Effect of bed rest on distribution and elimination of drugs

Supplying a pharmacy for NASA exploration spaceflight: challenges and current understanding

In order to maintain crew health and performance during long-duration spaceflight outside of low-Earth orbit, NASA and its international partners must be capable of providing a safe and effective pharmacy. Given few directed studies of pharmaceuticals in the space environment, it is difficult to characterize pharmaceutical effectiveness or stability during spaceflight; this in turn makes it challenging to select an appropriate formulary for exploration. Here, we present the current state of literature regarding pharmaceutical stability, metabolism, and effectiveness during spaceflight. In particular, we have attempted to highlight the gaps in current knowledge and the difficulties in translating terrestrial-based drug studies to a meaningful interpretation of drug stability, safety, and effectiveness in space. We hope to identify high-yield opportunities for future research that might better define and mitigate pharmaceutical risk for exploration missions.

Factors influencing the absorption and disposition of mecillinam and pivmecillinam in man

In a pharmacokinetic study in six volunteers peak serum mecillinam concentrations were proportional to the oral dose of pivmecillinam at two dose levels of 200 and 400 mg. Effects of bed rest, probenecid and a 6 day course of treatment with pivmecillinam on serum mecillinam concentrations after an oral dose of pivmecillinam (two 200 mg capsules) have been investigated. Resting subjects had lower peak serum levels and a decreased rate of clearance than moderately active subjects, changes which are similar to those previously reported for benzylpenicillin. Pretreatment with probenecid produced significantly higher serum mecillinam levels, a longer serum antibiotic half-life and a decreased rate of drug clearance which suggests that mecillinam is actively excreted by kidney tubules. Plasma mecillinam level profiles obtained after the first dose of a 6 day treatment period were not significantly different from corresponding values after the first dose on the seventh day which indicates that each dose of mecillinam is eliminated in healthy young adults before succeeding doses are taken.

The influence of weightlessness on pharmacokinetics

The primary hostile factor during a spaceflight is the lack of gravity, which can induce space motion sickness and act on bones, muscles and the cardiovascular system. These physiological effects may modify the pharmacokinetics of the drugs administered during the flight producing reduced pharmacological activity or appearance of adverse effects. Given the small number of spaceflights and the difficulties of conducting experiments during missions, pharmacokinetic data obtained in flight are insufficient to determine if drug monitoring is necessary for the drugs present in the onboard medical kit. Therefore, validated earthbound models like tail-suspension performed with animals and long-term bedrest performed with human volunteers are used to simulate weightlessness and to study the pharmacokinetic variations of either absorption, distribution, or elimination of drugs. As a result of these studies, it is possible to make some dosing recommendations but more information is necessary to predict with precision all of the pharmacokinetic variations occurring in spaceflight. To collect more pharmacokinetic information, head-down bedrest studies are still the best solution and as saliva is an appropriate substitution for plasma for some drugs, salivary sampling can be planned during flights.

Effect of time of administration on the pharmacokinetics and tolerance of doxazosin in healthy male volunteers

A randomized, open-label, two-way crossover study of 24 normotensive, healthy male volunteers with nocturia was conducted to compare morning and evening administration of doxazosin in terms of pharmacokinetics and tolerance. In both the morning and evening phases, participants received doxazosin 1 mg once daily for 10 days, followed by 2 mg once daily for 5 days. Pharmacokinetic data were evaluated from blood samples serially collected for 72 hours after drug administration on the last day of each phase. Vital signs and adverse events were recorded throughout the study. Mean peak plasma concentrations (C(max)) were 16.98 and 15.76 ng/mL after morning and evening administration, respectively. Corresponding mean values of area under the plasma concentration-time curve (AUC0-24) were 227.90 and 253.66 ng.hr/mL, respectively. Statistical analysis of the log-transformed values for C(max) and AUC0-24 indicated that morning and evening administration of doxazosin were bioequivalent. There were no statistically or clinically significant differences between phases for mean apparent half-life (t1/2) or total body clearance. There were no clinically relevant differences in blood pressure or in pulse rate between phases, and no occurrences of orthostatic hypotension. The incidence of adverse experiences during morning and evening administration was similar. Morning and evening administration of doxazosin are equivalent and have similar tolerance profiles.

