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PubMed2001

Self-rated health and limiting longstanding illness: inter-relationships with morbidity in early adulthood.

BACKGROUND: Self-rated health and limiting longstanding illness are both widely used global measures of health, but understanding is poor of their meaning and validity at younger ages. METHODS: We examined the association between self-rated health and limiting longstanding illness and specific health problems at two ages (23 and 33 years), and assessed change over the 10-year period for each health measure relative to another. Longitudinal data were taken from the nationally representative British birth cohort for which health measures were obtained at ages 23 and 33. RESULTS: Self-rated health and limiting longstanding illness were strongly associated with each other as well as with specific health problems, particularly with serious conditions (e.g. epilepsy, cancer, diabetes) and more weakly with less serious conditions (e.g. eczema and hay fever). Rating of overall health and limiting longstanding illness was highly stable during the 10-year period with most, but not all, health change reflecting a deterioration in health status. Deterioration in limiting illness corresponded to an even greater health decline in specific conditions. CONCLUSIONS: Self-rated health and limiting longstanding illness are valid health measures appropriate for use in general health surveys.

Adult↗

PubMed2000

An association between length of stay and co-morbidity in chronic airflow limitation.

OBJECTIVE: To examine factors which impact on the length of stay and readmission for patients with chronic airflow limitation at a South Australian hospital from December 1996 until March 1998. DESIGN: Discharges from Flinders Medical Centre for patients aged > or = 18 years, where chronic airflow limitation was an active problem, and including a subset with a primary diagnosis of chronic airflow limitation, were identified, retrospectively, by the center's Clinical Coding Service from the hospital's in-patient separation database. SETTING: Flinders Medical Centre, Adelaide, South Australia. OUTCOME MEASURES: Length of stay; number of co-morbidities; readmission within 28 days. RESULTS: Five-hundred and twenty discharges (male:female, 258:262) with a primary diagnosis of chronic airflow limitation (ANDRG-3 177, chronic obstructive airways disease) were identified. Readmission within 28 days was related to the number of co-morbidities and to age. A relationship between length of stay and the number of co-morbidities was identified. A mean length of stay of 6.39 days was found for patients with less than five co-morbidities, 5.36 at their first admission to Flinders Medical Centre and 3.25 at their first admission to Flinders Medical Centre with no co-morbidities. These mean lengths of stay fall below overseas data previously published and are consistent with Kong's estimate of an ideal mean length of stay of 3.2 days when a clinical management guideline is used in low-risk chronic airflow limitation patients. CONCLUSIONS: Length of stay and readmission to hospital within 28 days of patients with a primary diagnosis of chronic airflow limitation is at least partly related to the number of co-morbidities and to age. The study has highlighted the difficulty of relying on changes to aggregate data as outcome measures for these patients.

Adult↗

PubMed1986

Response of rats to diets of equal chemical score: effect of lysine or threonine as the limiting amino acid and of an amino acid excess.

The effect of lysine or threonine deficiency with or without excesses of all other amino acids was evaluated in a 21-d feeding study with male rats. Four amino acid mixtures were designed to be first limiting for the rat in lysine or threonine and contained either 0 or 50% excess of nonlimiting amino acids. These mixtures were incorporated into purified diets to provide seven levels [20-140% of the National Research Council (NRC) requirement] of the limiting amino acid. Food intake, body weight gain and carcass composition were measured for each rat to determine the effects of the identity of the limiting amino acid and of amino acid excess on the response to dietary chemical score. Significant effects and/or interactions of the identity of the limiting amino acid (i.e., Lys or Thr) and the presence of excess amino acids were seen for each of the measured responses. At equivalent dietary percentages of the NRC requirement, threonine deficiency supported greater body weight gain than did lysine deficiency. At equivalent deficiencies (Lys vs. Thr) threonine-deficient rats were more susceptible to adverse effects of excess amino acids. When the limiting amino acids were incorporated into the diet through incremental addition of the deficient amino acid mixture, rats responded to levels of lysine or threonine in excess of the NRC requirement. These results suggest that the current NRC requirements for these amino acids are too low and that aspects of the dietary amino acid composition other than the percentage deficit of the limiting amino acid can be important determinants of animal response.

