point A, based on the linear-quadratic model and our clinical experience. We used a combination of brachytherapy and external beam pelvic and parametrial irradiation in 88 consecutively seen patients with stage IB1-IIB treated by irradiation alone (1995-1998). The modeled HDR schedule consisted of three insertions on three treatment days separated by 10 days, with six 7 Gy planned brachytherapy fractions to point A, at 14 Gy/h, two on each treatment day with an interfraction interval of 6 h, plus an 18 Gy external whole-pelvic dose followed by additional parametrial irradiation. The calculated biologically effective dose (BED) was 92 Gy10 for tumor and 110 Gy3 for the rectum, equivalent to 77 and 66 Gy in 2 Gy fractions, respectively. The median overall treatment time was 41 days. The actuarial 4-year central recurrence-free rate, pelvic control, and disease-free survival rate were 97%, 93%, and 88% for stages IB-IIA and 79%, 75%, and 75% for stage IIB. The actuarial 4-year late complication rate for grades 2-3 was 4.7% (scale 0-3). We conclude that preliminary results of this HDR brachytherapy schedule for early-stage disease at a median follow-up of 52 months are as effective as the previously used low dose rate (LDR) at 0.44 Gy/h at point A. They are also as effective as medium-dose-rate schedules (MDR) at 1.6-1.5 Gy/h at this institution and do not require a further increase in fractionation of intracavitary treatments or in the whole-pelvic external beam irradiation dose common to standard HDR schedules. In addition, more patients per machine can be treated per day compared with MDR. Longer follow-up is required for a complete assessment of late complications.

Adenocarcinoma↗
PubMed2006

Fitting the linear-quadratic model to detailed data sets for different dose ranges.

Survival curve behaviour and degree of correspondence between the linear-quadratic (LQ) model and experimental data in an extensive dose range for high dose rates were analysed. Detailed clonogenic assays with irradiation given in 0.5 Gy increments and a total dose range varying from 10.5 to 16 Gy were performed. The cell lines investigated were: CHOAA8 (Chinese hamster fibroblast cells), U373MG (human glioblastoma cells), CP3 and DU145 (human prostate carcinoma cell lines). The analyses were based on chi2-statistics and Monte Carlo simulation of the experiments. A decline of LQ fit quality at very low doses (<2 Gy) is observed. This result can be explained by the hypersensitive effect observed in CHOAA8, U373MG and DU145 data and an adaptive-type response in the CP3 cell line. A clear improvement of the fit is discerned by removing the low dose data points. The fit worsening at high doses also shows that LQ cannot explain this region. This shows that the LQ model fits better the middle dose region of the survival curve. The analysis conducted in our study reveals a dose dependency of the LQ fit in different cell lines.

Animals↗
PubMed2002

The dynamics of prostate specific antigen during watchful waiting of prostate carcinoma: a study of 94 Japanese men.

BACKGROUND: For the moment, there is uncertainty about the usefulness of early treatment of localized prostate carcinoma, uncertainty about whether some patients with early cancer can be managed expectantly, and uncertainty about how such patients might be recognized. METHODS: The authors studied serial values of prostate specific antigen (PSA) in 94 Japanese men with diagnosed prostate carcinoma and who were managed by watchful waiting. Their median follow-up duration was 32 months (range, 1.6-118). The authors used a log-linear model to fit the values of PSA over time, and then they used the Cox survival model to relate the intercept (PSA amplitude) and slope (relative velocity) to observed local or systemic outcomes that were independent of PSA. RESULTS: The authors found that the log-linear model fit the serial values of PSA during watchful waiting very well. Prostate specific antigen amplitude related significantly to T classification (P = 0.0006), but not to grade (P > 0.2), and the relative velocity related significantly to both T classification (P = 0.009) and to grade (P = 0.02). Although the T classification, histologic grade, and log(PSA) at diagnosis were associated significantly with time to outcome, the combination of amplitude and relative velocity provided more information. These 2 PSA parameters resulted in a higher model likelihood ratio, and their individual P values in the Cox model were 0.0005 and 0.005, respectively. With these two in the Cox model, T classification, grade, log(PSA), and PSA doubling time provided no further significant information. CONCLUSIONS: A log-linear model seems to fit serial measurements of PSA during watchful waiting, and preliminary results suggest that both the amplitude and the relative velocity relate closely to clinical outcomes.

Aged↗