Mathematical Index Research Articles

IN VITRO GLYCOLYSIS OF WHOLE BLOOD CAN DETECT PRIMED NEUTROPHILS IN SEPTIC ICU PATIENTS

The purpose of this study was to develop a bedside assay based on the in vitro glycolysis of a whole blood sample that could detect primed neutrophils (PMNs). A mathematical index of the PMN response to exogenous stimulation with phorbol myristate 13-acetate (PMA), called the Delta value, was derived by comparing the increase in glycolysis for paired blood samples with and without PMA to that expected from normal subjects. Delta values for systemic inflammatory response syndrome/sepsis patients (9.09 +/- 7.61) (N = 36) were significantly higher than normal controls (2.02 +/- 1.76) (N = 51), nonsepsis ICU patients (3.81 +/- 2.80) (N = 14) and patients in septic shock (2.33 +/- 3.04) (N = 10) (p < .05). Delta values were consistently reflected in parallel measurements of increased reactive oxygen species production by neutrophils detected cytofluorometrically. PMN priming can be simply and rapidly detected by an assay based on the numbers of PMNs and erythrocytes and the measured rates of in vitro glycolysis of paired whole blood samples with and without PMA.

IN VITRO GLYCOLYSIS OF WHOLE BLOOD CAN DETECT PRIMED NEUTROPHILS IN SEPTIC ICU PATIENTS

The purpose of this study was to develop a bedside assay based on the in vitro glycolysis of a whole blood sample that could detect primed neutrophils (PMNs). A mathematical index of the PMN response to exogenous stimulation with phorbol myristate 13-acetate (PMA), called the Delta value, was derived by comparing the increase in glycolysis for paired blood samples with and without PMA to that expected from normal subjects. Delta values for systemic inflammatory response syndrome/sepsis patients (9.09 ± 7.61) (N = 36) were significantly higher than normal controls (2.02 ± 1.76) (N = 51), nonsepsis ICU patients (3.81 ± 2.80) (N = 14) and patients in septic shock (2.33 ± 3.04) (N = 10) (p < .05). Delta values were consistently reflected in parallel measurements of increased reactive oxygen species production by neutrophils detected cytofluorometrically. PMN priming can be simply and rapidly detected by an assay based on the numbers of PMNs and erythrocytes and the measured rates of in vitro glycolysis of paired whole blood samples with and without PMA.

Water quality in Salmonid culture

Abstract This article reviews the relationship between salmonid aquaculture, both in fresh and saltwater, and water quality, focusing on the effects of bad water quality at the lethal and sublethal level, water quality assessment using physicochemical parameters, and new developments for water quality estimations: from mathematical indices and models for the interpretation and/or prediction of analytical results, to the assessment of water quality by biological methodologies. The main problems of different rearing systems, for example, land‐based farms and caged and net‐pen salmonid cultures, are also considered, taking into account not only the water quality problems originated by the culture conditions but also those related to external causes of water pollution. Particular attention is conceded to micropollutants, chemicals dumped into the environment by human activities, chemicals that can be toxic at very low concentrations, usually at the range of μg/1. Many of these chemicals are highly persistent in the environment and are a hazard even for culture areas located far from industrial pollution sources. Acid rain and the related risk associated to both pH and heavy metals are the major global hazard in freshwater systems, which are also threatened by industrial effluents and local accidental spills. Persistent pollutants, including heavy metals, organochlorine compounds, and petroleum hydrocarbons are of major concern in marine aquaculture. The toxicological risk related to these micropollutants focuses on sublethal problems, such as histopathological lesions, alterations in growth or reproduction, and increases in susceptibility to infectious diseases. Additionally, some of them, such as mercury, planar PCBs, or chlorinated dioxins, can also be a risk for human consumers. Biological methodologies, including the study of stress response and specific biomarkers, offer a cost‐effective system to monitor the risk of micropollutants and can be considered almost ready‐to‐use in culture conditions.

Mathematical descriptions of the glucose control in diabetes therapy. Analysis of the Schlichtkrull "M"-value.

Mathematical indices describing metabolic control of the diabetic patients during a short-term (24 hours) monitoring period have been reviewed. Two groups of indices were selected: those related to the glucose level and those related to the glycaemia variations. Then a presentation of the most universal mathematical index, which is presently used in clinical practice, -M value - was performed. Due to certain discrepancies related to several versions of the M-index, an analysis of all variants (M80, M90, M100, M120) had been carried out. It was found that comparison of the M values calculated based on different glucose reference levels led to totally different results. Analysis indicated that for the considered profiles the best description of the glycaemic state can be obtained when levels of 80 mg/dl (M80) and 90 mg/dl (M90) are applied.

Automated image analysis DNA cytometry in testicular cancer.