Animals↗

PubMed2004

The photosynthetic limitation posed by internal conductance to CO2 movement is increased by nutrient supply.

The internal conductance to CO(2) supply from substomatal cavities to sites of carboxylation may pose a large limitation to photosynthesis, but little is known of how it is affected by nutrient supply. Knowing how internal conductance responds to nutrient supply is critical for interpreting the biochemical responses from A-C(i) curves. The aim of this paper was to examine the response of g(i) and photosynthetic parameters to nutrient supply in glasshouse-grown seedlings of the evergreen perennial Eucalyptus globulus Labill. Seedlings were grown with five different nutrient treatments and g(i) was estimated from concurrent measurements of gas exchange and fluorescence. Internal conductance varied between 0.12 and 0.19 mol m(-2) s(-1) and the relative limitation of photosynthesis due to internal conductance was greater than the stomatal limitation. In most species these two limitations are rather similar, but in E. globulus stomatal limitations were abnormally low due to high stomatal conductance (0.31 to 0.39 mol m(-2) s(-1)). The large positive response of photosynthesis to nutrient supply was not matched by changes in internal conductance, and thus the relative limitation of photosynthesis due to internal conductance increased with increasing nutrient supply. Failure to account for finite internal conductance led to estimates of V(cmax) that were 60% of the true value, which, in turn, led to an underestimation of in vivo Rubisco specific activity (as V(cmax)/Rubisco content). The specific activity of Rubisco in E. globulus (21 mol mol(-1) s(-1)) was close to the maximum published estimates, and thus, despite these leaves containing a large fraction of N as Rubisco (38-44%) there was no evidence that Rubisco activity was down-regulated or that the enzyme was in excess.

Carbon Dioxide↗

PubMed2005

Is root growth under phosphorus deficiency affected by source or sink limitations?

Reduced net photosynthesis (Pn) and decreasing shoot and root biomass are typical effects of phosphorus deficiency in plants. Lower biomass accumulation could be the result of reduced Pn (source limitation), but may also be due to direct negative effects of low P availability on growth (sink limitation). Because of the principal importance of root growth for P uptake, this study specifically examined the question whether source or sink limitations were responsible for reduced root growth rates under P deficiency. Rice plants were grown in nutrient solutions with four levels of P supply and at two light treatments and the effect of Pxlight treatments on growth and carbohydrate distribution was observed. Plants had up to 70% higher Pn when grown with natural (high) light compared with low light. Higher Pn, however, did not lead to additional growth under P deficiency, suggesting that assimilate supply from source leaves to roots was not a limiting factor under P deficiency. This was supported by observations that root starch concentrations increased in P-deficient roots. The comparison of two genotypes with different tolerance to P deficiency showed that the more tolerant one preferentially distributed P to roots where the additional P stimulated root growth and, ultimately, P uptake. The results therefore suggest that source limitation is of little importance under P deficiency. Even at highly sub-optimal tissue P concentrations of below 0.7 mg P g(-1) dry weight, plants were able to produce enough assimilates to sustain growth rates that were directly limited by low P availability.

Biological Transport, Active↗

PubMed1984

Limited hepatic resection effective for selected cirrhotic patients with primary liver cancer.

We evaluated in retrospect the applicability of limited hepatic resection in cases of primary liver cancer in cirrhotic patients. According to the severity of impaired liver function, 37 patients underwent limited resection, and for 13, standard major hepatic resection was done. The mortality rate in case of limited resection was 10.8%, and the rate in case of massive excision was 15.4%. One, two- and five-year survival rates of limited operation were 79.9, 60.3, and 32.6%, respectively. After standard resection, the rates were 78.7, 67.5, and 22.5%, respectively. There were no significant differences in the mortality and survival rates between the two groups. These results indicate that, for the patient with a small liver cancer, and poor liver function, the limited procedure leads to a comparatively longer survival. This limited resection can be selectively used to treat cancer associated with cirrhosis and encapsulated tumors. For the preoperative evaluation, hepatic arteriograms aid in patient selection.