Plasma concentrations of pralidoxime methylsulphate in organophosphorus poisoned patients

Using pharmacokinetic data from healthy human volunteers in a bicompartmental pharmacokinetic model, a repeated dose scheme for pralidoxime methylsulphate (Contrathion) was developed producing plasma levels remaining above the assumed "therapeutic concentration" of 4 mg.l-1. Using the same data, it was found that a concentration of 4 mg.l-1 could also be obtained by a loading dose of 4.42 mg.kg-1 followed by a maintenance dose of 2.14 mg.kg-1.h-1. In order to study the pharmacokinetic behaviour of pralidoxime in poisoned patients, this continuous infusion scheme was then applied in nine cases of organophosphorus poisoning (agents: ethyl parathion, ethyl and methyl parathion, dimethoate and bromophos), and the pralidoxime plasma levels were determined. The mean plasma levels obtained in the various patients varied between 2.12 and 9 mg.l-1. Pharmacokinetic data were calculated, giving a total body clearance of 0.57 +/- 0.27 l.kg-1.h-1 (mean +/- SD), an elimination half-life of 3.44 +/- 0.90 h, and a volume of distribution of 2.77 +/- 1.45 l.kg-1.

Drug use and effects in older adults in the United States

Aging markedly influences drug use and drug effects. The purpose of this review is two-fold: (i) to examine how social, economic, and psychological factors, compliance, and prescribing patterns affect drug use in institutionalized and non-institutionalized older adults in the United States, and (ii) to illustrate how physiological aging, actions of drugs, and adverse drug reactions influence drug effects. Recommendations for further study include identification of adverse reactions, and examination of drug taking behavior in older adults who are alone or debilitated. Research is especially needed for those in nursing homes and for those who are old-old (over 85 years).

Pharmacodynamic aspects of spaceflight

Little is known at present about the effects of human exposure to microgravity on the pharmacodynamics of medicinal agents. Considering the known physiologic perturbations associated with spaceflight and the effects of some of these perturbations on the pharmacodynamics of certain medicinals that act on the central nervous system, it is likely that the pharmacodynamics of at least some of these agents will be altered in individuals who are subjected to microgravity and other conditions of spaceflight. It is timely to initiate formal studies, initially in ground-based animal models and human volunteers during prolonged, head-down bed rest and eventually in animals and human volunteers exposed to microgravity, of pharmacodynamics and pharmacokinetics during spaceflight.

Single- and multiple-dose pharmacokinetics of ceftazidime in infected patients with varying degrees of renal function

To determine the single- and multiple-dose ceftazidime kinetics, we administered ceftazidime, 2 gm intravenous bolus every 12 hours, to 14 infected Chinese patients with various degrees of renal function. Blood samples were drawn in serial after the first and 7th dose and serum ceftazidime concentrations were measured by high pressure liquid chromatography. Ceftazidime concentration-time data were fitted to a two-compartment model with a nonlinear regression program. Ceftazidime kinetics was unaltered by repeated dosing. Both total body clearance and elimination rate constant of ceftazidime decrease significantly in proportion to the creatinine clearance estimated by Bjornsson's method. Renal insufficiency did not modify the steady-state volume of distribution (Vdss) of ceftazidime which, however, appeared to be larger than those reported previously. This larger Vdss may be explained by acute infection process, confinement to bed, and increased extracellular fluid volume as a result of hypoalbuminemia. Our study indicates the estimated creatinine clearance as a useful guide to ceftazidime dosage adjustment and also emphasizes the clinical relevance of conducting kinetic studies of antibiotics in infected patients.

Research in Long-term Care Facilities

Clinical research in geriatrics, to date, has focused on the ambulatory and acutely ill patient populations. However, the unique host, disease, and environmental factors common to the nursing home resident and facility underline the need to study drug use and response in the long-term care facility. Five specific areas require investigation: efficacy, safety, dosages, utilization, and cost. To adequately study these topics, interdisciplinary research teams may use methodologies from various backgrounds, including the biologic, agricultural, epidemiologic, economic, and ethnographic research traditions. Even with the numerous methodologies available, significant procedural and design issues confront the development and performance of long-term care research. While procedural problems usually involve legal and administrative issues, methodologic concerns often stem from the need to deal with multiple confounding variables or the limitations of available research tools and clinical data bases. Continued improvement in the existing quality-of-life and functional assessment instruments as well as the development of computerized nursing home data bases will enhance clinical research in the long-term care facility.

