Application of a programmable pocket calculator to a single compartment mathematical model of solute kinetics.

A single compartment mathematical model has been applied to kinetics of small solutes (urea and creatinine) in dialysis therapy. The model can be described by two equations requiring iterative solution of calculated values, given several measurable variables. The equations have been programmed onto a Hewlett-Packard 65 pocket calculator and recorded on 3 X 1/2" magnetic strips, facilitating clinical application to dialysis therapy.     

Four open mammillary and catenary compartment models for pharmacokinetics studies

A mathematical method is proposed to solve a fourth degree equation which gives the eigenvalues of the matrix connected with a four open compartment model used in pharmacokinetic studies. As examples, the method is applied to mammillary and catenary models.     

Automatic collection and processing of data from the ultracentrifuge using a programmable desk calculator.

Previous investigators [Trautman, R., Spragg, S. P., and Halsall, H. B. (1969) Anal. Biochem.28, 396–415] have published a detailed protocol for the analysis of sedimentation velocity measurements which is adaptable to data generated by an ultraviolet scanning system. The advent of programmable desk calculators capable of sampling the output of digital measuring devices has made it possible to develop inexpensive and highly convenient systems for collecting and processing scanner data. Basing our approach on the referenced protocol, we have developed algorithms for dealing with real data, that is, data characterized by a relatively high level of noise. The techniques are applieable to both sedimentation equilibrium and sedimentation velocity measurements using the seanning system and multicell rotors. With known concentration dependence, valid estimates of weight-average sedimentation coefficients, diffusion coefficients, and heterogeneity parameters have been obtained for both simulated and actual sedimenting anddiffusing macromolecular solutes. We find, however, that concentration dependence derived internally from a single sedimentation velocity measurement is unreliable.     

Gentamicin: use of a programmable calculator to determine dosages from pharmacokinetic data for individual patients.

Gentamicin, an antibiotic frequently used in the treatment of gram-negative infections, has a narrow therapeutic index, so the correct prediction of its serum concentrations is important. Recent studies have emphasized the dubious accuracy of commonly used formulas, and computer programs that provide pharmacokinetic data for individual patients from multiple blood samples have helped to adjust dosages but are expensive. This study tested the applicability of a method using only two blood samples and a programmable calculator to estimate pharmacokinetic parameters for individual patients and adjust dosages to aim at peak and trough serum levels of 6 and 1 micrograms/ml respectively. In the 48 patients with normal renal function this method produced peak serum concentrations of gentamicin within 1 microgram/ml of the desired level in 22 (46%) and therapeutic peak concentrations (between 4 and 10 micrograms/ml) in all the patients. In 10 patients with renal failure it produced peak serum concentrations within 1 microgram/ml of the desired value in 4 and therapeutic serum concentrations in 7. Two patients had peak concentrations below 4 micrograms/ml and one had a peak concentration above 10 micrograms/ml. Two of the three patients whose serum levels were outside the therapeutic range had unstable renal insufficiency. Thus, patients with renal insufficiency need continued monitoring of the serum level of gentamicin, particularly when their renal function is changing.     

The fitting of dynamic models to observed data

The question of how to fit a general cubic model of a multicomponent, interactive growth system to observed data is addressed. A multidimensional-polynomial type of regression analysis is used, with a least-squares criterion. By testing the scheme on a problem with known solution, the way in which the accuracy of the results varies with the number of datum points used is investigated in an heuristic manner.     

Two-pool model analysis of data in hemodialysis by means of programmable pocket calculator TI 59

Four parameters of a two-pool model are evaluated by an iterative method using the explicit solutions of the linear differential equations. For this it was presumed that the residual renal clearance is sufficiently small. Five data pairs of measured plasma concentrations ci for the time points ti (i = 0 to 4), as well as the dialyzer and residual renal clearances (KD and KR), must be given and put in the calculator. A sample run is shown for urea kinetics. The parameter estimation takes about 10 min. The program is suitable to assist in the individualization of dialysis therapy.     