Adult↗

PubMed2000

Limited resection for early adenocarcinoma in Barrett's esophagus.

OBJECTIVE: To assess the extent of disease in patients with pT1 esophageal adenocarcinoma and to evaluate the feasibility and outcomes of a limited surgical approach. SUMMARY BACKGROUND DATA: Radical esophagectomy with systematic lymphadenectomy is widely advocated as the treatment of choice in patients with early adenocarcinoma of the distal esophagus. This approach, however, is associated with substantial complications and long-term side effects. The extent of resection necessary to achieve cure in such patients is not clear. METHODS: Seventy-one patients with pT1 adenocarcinoma of the distal esophagus underwent transmediastinal or transthoracic esophagectomy with two-field lymphadenectomy. Twenty-four patients with uT1N0 tumors underwent a limited resection of the distal esophagus and esophagogastric junction, regional lymphadenectomy, and reconstruction by interposition of an isoperistaltic pedicled jejunal segment. The two groups were compared for extent and multicentricity of the primary tumor and associated high-grade dysplasia, pattern of lymph node metastases, complications, deaths, and outcome of surgical treatment. RESULTS: Multicentric tumor growth or associated high-grade dysplasia was observed in 60.6% of the resection specimens. Complete resection of the tumor and the entire segment with intestinal metaplasia was achieved in all patients, irrespective of the surgical approach. Patients undergoing limited resection had fewer complications. Lymph node metastases or micrometastases were present in none of the 38 patients with tumors limited to the mucosa (pT1a) versus 10 of the 56 (17.9%) patients with tumors invading the submucosa (pT1b). Distant lymph node metastases occurred only in patients with more than three positive regional lymph nodes. Lymph node metastases were prognostic, but the pT1a/pT1b category and the surgical approach were not. The mean Gastrointestinal Quality of Life Index after limited resection did not differ from that of healthy controls: 20 of the 24 patients were completely asymptomatic. CONCLUSIONS: In patients with early adenocarcinoma in the distal esophagus, resection of the distal esophagus and esophagogastric junction, with regional lymphadenectomy and jejunal interposition, is an attractive limited surgical alternative to radical esophagectomy.

Adenocarcinoma↗

PubMed2000

Are public dose limits necessary?

The distinction between practices and interventions in the System of Radiation Protection has created a lot of confusion in the population and amongst decision-makers, especially with regards to the concepts of dose limits and intervention levels. The experience gained after the Chernobyl accident indicated that many actions taken led to an unnecessarily large expenditure of national resources and many instances occurred of contradictory national responses. A major reason was the mixture of dose limits for the population, which apply only to exposures from practices, and intervention levels, which apply only to protective measures in de-facto exposure situations. The existing System of Radiation Protection is revisited and it is suggested that the System can be revised with no dose limits for the public without causing a lower degree of protection of the population. With the widespread use of source-related dose constraints and practical restrictions on the sources of public exposure from practices, generally applicable dose limits are rarely limiting in any practical situation, even if dose constraints might, at least in principle, fail to take adequate account of the exposures from other practices. Constraints can be expressed as operational protection quantities, e.g., nuclide-specific release rates, dose rate at the fence of a facility, or nuclide-specific surface contamination density in the environment. A revised System of Radiation Protection without public dose limits would not cause any reduced protection of the public compared to the existing System, and it has a potential for removing much of the confusion with regards to application of intervention/action levels. It would also have the potential for improving public perception of radiation protection and radiation risks as well as for saving vast resources in intervention situations for better application in general health care of the public.