The value of automated DNA cytometry for differentiation of testis cancer was evaluated in 54 seminomas, 13 HCG-positive seminomas, and 48 embryonal carcinomas. Slices of paraffin embedded tissue were enzymatically digested and stained with Feulgen SITS after fixation on glass slides. Automated DNA cytometry was performed with a Modular Image Analysis Computer (MIAC). DNA histogram phenotpye and computed DNA indices were correlated with the different tumor types. The ratio of hypertriploid to hypotriploid increased from HCG-positive seminoma over embryonal carcinoma to seminoma. The following mathematical DNA indices were found to correlate with tumor type: mean ploidy, 2c deviation index, 5c exceeding rate, variation coefficient of the GO/1 fraction and DNA nucleus diameter correlation.

Successful identification of acute renal allograft rejection with duplex ultrasonography

Duplex ultrasonography has met with variable accuracy in identifying acute renal allograft rejection. These published studies have focused on using mathematical indices. We have applied duplex ultrasonography differently by insonating the site of rejection, i.e. renal cortex, to identify by subjective analysis the changes of the velocity spectral patterns. This subjective analysis method was compared to the mathematical indices of diastolic/systolic ratio and pulsatility index in 126 episodes of clinical acute renal allograft rejection which all had biopsy correlation. This present study represents the largest published experience with duplex ultrasonography and renal transplant rejection. Subjective analysis of velocity spectral patterns (SUBJ) resulted in sensitivity of 87%, specificity of 94% and overall accuracy of 88%. This technique was statistically better than the diastolic/systolic ratio (DSR) sensitivity of 40%, specificity of 72% and overall accuracy of 49%, or the pulsatility index (PI) sensitivity of 47%, specificity of 75% and overall accuracy of 55%. The superior results of the subjective analysis technique of duplex ultrasonography to identify acute renal allograft rejection suggests that this diagnostic approach has sufficient accuracy to avoid invasive allograft biopsies.

Derivation of an index for assessing the resistance of zebu cattle to Rhipicephalus appendiculatus Neumann (Acarina: Ixodidae)

A quantitative measure for assessing the level of resistance of zebu cattle to Rhipicephalus appendiculatus is discussed. Basic data for the derivation of the mathematical index were from artificial infestation of cattle to adults, nymphs and larvae of the Rusinga Island stock of the tick species. Observed variables were the weights and numbers of the engorged/detached instars. The index derivation process was by the use of the stepwise discriminant function procedure and the Mahalanobis distance. These procedures led to die derivation of an index which was a function of the engorged weights of the female and nymphal instars, the numbers of detached females and the Mahalanobis distance. Variables associated with the larval instar were found to be insignificant and were therefore not included in the index function. The derived index is capable of discriminating between susceptible and resistant cattle, and can be used to monitor changes in the resistance levels of cattle over time.

Postoperative intra-abdominal sepsis requiring reoperation. Value of a predictive index.

In this study we analyze the results of the use of a predictive index to decide whether to perform abdominal reoperation in the event of septic complications. During a 5-year period, a population of 542 critically ill patients received major abdominal surgery. Patients were divided into two groups: (1) the control group, for which the decision to reoperate was made routinely, based on clinical consensus of the medical team; and (2) the Abdominal Reoperation Predictive Index group, for which the decision to reoperate was made with the help of a mathematical index involving eight mainly clinical variables. The use of Abdominal Reoperation Predictive Index enabled mortality among patients undergoing reoperation to be lowered, the time elapsing between the first operation and relaparotomy to be reduced, and the length of stay in the intensive care unit to be shortened. We conclude that the systematic application of an index, without disregarding clinical judgment, allows the quality of attention to be improved, cost to be lowered, and the level of conflicts generated by the difficult decision to perform reoperation to be curtailed.

Strawberry Cultivar Evaluation Using Mathematical Indices

Three mathematical indices were developed to estimate: a) potential for early dollar return or early ripening (IE), b) concentrated cropping (IC), and deviation or similarity of a genotype to known cultivars (ID). Early ripening genotypes with high yield early in the season will have larger IE values than late genotypes with lower yield early in the season. Genotypes with few harvests will have larger IC values than those requiring several harvests. The ID index helps to identify and group genotypes with similar characteristics. These indices condense large numbers of values or arrays of traits into single index values, thereby simplifying genotype comparisons.