A new approach of fitting biomass dynamics models to data

A non-traditional approach of fitting dynamic resource biomass models to data is developed in this paper. A variational adjoint technique is used for dynamic parameter estimation. In the variational formulation, a cost function measuring the distance between the model solution and the observations is minimized. The data assimilation method provides a novel and computationally efficient procedure for combining all available information, i.e., the data and the model in the analysis of a resource system. This technique will be used to analyze data for the North-east Arctic cod stock. Two alternative population growth models: the logistic and the Gompertz model are used for estimating parameters of simple bioeconomic models by the method of constrained least squares. Estimates of the parameters of the models dynamics are reasonable and can be accepted. The main inference from the work is that the average fishing mortality is found to be significantly above the maximum sustainable yield value.     

A calculator program to determine k and V from measured serum drug concentrations by a two point curve fitting method

A calculator program is presented which determines k and V from two drug levels or k from an assumed V and one drug level during maintenance dosing with any of four dosing schedules: intermittent, fixed interval; intermittent, two fixed intervals; intermittent, non-uniform dose, non-uniform interval; continuous intravenous infusion/sustained release. A loading dose and or one additional level taken before maintenance dosing begins can be taken into account for additional flexibility. Steady state concentrations are projected when dosage regimen and pharmacokinetic parameters are known.     

Measurement and analysis of gas exchange during exercise using a programmable calculator

Although exercise testing is useful in the diagnosis and management of cardiovascular and pulmonary diseases, a rapid comprehensive method for measurement of ventilation and gas exchange has been limited to expensive complex computer-based systems. We devised a relatively inexpensive, technically simple, and clinically oriented exercise system built around a desktop calculator. This system automatically collects and analyzes data on a breath-by-breath basis. Our calculator system overcomes the potential inaccuracies of gas exchange measurement due to water vapor dilution and mismatching of expired flow and gas concentrations. We found no difference between the calculator-derived minute ventilation, CO2 production, O2 consumption, and respiratory exchange ratio and the values determined from simultaneous mixed expired gas collections in 30 constant-work-rate exercise studies. Both tabular and graphic displays of minute ventilation, CO2 production, O2 consumption, respiratory exchange ratio, heart rate, end-tidal O2 tension, end-tidal CO2 tension, and arterial blood gas value are included for aid in the interpretation of clinical exercise tests.     

Analysis and identification of stochastic compartment models in pharmacokinetics: implication for cancer chemotherapy

One of the fundamental problems in pharmacokinetics is determining the parameters of multicompartment models from the measured excretion rate and observations on one of the compartments. Since it is frequently impractical to obtain observations for all physiological compartments, and due to the inherent variations in biological systems, a stochastic approach to multicompartment analysis is suggested. The objective of this article is to consider the identification of multicompartment models from a stochastic point of view, with particular emphasis on two- and three-compartment models.The essential part of this investigation is the statistical simulation of the C-T curves of the observed compartment for different biological conditions. We then present a probabilistic characterization of the multirandom parameter family of the rate constant matrix and evaluate the statistical properties of the solution processes for the unobservable compartments.     

Two simple programs for the analysis of data from enzyme-linked immunosorbent (ELISA) assays on a programmable desk-top calculator

We have designed two programs for use with an inexpensive programmable calculator which rapidly and accurately convert raw data generated from enzyme-linked immunosorbent assays directly into antigen concentration. The first program computes and compares effective doses (ED₅₀)'s between a standard and each unknown sample assayed. The ED₅₀ from the unknown sample is then multiplied by a concentration factor which yields the unknown concentration. The second program linearizes the sigmoidal enzyme-linked immunosorbent assay titration curve using a logit-log transformation of the data in order to compute unknown concentration values. Both programs employ stringent limit conditions to decrease “nonsense” calculations. Data are then processed by a least-squares best-fit linear regression analysis.     

Analysis of electrophoretic mobility data for human erythrocytes according to sublayer models

An attempt was made to analyze the electrophoretic mobility data of human erythrocytes in media of different pH values and ionic strengths through cell surface models in which the surface charge layer consists of several ion-penetrable sublayers with a uniform charge distribution in each sublayer. As a result, the three-sublayer model was found to explain the mobility data much better than the two-sublayer model in a wide range of ionic strength at all pH values studied.     

A single-parameter family of adjustments for fitting enzyme kinetic models to progress-curve data.