Humans↗

PubMed2002

Dealing with uncertainty in formulating occupational and public exposure limits.

Scientists are forced to address many sources of uncertainty in the setting of exposure limits. This paper discusses the rationale for some of the approaches that have been used for many years to address uncertainties encountered in the setting of occupational and public exposure limits to protect against non-cancer effects of chemicals. These approaches are quite different from the methodology that has been adopted for the setting of exposure limits to power-frequency electric and magnetic fields to avoid adverse effects of induced electric fields and currents. The limitations of the non-standard electric and magnetic fields guideline methodology are described. To address these limitations, a probabilistic approach to developing exposure limits for electric and magnetic fields has been proposed. As a demonstration, this approach has been applied to the estimation of magnetic field exposures that would not pose significant risks of cardiac stimulation from electric fields induced in the torso. The results of this probabilistic analysis demonstrate the importance of explicitly characterizing potential sources of uncertainty and variability. Furthermore, the use of fixed, single point estimates of dosimetric parameters by electric and magnetic fields guideline-setting organizations provides more than adequate protection to individuals from the risk of cardiac stimulation. The mean magnetic field level that would increase the risk of cardiac stimulation is shown by this approach to be about three times higher than is predicted by dosimetric formulas used by the ACGIH and ICNIRP. If input data for parameters affecting the risk of adverse effects with lower thresholds, i.e., nerve stimulation, are developed and validated, this method could be used in the setting of electric and magnetic fields standards based more strongly on quantitative assessments of experimental data.

Electromagnetic Fields↗

PubMed1998

Determinants of the limits of agreement between the sphygmomanometer and the SpaceLabs 90207 device for blood pressure measurement in health volunteers and insulin-dependent diabetic patients.

OBJECTIVE: To compare the limits of agreement between the SpaceLabs 90207 oscillometric blood pressure measurement device and the sphygmomanometer for patients with insulin-dependent diabetes mellitus (IDDM) versus healthy control subjects. DESIGN: A retrospective analysis of six simultaneous blood pressure measurements in 106 IDDM patients aged 32.6+/-12.0 years (mean +/- SD) and 92 healthy control subjects aged 27.1+/-8.9 years with the SpaceLabs device and a sphygmomanometer. RESULTS: For both groups, overestimation of the systolic blood pressure occurred with the SpaceLabs device, being more severe for the IDDM group (1.7 mmHg more overestimation, P= 0.009). Mean arterial blood pressure was underestimated for the control group and overestimated for the IDDM group (2.7 mmHg underestimation and 0.8 mmHg overestimation, respectively). Diastolic blood pressures for both groups were underestimated by use of the SpaceLabs device, but less severely so for the IDDM group (4.2 mmHg, P< 0.0001 less underestimation). Multiple regression analysis revealed that these differences were mainly due to the presence of diabetes. Other determinants of these limits of agreement were age (for control group subjects) and duration of diabetes (for IDDM group patients). CONCLUSION: Limits of agreement between the SpaceLabs 90207 device and the sphygmomanometer differ between IDDM patients and healthy controls. These limits are influenced by the presence of diabetes, age and duration of diabetes. Available protocols for the evaluation of automated blood pressure measurement devices of the British Hypertension Society and the Association for the Advancement of Medical Instrumentation do not consider limits of agreement in subpopulations such as diabetic patients. Therefore, we recommend that tests for the limits of agreement of blood pressure measurement devices for subgroups should be added to these protocols.

Adolescent↗

PubMed1998

CP-060S, a novel cardioprotective drug, limits myocardial infarct size in anesthetized dogs.