Mathematical assessment of the spatial distribution of Langerhans cells in guinea pig epidermis

Two mathematical indexes, Hopkins-Skellam index (HSI) and Morisita index (MI), were applied to assess the distribution of ATPase-stained epidermal Langerhans cells (ELC) in the guinea pig skin. To our knowledge, this is the first report in which the degree of regularity has been expressed numerically by computation based on theoretical equations. The regularity of ELC in the normal skin was confirmed by the value of HSI ( P<0.0001). In the topical steroid applied skin, the number of ELC decreased significantly but the value of HSI was similar to that of the normal skin; while in the ultraviolet B (UVB) exposed skin, both number of ELC and regularity of ELC distribution decreased significantly. The graph of MI for the UVB exposed skin clearly showed that the distribution of ELC had local clumps. The two indexes, HSI and MI have been quite useful for determining the regularity of ELC. These indexes may have a wide application to other cells.

Mathematical Indices for Comparing Small Fruit Crops for Harvest Time and Trait Similarity

Three mathematical indices were developed to estimate: 1) potential for early dollar return or early ripening (IE), 2) concentrated cropping (IC), and 3) deviation or similarity of a genotype to known cultivars (ID). Early ripening genotypes with high yield early in the season will have larger IE values than late genotypes with lower yield early in the season. Genotypes with few harvests will have larger IC values than those requiring several harvests. The ID index helps to identify and group genotypes with similar characteristics. These indices condense numerous values or arrays of traits into single index values, thereby simplifying genotype comparisons.

Effect of Oxymorphone Hydrochloride on Ovine Fetal Heart Rate Variability

In order to determine the effect of the narcotic analgesic oxymorphone hydrochloride (Numorphan, DuPont) on fetal heart rate (FHR) variability, mathematical indices of short-term and long-term FHR variability were determined continuously from R–R intervals of the electrocardiogram in eight chronically instrumented ovine fetuses for 60 min before and after a maternal intravenous bolus of 0.04 mg/kg oxymorphone. The index of short-term variability decreased from 12.7 ± 2.0 during control to 9.7 ± 1.7 during the period from 10 to 30 min after oxymorphone administration during periods of low-voltage, high-frequency electrocortical activity (LVHF ECoG) (P < 0.05). Mean FHR was decreased from 169 ± 8 beats per minute (bpm) during control to 155 ± 7 bpm 30 to 50 min after oxymorphone (P < 0.05). Fetal electrocortical activity was also determined and the decrease in FHR short-term variability occurred despite an increase in the percent time spent in LVHF electrocortical activity from 53 ± 4% during the control pe...

Comment on Gallagher's ‘proportionality, disproportionality and electoral systems’

Michael Gallagher, in a recent article published in this journal, argues against the notion that there is some single, obviously best standard of proportionality against which real-world PR methods can be judged. As he notes in his conclusion, all PR methods ‘set out to minimize disproportionality. They ditTer from each other not because some try harder than others, or because some are ‘fairer’ than others, but because they embody different ideas as to how disproportionality should be measured’ (p. 49). We certainly agree with this point; indeed, we have found it useful in structuring our own research agenda. But the conclusions we have drawn from it are somewhat different from those that Gallagher draws. Hence this note. Let us first recap the argument showing that there is no single notion of disproportionality against which real-world methods of PR can fairly be judged. The argument consists simply of pointing out two indisputable facts: first, that every method of PR currently in use minimizes some particular notion of disproportionality; second, that the notions of disproportionality inherent in the various PR methods differ. To illustrate the first point, one can do no better than recall the origin of the wellknown Sainte-Lagui? method of PR. Sainte-Laguti introduced his method in a French mathematical journal in 1910. If one reads his article (see Lijphart and Gibberd, 1977 for an English translation), one finds that Sainte-Lague proposes a mathematical index of disproportionality and that his method of PR is defined as the one that allocates seats in such a fashion as to minimize this index. In this regard, SainteLag& was not unusual. As he notes in his article, d’Hondt also had in mind a specific notion of disproportionality-which his method minimized. Even those PR methods whose inventors do not seem to have had the minimization of a measure of disproportionality explicitly in mind (for example, the largest remainders method invented by Alexander Hamilton) none the less all do minimize some such measure.

Functional Assessment of Neurologic Impairment

A laboratory approach to measuring neurologic impairment has been developed that is applicable to systemic disease as well as localized nerve injury. This approach compares individual parameters of the experimental rat hind footprint (walking track) with weight- and sex-matched control track parameters; classic mathematical indexing is not utilized. The normal track data obtained for the Sprague-Dawley rat showed a significant increase in print length (PL), toe spread (TS), and intermediate toe spread (ITS) with increasing rat weight. A significant difference between male and female rats above 400 gm also was noted. For a localized injury (sciatic nerve cut), this approach demonstrated that the contralateral hind footprint was a "compensated" rather than a normal track. This approach to track analysis also was capable of demonstrating progressive neurologic impairment for a sciatic nerve compression model and a systemic disease such as diabetes, as well as demonstrating reversal of these abnormal patterns when the "disease state" was treated.