Experimental model for the investigation of kinetic and/or dynamic interactions between drugs and ethanol in humans

This study was performed to establish an experimental method for the investigation of interactions between ethanol and drugs under predictable and controlled conditions. The model was tested with flumazenil (Ro 15-1788), a short-acting benzodiazepine antagonist with an elimination half-life of 1 h. Six healthy volunteers (5 males, 1 female) were administered ethanol by intravenous infusion with stepwise changing rates. The infusion rates were adapted to each subject on the basis of individual disposition parameters of ethanol, which were derived from preceding short-term infusions of 120 min duration (1.0 mg/kg in males, 0.8 mg/kg in the female). This two-step procedure led to individual ethanol plasma levels between 1.47 +/- 0.04 and 1.71 +/- 0.03 g/L, which were reached after 2.5 h and thereafter maintained over another 6 h. Within the period of constant ethanol levels, single doses of flumazenil and placebo, respectively, were injected intravenously as a bolus (2 min) in a double-blind fashion according to a randomized two-way crossover design. Three subjects received a dose of 0.10 mg/kg of flumazenil, and the remaining three subjects received a dose of 0.20 mg/kg. Evaluation of the plasma concentration time curves of flumazenil did not reveal evidence of an effect of ethanol on the pharmacokinetics of this drug.

The effects of posture on the pharmacokinetics of intramuscular benzylpenicillin

Previous reports have produced conflicting results as to whether changes in posture affected the pharmacokinetics of the penicillins. We have studied the pharmacokinetics of intramuscularly administered benzylpenicillin in normal subjects during bedrest and ambulation and compared it with data obtained following intravenous administration of the same dose to the same subjects under the same conditions. The values of area under the curve, total clearance, mean residence time and renal clearance found during ambulation were 1175 (min.min.l-1), 488 (ml.min-1), 101 (min), and 264 (ml.min-1) (means). The corresponding values for bedrest were 1032 (min.mg.l-1), 544 (ml.min-1), 96.7 (min), and 315 (ml.min-1). There was a significant difference between the areas under the curve with change of posture but not between any of the other pharmacokinetic variables. The differences observed in this study are unlikely to be of clinical relevance. We suggest that the differences between the results of this study and those of previous studies may be related to the level of exercise undertaken by the subjects in the various studies.

Dosage adjustment for ceftazidime in patients with impaired renal function

Ceftazidime has good antibacterial activity against many Gram-negative micro-organisms including Ps. aeruginosa. The aim of the present study was to calculate a dosage adjustment regimen for renal failure patients and to test it in a second group of patients. A study was made of the pharmacokinetics of ceftazidime 1 g given as a single bolus i.v. injection in 20 patients in an intensive care unit with varying degrees of renal function, including patients on regular haemodialysis. The serum half-life of elimination (t1/2 beta) varied from 1.6 to 45 h depending on renal function. During haemodialysis the mean t1/2 was 4.7 h. A good correlation between the renal clearance of creatinine and ceftazidime was observed. In most patients protein binding was lower than previously observed. From the pharmacokinetic data, a dosage adjustment regimen for patients with renal insufficiency was calculated, which studies in 7 further patients showed to be effective.

The effect of posture on the pharmacokinetics of intravenous benzylpenicillin

We have studied the pharmacokinetics of intravenously administered benzylpenicillin in normal subjects during bedrest and during ambulation. The values of total body clearance, mean residence time, and renal clearance found during ambulation were 487.4 +/- 100.5 ml/min, 36.23 +/- 13.45 min, and 309.4 +/- 93.4 ml/min (means +/- SD). The corresponding values for bedrest were 543.6 +/- 122.6 ml/min, 35.27 +/- 10.21 min, and 324.1 +/- 145.3 ml/min. There were no significant differences between any of these pharmacokinetic variables with the change in posture. These results differ from previously reported results for the effects of posture on the pharmacokinetics of penicillins administered by extravascular routes, and suggest that the absorption of benzylpenicillin may be dependent on posture.