The myocardial infarct size (IS)-limiting effect of CP-060S, a novel cardioprotective drug that prevents Na+-, Ca2+-overload and has Ca2+ channel-blocking activity, was compared with that of diltiazem, a pure Ca2+ antagonist, to determine whether the prevention of Na+-, Ca2+-overload contributes to this IS-limiting effect. Dogs were subjected to 90 min of left circumflex coronary artery (LCx) occlusion followed by 5 h of reperfusion. Either CP-060S (300 microg/kg) or diltiazem (600 microg/kg) was administered intravenously 20 min before the occlusion. CP-060S significantly limited IS compared with that of vehicle (percentage of the area at risk: vehicle, 50.64 +/- 6.08%; CP-060S, 21.13 +/- 3.75%; p < 0.01 vs. vehicle). Although diltiazem exerted a significant decrease in rate-pressure product (RPP; an index of myocardial oxygen consumption) during occlusion equal to that of CP-060S, diltiazem did not significantly reduce IS (33.90 +/- 4.30%). Regional myocardial blood flow (RBF) was not significantly different between any of the groups. Therefore the IS-limiting effect of CP-060S cannot be explained in terms of changes in RPP or RBF. Thus the IS limitation induced by CP-060S is probably the consequence of a direct cardioprotective effect on myocytes. The prevention of Na+-, Ca2+-overload may be the primary reason for this IS-limiting effect.

Animals↗

PubMed2001

Ventilatory limitations in chronic obstructive pulmonary disease.

Chronic obstructive pulmonary disease (COPD) is a heterogeneous disorder characterized by dysfunction of the small and large airways, as well as by destruction of the lung parenchyma and vasculature, in highly variable combinations. Breathlessness and exercise intolerance are the most common symptoms in COPD and progress relentlessly as the disease advances. Exercise intolerance is multifactorial, but in more severe disease, ventilatory limitation is often the proximate exercise-limiting event. Multiple factors determine ventilatory limitation and include integrated abnormalities in ventilatory mechanics and ventilatory muscle function as well as increased ventilatory demands (as a result of gas exchange abnormalities) and alterations in the neuroregulatory control of breathing. Despite its heterogeneity, the pathophysiological hallmark of COPD is expiratory flow limitation. When ventilation increases in flow-limited patients during exercise, air trapping is inevitable and causes further dynamic lung hyperinflation (DH) above the already increased resting volumes. DH causes elastic and inspiratory threshold loading of inspiratory muscles already burdened with increased resistive work. It seriously constrains tidal volume expansion during exercise. DH compromises the ability of the inspiratory muscles to generate pressure, and the positive intrathoracic pressures likely contribute to cardiac impairment during exercise. Progressive DH hastens the development of critical ventilatory constraints that limit exercise and, by causing serious neuromechanical uncoupling, contributes importantly to the quality and intensity of breathlessness. The corollary of this is that therapeutic interventions that reduce operational lung volumes during exercise, by improving lung emptying or by reducing ventilatory demand (which delays the rate of DH), result in clinically meaningful improvement of exercise endurance and symptoms in disabled COPD patients.

Dyspnea↗

PubMed1989

Threshold limit values: historical perspectives and current practice.

A 1989 Occupational Safety and Health Administration standard mandates that workplace air concentrations be held below new permissible exposure limits for 376 substances. As more than 350 of these limits came from the 1987 list of "Threshold Limit Values" (TLVs), the medical basis of the TLVs is of direct importance to the health of millions of workers. However, the TLV development process has been gravely flawed by lack of scientific rigor, inadequate medical input, and lack of attention to financial conflicts of interest. The adoption by the Occupational Safety and Health Administration of many poorly supported values as permissible exposure limits reflects also the underutilization of industrial medicine in identifying health effects of exposures below the TLVs. It is thus the responsibility of the medical profession to act on the presumption that the TLV permissible exposure limits are unsafe limits until a sound underlying body of medical and scientific literature exists for the substances on the list. It is industry's responsibility to commit itself seriously to medical and exposure monitoring and to begin to remedy the knowledge deficit that exists about the less immediate health effects of most industrial materials.

Air Pollutants, Occupational↗

PubMed2006

A prospective controlled study of limited versus subtotal posterior discectomy: short-term outcomes in patients with herniated lumbar intervertebral discs and large posterior anular defect.