Duplicate Breath Alcohol Analysis: Some Further Parameters for Evaluation

An individual exhaling into a breath alcohol instrument produces a breath alcohol concentration (BrAC) profile which is a continuous function of time. Microprocessor based breath alcohol instruments provide the capability to collect and store the BrAC profile data in discrete format. The present study collected duplicate BrAC profile data arrays on 11 field tested subjects and 16 experimentally tested subjects. The field subjects provided duplicate breath samples under normal field conditions. The experimental group provided one sample following normal breathing and one following breath holding. Each profile was subjected to ten different mathematical procedures. The duplicate results were then evaluated by a t-test for paired data. The experimental group showed statistical significance (P less than 0.01) for all but one mathematical parameter evaluated. The field group showed no statistical significance on any of the mathematical parameters. The results showed that BrAC profiles can be evaluated in a variety of ways and provide an index for detecting differences in breathing pattern prior to breath exhalation. The field data showed remarkable reproducibility by all mathematical indices. The results have forensic as well as physiological implications.

Barefoot Impressions—A Preliminary Study of Identification Characteristics and Population Frequency of Their Morphological Features

Footprint impressions of 107 male adults ranging in age from 19 to 67 years were recorded and examined. Included in this study were foot impressions from a pair of monozygotic twins as well. The impressions were recorded and converted into a set of indices which essentially are width-versus-length ratios of prominent features of the human foot. These indices were then correlated to yield probability values for use in this study and for comparison to data published by previous investigators Qamra, Abbott, Lovejoy, Cassidy, and Robbins. Friction ridge minutae were not considered in this study. Crease marks, well impressions, and toe step measurements were considered, but not incorporated in the probability values, because of the unique aspect of these features and the inability, at present, to convert these features to mathematical indices. These features do, however, introduce a subjective nature to the analysis scheme. This study uses the combined index probabilities of foot impressions so that the data generated can be used to assign a given probability that a particular foot impression, even without clear definable individual features, can be linked to the person who made the impression.

Axial and parity anomalies and vacuum charge: A direct approach.

We study the axial and parity anomalies in Abelian gauge theories using the direct yet intuitive approach of counting the relative number of states of one chirality with respect to the other. A fundamental gauge-invariant quantity, the determinantal ratio, is introduced for this purpose. We find that the number of states is conserved and that the gauge fields differentially phase shift states of opposite chirality at infinite energies. This implies a relative flow of states at very large energies which must be compensated by a rearrangement of the density of states at finite energies. We then derive a sum rule which yields two alternative formulas for the index of a Dirac operator. One expresses the index in terms of its high-energy behavior, and the other in terms of the low-energy properties; these are the ``zero modes'' of definite chirality. Two examples are worked out in detail to clarify our general result. The physics of the axial anomaly is shown to translate into that of the parity anomaly in 2+1 dimensions, in which parity and chirality have interchanged roles. We also analyze the vacuum charge in regard to its high- and low-energy origin. The possibility of spectral flow is formulated and briefly discussed. In short, we provide a physical interpretation of certain mathematical indices, relate them to an extended version of Levinson's theorem of potential scattering, and simplify their evaluation.

Flicker fusion as a typological index of nervous system 'reactivity'.

Flicker fusion responses were determined under varying stimulus intensities for 43 subjects. A mathematical index of the responses was derived for each individual and compared to a single flicker fusion response. A correlation demonstrated independence between the two measures.

A mathematical approach to problems of cephalopelvic disproportion at the pelvic inlet

So many problems have been left unsolved by x-ray pelvimetry for the prognostic diagnosis of cephalopelvic disproportion that the clinical usefulness of x-ray pelvimetry has been questioned and a more scientific approach to evaluation of cephalopelvic disproportion has been sought. By unifying various factors that impose problems in cephalopelvic relationships into one index via new mathematical models, we attempted to estimate quantitatively the potential dystocia caused by inlet disproportion. The index is calculated from ten measurements of data obtainable on roentgenograms, and the practical calculations can be readily done with a programmable calculator. The validity of the assumptions used in the mathematical models and the reliability of the developed index were retrospectively analyzed in 300 primiparous women with cephalic presentations. This study suggests that the mathematical index could serve as a useful prognostic guide to the proper management of labor in association with disproportion.

Development of a mathematical index that describes ozone concentration, frequency and duration

After carefully reviewing the existing mathematical approaches that have been utilized for describing pollutant exposures, the authors have developed a mathematical parameter which (a) utilizes readily available data, and (b) provides a description of concentration, frequency, and duration. The application of the parameter makes possible the utilization of key monitoring data for establishing (a) ozone trend patterns; (b) mathematical equations describing health effects; and (c) mathematical relationships describing crop yield reductions.