Effect of posture on ampicillin pharmacokinetics, glomerular filtration rate and renal plasma flow in resting subjects

Differences in drug kinetics between supine rest and ambulation have been reported, but the relative contribution of postural changes and changes in the level of physical activity has not been evaluated. Ampicillin pharmacokinetics, glomerular filtration rate (GFR) and renal plasma flow (RPF) were studied in six male volunteers at rest in the sitting and lying position with an interval of 1 week. After intravenous administration ampicillin kinetics, analyzed according to a two-compartment open model, demonstrated significant changes in drug distribution when the position was changed from lying to sitting: alpha-increased by 50%, V1 and V beta increased by 19% and 22% respectively. Ampicillin clearance, the fraction of dose recovered from urine, GFR and RPF were, however, not influenced by the change in posture. Our data on effects of posture in resting subjects suggest that previously reported differences in drug elimination and RPF between lying and ambulatory subjects are largely due to differences in the level of physical activity.

The pharmacokinetics of furazlocillin in healthy humans

The pharmacokinetics of the novel acylureidopenicillin furazlocillin, 6-[D-2-(3-furfurylidenamino-2-oxo-imidazolidine-1-carboxamido)-2 -(4-hydroxyphenyl)-acetamido]-penicillanic acid and of its penicilloic acid derivative were investigated in five healthy male volunteers after intravenous administration of 2 and 4 g dosages. The volunteers were either in a lying or sitting position throughout the duration of the studies. The concentrations of the drug in plasma and urine were measured by two different methods in parallel: a microbiological assay and a newly developed high pressure liquid chromatography method. The latter method was also applicable for quantitation of the penicilloic acid derivative in these biological fluids. The drug's plasma protein binding (66%) and apparent red cell-plasma partition coefficient (0.055) were concentration independent. The pharmacokinetics of the drug were first order only at the lower dose level. The apparent half lives of three distinguishable phases were, respectively, 4(t1/21), 18 (t1/22), and 64 (t1/2z) min. The total and renal clearances of the drug were, respectively, 303 and 79 ml/min. The latter value implied tubular secretion of the drug. Graphical and digital computer analyses of the data were performed with a linear three compartment body model. Small but consistent deviations from linear kinetics caused by the nonrenal elimination route were observed after administration of the higher dose (4 g). In contrast, renal elimination showed no such dose dependency and was first order. The disposition kinetics of furazlocillin were body position independent. The penicilloic acid derivative of furazlocillin was found in plasma and urine in all the five subjects tested. The percentage of the dose excreted renally as the derivative amounted, respectively, to 5.2 and 7.0% after the lower and higher dosage of furazlocillin, with significant inter- and intrasubject variability. The renal clearance of the derivative was 41 ml/min.

Effect of complex formation between 4-hexylresorcinol and ethyl myristate on release rate of 4-hexylresorcinol from petrolatum base

The effect of ethyl myristate on the release rate of 4-hexylresorcinol from petrolatum base was studied at pH 7.4 and 37 degrees. 4-Hexylresorcinol was analyzed spectrophotometrically at 278 nm. The release rate of hexylresorcinol from the ointments was directly proportional to the square root of time and depended on the percentage of ethyl myristate in the ointment base. For 0, 0.5, 1, 3, and 5% of ethyl myristate, the release rates were 29.6, 35.4, 38.3, 55.7, and 70.0 micrograms/hr1/2/cm2, respectively. The solubility of hexylresorcinol in the petrolatum base was determined as a function of ethyl myristate using partitioning techniques. The enhancement in hexylresorcinol solubility was rationalized on the basis of 1:1 and 1:2 complexes between hexylresorcinol and ethyl myristate. The complexation constants of these complexes were estimated to be 10 M-1 and 206.1 M-2, respectively. The diffusion coefficient of hexylresorcinol in the petrolatum base was estimated to be 1.31 x 10(-8) cm2/sec.

Effect of posture and sleep on pharmacokinetics. I. Amoxycillin

The pharmacokinetics of amoxycillin in normal male volunteers was studied during the states of bedrest, sleep and ambulation. The absorption and disposition of amoxycillin in ambulatory subjects was found to be comparable to that reported previously by other workers. Serum amoxycillin concentrations were found to be significantly greater during ambulation than during bedrest and sleep. The difference in serum levels resulted from an increased apparent total serum clearance and amoxycillin renal clearance during bedrest and sleep compared to ambulation. No significant differences in the clearance was found between the states of bedrest and sleep. The change in renal clearance of amoxycillin during ambulation was attributed to a diminished renal blood flow. Although the terminal half-life of amoxycillin did not differ significantly, the apparent volume of distribution appears to be much greater during bedrest and sleep than during ambulation. This difference could be explained pharmacokinetically using a two compartment model. No significant difference was found between the rates of absorption of amoxycillin as reflected by the lag time and time to peak serum amoxycillin. The actual values for these parameters would suggest, however, that the absorption of amoxycillin is faster during ambulation than in bedrest and that the absorption rate during sleep is slowest. The clinical implications of the effect of posture and sleep on the pharmacokinetics of amoxycillin are discussed.