STUDY DESIGN: Prospective observational study with historical control. The prospective study population consisted of 30 patients undergoing a posterior lumbar subtotal discectomy for lumbar disc herniation. This group was compared to a historical cohort of 46 patients treated with limited discectomy alone. OBJECTIVE: To compare clinical outcomes after limited versus subtotal discectomy for lumbar disc herniations. SUMMARY OF BACKGROUND DATA: Large posterior anular defects found at posterior discectomy have been associated with more frequent reherniation when treated with limited discectomy (i.e., removing only extruded or loose intervertebral fragments). A trial of more aggressive discectomy (subtotal) was undertaken to determine if the rate of reherniation could be decreased with this technique. METHODS: A total of 30 patients undergoing a posterior lumbar discectomy for lumbar disc herniation were treated with an aggressive (subtotal) resection of intervertebral disc material after removal of the extruded or protruded fragments. This group was compared against a historical cohort of 46 patients treated with limited discectomy alone. Reherniation rates and clinical outcomes were determined by independent evaluation at 6, 12, and 24 months after surgery. RESULTS: The reherniation rate in the limited discectomy group was 18% versus 9% in the subtotal discectomy group at follow-up (P = 0.1). However, the back pain (visual analog scale) (P = 0.02) and Oswestry scores (P = 0.06) were worse in the subtotal discectomy group at 12-month follow-up. Time to return to work was longer, and pain medication usage was higher in the subtotal discectomy group at 12-month follow-up. Despite a trend toward a higher reherniation rate, the patient satisfaction at 2-year follow-up was higher in the limited discectomy group. CONCLUSIONS: The more aggressive removal of remaining intervertebral disc material may decrease the risk of reherniation, but the overall outcome was less satisfactory, especially during the first year after surgery.

Adult↗

PubMed2004

Arthritis and heart disease as risk factors for major depression: the role of functional limitation.

BACKGROUND: Major depression in later life is highest among people with chronic illness. Identifying amenable factors that mediate the relationship between known risk factors such as arthritis and heart disease with major depression is important to the design of clinical and public health strategies to reduce depression and its consequences. OBJECTIVE: This study investigates factors amenable to clinical and public health intervention that could mediate the relationship between chronic illness and major depression. DESIGN: Population-based national sample. SETTING: United States preretirement age (54-65) adults. PARTICIPANTS: A total of 7825 participants from the 1996 Health and Retirement Survey. MEASUREMENT: The outcome is major depression based on standardized assessment. Independent variables include sociodemographics chronic illness profile, functional limitation, health and medical access. RESULTS: A substantial burden of major depression is related to chronic illness, particularly arthritis (attributable risk [AR], 18.1%; 95% confidence interval [CI], 9.9-25.6) and heart disease (AR, 17.6%; 95% CI, 13.4-21.7). Functional limitation is the strongest investigated factor associated with depression (AR, 34.4%; 95% CI, 24.8-42.7) and attenuates the associations of arthritis and heart disease with depression. CONCLUSION: Functional limitation mediates the association of arthritis and heart disease with major depression. This relationship offers potential clinical and public health strategies to reduce major depression in older adults through intervention and management of functional limitation. Alternatively, it might be possible to reduce functional loss through screening for depression, particularly among people with functional limitation, and effective mental health treatment. The importance for clinical management of depression, comorbidity, and functional limitation spectrum supports the value of systems-based medicine.

Activities of Daily Living↗

PubMed1976

Regulation of the tricarboxylic acid cycle and poly-beta-hydroxybutyrate metabolism in Azotobacter beijerinckii grown under nitrogen or oxygen limitation.