We have investigated the rapid phosphorylation of proteins in B-lymphocytes incubated with the tumour-promoting phorbol ester 12-O-tetradecanoylphorbol 13-acetate (TPA), anti-Ig and combinations of TPA and the Ca2+ ionophore ionomycin. Two-dimensional electrophoretic analysis was used to identify the proteins phosphorylated in cells preincubated with [32P]Pi. TPA induced a characteristic pattern of labelled proteins, four of which (pp85, pp76, pp66 and pp63) showed a dose-dependent incorporation of 32P on serine residues. The phosphorylation of pp63 and pp66, in particular, correlated with the mitogenic dose-response curve. Addition of the Ca2+ ionophore ionomycin to B-cells also stimulated a characteristic incorporation of 32P into proteins, which included pp63 and pp66. With combined doses of TPA and ionomycin, these two proteins show an enhanced phosphorylation, which correlated well with the synergistic enhancement of proliferation shown by this combination of agents. Protein kinase C (PKC) was partially purified from B-cells and separated into alpha and beta subtypes. The activation of both PKCs was assessed with increasing doses of TPA and concentrations of Ca2+ of 0.1 microM and 2 microM. For both forms of PKC, in particular the beta form, higher concentrations of Ca2+ shifted the dose-response curve for TPA to the left and increased the maximum activation. Anti-Ig, which stimulated B-cells by cross-linking surface immunoglobulin and causing hydrolysis of PtdIns(4,5)P2, also caused increased phosphorylation of several proteins, which again included pp63 and pp66. These data suggest that PKC, particularly the beta form, is involved in the early part of the proliferation cascade for human B-lymphocytes. It is most probably activated in a synergistic manner by the increased Ca2+ and diacylglycerol levels which result from the earlier hydrolysis of PtdIns(4,5)P2.     

Four compartment mammillary model applied to the pharmacokinetics of a spiroarsorane administered orally to rabbits

Rekik et al.¹ dealt with the pharmacokinetics of two spiroarsoranes molecules^1,2 administered intravenously or orally to rabbits. For the intravenous study they used an open two-compartment model. For the oral study they admitted that they were unable to fit the data to a model. In this paper the plasma concentration profile of molecule 2 after oral administration using a four mammillary open compartment model is described. This type of model (which requires a fourth degree equation) has been previously described². Here it is applied to a concrete situation.     

The effects of climate data precision on fitting and projecting species niche models

Biosecurity agencies are particularly concerned to know the potential distribution of invasive alien species under present, and to a lesser extent, future climates; expensive decisions can hinge upon the degree of perceived threat a pest species poses. Climate‐based niche modelling techniques are available to inform these decisions. These tools now regularly employ gridded climate datasets of moderate spatial resolution (0.5 degree), though biosecurity decision‐makers continually seek greater spatial precision in the risk map products. Various splining techniques are capable of generating gridded climate datasets approaching the precision limits imposed by the availability of digital elevation model data. As the spatial precision of climate datasets increases, more detailed effects of topographic relief become apparent in the climatic data. When these datasets are used to develop and apply species niche models, the climate data is spatially intersected with species location data to infer relationships between the climate and the species’ geographic distribution. Here we investigate the effect of changing climate precision on projections of species’ niche models developed with CLIMEX, including the effect of upscaling and downscaling the outputs. We found that there were noticeable increases in sensitivity in models developed using more precise climate datasets. The largest differences in projections were noted where species range limits coincided with regions of strong climatic gradients such as where there was marked topographic relief in relation to the spatial precision of the climatic dataset. Upscaling (fitting a model with a fine resolution dataset and then projecting the results with a coarser grid), tended to produce smaller potential ranges for a species, albeit at the cost of model sensitivity. Downscaling had the opposite effect, identifying additional, mostly marginally climatically suitable habitat. It remains unclear how sensitive the fine resolution results are to the number and spatial arrangement of input location records used to build the model. The results indicate some benefits of improving the spatial resolution of climate datasets, though not at the expense of climatic data accuracy. Decision‐makers should be mindful of the inherent uncertainties in these models, and modellers have a responsibility to identify and convey these uncertainties to their intended audience.