Absolute bioavailability of chlorthalidone in man: a cross-over study after intravenous and oral administration

Seven normal human volunteers each received a constant-rate infusion of chlorthalidone for 2 h, and the same (commonly 50 mg) single oral dose on separate occasions. The concentration of unchanged chlorthalidone was analyzed over a 100 to 220 h period in plasma, red blood cells, urine and faeces after both dosage forms. A three compartment model was required to describe the intravenous plasma concentrations in five of the subjects. A two compartment model sufficed to account for the decay of the oral plasma concentrations in all seven subjects. The mean plasma t1/2 after i.v. dosing was 36.5 h (+/- 10.5 SD), and the mean plasma t1/2 after oral doses was 44.1 h (+/- 9.6 SD). The mean red blood cell concentration t1/2 after i.v. doses was 46.4 h (+/- 9.9 SD), and the mean red blood cell t1/2 after the oral doses was 52.7 h (+/- 9.0 SD). The shorter i.v. half-live was not equally manifest in all subjects, being mainly apparent in three of them. In all cases the urinary excretion rate plots were parallel to the plasma concentration curves. As the faster decay after i.v. administration was not accompanied by increased renal clearance, the difference must have been due to non-renal mechanism. The mean total of 65.4 (+/- 8.6 SD) % of the intranvenous dose was excreted in urine over infinite time, whereas the mean total excretion after the oral dose was 43.8 (+/- 8.5 SD) %. Faecal excretion ranged from 1.3--8.5% of dose in the i.v. study to 17.5--31.2% of dose in the oral study. The sum of the amounts present in urine plus faeces pointed strongly to an important metabolic route of elimination of chlorthalidone. Bioavailability estimates (F) from three sets of data were--a mean F of 0.61 from plasma concentrations, 0.67 from urinary excretion measurements and 0.72 from the erythrocyte concentrations. Simulations with a non-linear model indicated lesser validity of the estimate from erythrocyte concentrations. It was concluded that the average of plasma and urine data, F = 0.64, yielded the best estimate of the oral availability of chlorthalidone 50 mg in man.

The metabolism of methaqualone in patients with biliary cirrhosis or secondary carcinoma of the liver

The metabolism of methaqualone has been studied in three patients with secondary carcinoma of the liver and two with biliary cirrhosis. The urinary excretion of five C-monohydroxy metabolites and the N-oxide was studies in the 24 h period immediately after oral dosing with 250 mg methaqualone (Melsed). In both patients with biliary cirrhosis and one with primary carcinoma of the bile duct or pancreas with secondaries in the liver the pattern of metabolites was normal. In a patient with oat cell carcinoma with secondaries in the liver some metabolite patterns were disturbed and increased metabolite excretion occurred. A patient with primary carcinoma of the breast with secondaries in the liver gave a completely abnormal metabolite pattern.

Influence of bed rest on the pharmacokinetics of phenazone

The pharmacokinetics of a single dose of phenazone was studied in six objects while ambulant and during bed rest for 3 days. Elimination of the drug was followed for 12 h after oral and intravenous administration. The elimination rate constant and total body clearance were significantly increased during bed rest as compared to the ambulant period, but the differences were small. The apparent volume of distribution decreased significantly. No consistent change due to bed rest was found in the rate of absorption or bioavailability of the oral dose.