Azotobacter beijerinckii was grown in ammonia-free glucose/mineral salts media in chemostat culture under oxygen or nitrogen limitation. Selected enzymes of the tricarboxylic acid cycle and poly-beta-hydroxybutyrate metabolism were monitored in relation to oxygen supply for both steady and transition states. Two dissolved oxygen concentrations were used for the nitrogen-limited steady state to investigate the possible effects of respiratory protection of nitrogenase on these enzymes. The levels of NADH oxidase, isocitrate dehydrogenase and 2-oxoglutarate dehydrogenase increased markedly on relaxation of oxygen limitation while pyruvate dehydrogenase and citrate synthase were relatively unaffected. beta-Ketothiolase and acetoacetyl-CoA reductase levels decreased as oxygen limitation was relaxed. Respiratory activity, as measured by the QO2 value, increased with oxygen supply rate. Imposition of oxygen limitation on a nitrogen-limited culture caused an immediate increase in the NADH/NAD ratio but this rapidly readjusted to its previous steady-state value. These changes are discussed in relation to respiratory protection of nitrogenase and poly-beta-hydroxybutyrate metabolism in A. beijerinckii.

Acetyl-CoA C-Acetyltransferase↗

PubMed1994

The physiological function of periplasmic glucose oxidation in phosphate-limited chemostat cultures of Klebsiella pneumoniae NCTC 418.

Periplasmic oxidation of glucose into gluconate and 2-ketogluconate in Klebsiella pneumoniae occurs via glucose dehydrogenase (GDH) and gluconate dehydrogenase (GaDH), respectively. Since, as is shown here, in the presence of glucose, gluconate and 2-ketogluconate are not further metabolized intracellularly the physiological function of this periplasmic route was studied. It was found that periplasmic oxidation of glucose could function as an alternative production route of ATP equivalents. Instantaneous activation of either GDH or GaDH reduced the rate of degradation of glucose via glycolysis and the tricarboxylic acid (TCA) cycle in vivo. Furthermore, aerobic, magnesium- and phosphate-limited chemostat cultures with glucose as the carbon source showed high GDH plus GaDH activities in contrast to nitrogen- and sulphate-limited cultures. However, when fructose, which is not degraded by GDH, was the carbon source, specific oxygen consumption rates under these four conditions were essentially the same. The latter observation suggests that high transmembrane phosphate gradients which are supposedly present under phosphate-limited conditions do not cause high energetic demands due to futile cycling of phosphate ions. In addition, dissipation of the transmembrane phosphate gradient of phosphate-limited cells immediately increased the rate of intracellular glucose degradation. It is concluded that under phosphate-limited conditions (i) extensive futile cycling of phosphate ions is absent and (ii) low concentrations of phosphate ions limit intracellular degradation of glucose.(ABSTRACT TRUNCATED AT 250 WORDS)

Adenosine Triphosphate↗

PubMed2005

Fine structure of distributions and central limit theorem in diffusive billiards.

We investigate deterministic diffusion in periodic billiard models, in terms of the convergence of rescaled distributions to the limiting normal distribution required by the central limit theorem; this is stronger than the usual requirement that the mean-square displacement grow asymptotically linearly in time. The main model studied is a chaotic Lorentz gas where the central limit theorem has been rigorously proved. We study one-dimensional position and displacement densities describing the time evolution of statistical ensembles in a channel geometry, using a more refined method than histograms. We find a pronounced oscillatory fine structure, and show that this has its origin in the geometry of the billiard domain. This fine structure prevents the rescaled densities from converging pointwise to Gaussian densities; however, demodulating them by the fine structure gives new densities which seem to converge uniformly. We give an analytical estimate of the rate of convergence of the original distributions to the limiting normal distribution, based on the analysis of the fine structure, which agrees well with simulation results. We show that using a Maxwellian (Gaussian) distribution of velocities in place of unit speed velocities does not affect the growth of the mean-square displacement, but changes the limiting shape of the distributions to a non-Gaussian one. Using the same methods, we give numerical evidence that a nonchaotic polygonal channel model also obeys the central limit theorem, but with a slower convergence rate.

Journal Article↗