Effect of exercise on the serum level and urinary excretion of tetracycline, doxycycline and sulphamethizole

The serum level and urinary excretion of sulphamethizole, tetracycline and doxycycline were studied in healthy volunteers subjected to intensive exercise and bed rest in a cross-over trial. Each group consisted of 7--8 subjects. The exercise or bed rest began 15 min before oral administration of the drug and was continued for the following 4 hours. During exercise serum drug concentration and the area under the serum concentration-time curve for each agent was significantly higher (p less than 0.05) than the corresponding values at rest. Exercise greatly suppressed the renal excretion of tetracycline and doxycycline, but the decrease alone appeared insufficient to account for the pronounced increase in serum drug concentration. Total drug excretion in urine was unchanged. Thus, it seemed most unlikely that overall absorption from the gastrointestinal tract had been altered by exercise. However, the rate of absorption appeared to be more rapid in the exercise than in the rest period. Marked haemoconcentration was not produced by the exercise. In addition to changes in absorption and elimination rates, alteration in the volume of distribution might contribute to the higher serum drug concentration during exercise. Therefore, the level of physical activity should be considered in the interpretation of pharmacokinetic data both in clinical practice and in pharmacokinetic studies.

Bioavailability of a sustained-release dyphylline formulation

The bioavailability of dyphylline from sustained-release tablets, studied in seven normal subjects given a single dose of the drug, was 67.8 per cent of that from conventional tablets. In three subjects given 40 mg/kg dyphylline as sustained-release tablets every 8 hours for four days, serum dyphylline concentrations were maintained above 7.88 microng/ml once steady state was achieved. No adverse effects were noted, though in one subject peak serum dyphylline concentrations reached 30 microng/ml after multiple doses.

Drug metabolism under pathological and abnormal physiological states in animals and man

The activity of microsomal drug-metabolizing enzymes is altered by several pathological or abnormal physiological states, such as changes in nutritional status, liver, heart or kidney diseases, hormonal disturbances, pregnancy, tumour-bearing state, adjuvant arthritis, changes in reticuloendothelial system and environmental factors (stress, irradiation, heavy metals). The activities of other metabolic pathways, such as glucuronidation, sulphate conjugation, acetylation and alcohol oxidation are generally affected to lesser extents. Rats are most commonly used in drug metabolism studies, and it is important to know that the activity of most of the microsomal drug-metabolizing enzymes is higher in males than in females through androgen action which is readily impaire drug-metabolizing enzymes in male rats are thus manifested by two mechanisms; one is by impairment of androgen action and the other is by depression of the basic enzymic activity. Therefore, those effects of pathological states, observed only in male rats but not in females, are generally not seen in other species of animals, including man. The effects of starvation, hyperthyroidism, adrenal insufficiency, diabetes and morphine administration are cases where changes in metabolism are due solely to impairment of androgen action. In other pathological cases, those drug-metabolizing enzymes showing sex differences are depressed more markedly in male rats than those showing no clear sex difference. The author therefore recommends the use of female rats in the evaluation of the effects of pathological states on hepatic microsomal drug-metabolizing enzymes. Generally, changes in activity of the hepatic enzymes reflect closely the changes in the rates of drug metabolism in vivo. However, the protein-binding of drugs, hepatic blood flow and renal function are also known to affect the rate of drug metabolism and excretion in vivo, and therefore changes of these factors in pathological states should also be taken into consideration.

Chronopharmacokinetics of ethanol. II. Circadian rhythm in rate of blood level decline in a single subject

A male human subject administered single, oral doses of ethanol was examined repeatedly for venous ethanol levels. Four separate trials, begun at 03.00, 09.00, 15.00, and 21.00 h, on different days yielded four different estimates of the slope of the apparently linear ethanol disappearance curve. The slopes appeared to exhibit circadian rhythmicity. In a second study of the same subject, the slope was estimated 7 times over a period of 26 h following repeated oral doses. These slopes also appeared to vary in a daily fashion. These preliminary results suggest that pharmacokinetic parameters may not be invariable with time of day.

Release of corticoids from oleaginous ointment bases containing drug in suspension

Simplified methods for studying the release of drugs suspended in oleaginous ointment bases were developed. These procedures were used in studying the release rates of two corticoids, fluocinonide and flucloronide, from white petrolatum and petrolatum containing various adjuvants. A practical method for measuring drug solubilities was developed and used in determining solubilities of these corticoids in ointment bases. When using physical data obtained from model ointments, the release rates of drugs from modified ointment bases were predicted. Comparisons of the observed and predicted rates from ointments containing hydrophobic adjuvants indicated the usefulness of the physical model approach in predicting the release rates. For ointments containing emulsifying agents, the simple model used did not provide useful predictions.