Rumack Matthew Nomogram with treatment line added at 150 Rumack-Matthew Nomogram The Rumack-Matthew nomogram, also known as Rumack-Matthews nomogram or the acetaminophen nomogram is an acetaminophen toxicity nomogram plotting serum concentration of acetaminophen against the time since ingestion in an attempt to prognosticate possible liver toxicity as well as allowing a clinician to decide whether to proceed with N-Acetylcysteine (NAC) treatment or not. It is a logarithmic graph starting not directly from ingestion, but from 4 hours post ingestion after absorption is considered likely to be complete. In hands of skilled clinicians this nomogram allows for timely management of acetaminophen overdose. Generally, a serum plasma concentration (APAP) of 140–150 microgram/mL (or milligrams/L) at 4 hours post ingestion, indicates the need for NAC treatment.
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Nomogram for the law of sines Nomogram for solving the quadratric x^2+px+q=0 Nomogram for solving the cubic x^3+px+q=0 Using a ruler, one can readily read the missing term of the law of sines or the roots of the quadratic and cubic equation.
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Rumack Matthew Nomogram with treatment line added at 150 A person's history of taking paracetamol is somewhat accurate for the diagnosis. The most effective way to diagnose poisoning is by obtaining a blood paracetamol level. A drug nomogram developed in 1975, called the Rumack-Matthew nomogram, estimates the risk of toxicity based on the serum concentration of paracetamol at a given number of hours after ingestion. To determine the risk of potential hepatotoxicity, the paracetamol level is traced along the nomogram.
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Components of a parallel-scale nomogram A nomogram for a three-variable equation typically has three scales, although there exist nomograms in which two or even all three scales are common. Here two scales represent known values and the third is the scale where the result is read off. The simplest such equation is u1 \+ u2 \+ u3 = 0 for the three variables u1, u2 and u3. An example of this type of nomogram is shown on the right, annotated with terms used to describe the parts of a nomogram.
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Nomogram for sample size estimation This nomogram can be used to estimate the sample size requirements for statistical analyses. It uses four parameters: α (fixed), effect size (ρ or δ), statistical power, and number of cases N (two scales for α = .05 (liberal) or .01 (conservative)).
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Nomogram for the starting dosage of FSH preparation as estimated from age, antral follicle count (AFC) and endogenous serum FSH taken day 3 of the menstrual cycle. An example is given in the nomogram, wherein an age of 32 years and an AFC of 12 gives a point on the middle line that, when continued to an FSH of 5 IU/l, results in a starting FSH dosage of almost 200 IU/l. Nomogram for the starting dosage of FSH as estimated from age, anti-Müllerian hormone (AMH) and endogenous serum FSH taken day 3 of the menstrual cycle (same as previous nomogram but with AMH instead of AFC). In most patients injectable gonadotropin preparations are used, usually FSH preparations.
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"A nomogram for predicting complications in patients with solid tumours and seemingly stable febrile neutropenia." British Journal of Cancer (2016): 1191-1198.
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These do not meet the strict definition of a nomogram as a graphical calculator whose solution is found by the use of one or more linear isopleths.
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A typical parallel-scale nomogram. This example calculates the value of T when S = 7.30 and R = 1.17 are substituted into the equation. The isopleth crosses the scale for T at just under 4.65. A nomogram (from Greek νόμος nomos, "law" and γραμμή grammē, "line"), also called a nomograph, alignment chart, or abaque, is a graphical calculating device, a two-dimensional diagram designed to allow the approximate graphical computation of a mathematical function.
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This nomogram is not used alone if the patient has altered mental status or if the history is not reliable. Rather, a second level should be drawn and plotted to see if the slope of the line remains at or above the nomogram. A formal half life may also be determined. Measure at time upon admission of the patient to the emergency department, and a blood value at time (t=4 hrs) should be obtained and half-life calculated.
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More complicated equations can sometimes be expressed as the sum of functions of the three variables. For example, the nomogram at the top of this article could be constructed as a parallel-scale nomogram because it can be expressed as such a sum after taking logarithms of both sides of the equation. The scale for the unknown variable can lie between the other two scales or outside of them. The known values of the calculation are marked on the scales for those variables, and a line is drawn between these marks.
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Frances Cope, also known as Frances Thorndike (August 19, 1902 - May 14, 1982), was an American mathematician who published on irregular differential equations. The Thorndike nomogram, a two-dimensional diagram of the Poisson distribution, is named for her.
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Maurice d'Ocagne, French mathematician, inventor of Nomography. Philbert Maurice d'Ocagne (25 March 1862 – 23 September 1938) was a French engineer and mathematician. He founded the field of nomography, the graphic computation of algebraic equations, on charts which he called a nomogram.
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Many nomograms include other useful markings such as reference labels and colored regions. All of these provide useful guideposts to the user. An impedance Smith chart (with no data plotted) Like a slide rule, a nomogram is a graphical analog computation device, and like the slide rule, its accuracy is limited by the precision with which physical markings can be drawn, reproduced, viewed, and aligned. While the slide rule is intended to be a general-purpose device, a nomogram is designed to perform a specific calculation, with tables of values effectively built into the construction of the scales.
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The pair of nomograms at the top of the image determine the probability of occurrence and the availability, which are then incorporated into the bottom multistage nomogram. Lines 8 and 10 are ‘tie lines’ or ‘pivot lines’ and are used for the transition between the stages of the compound nomogram. The final pair of parallel logarithmic scales (12) are not nomograms as such, but reading-off scales to translate the risk score (11, remote to extremely high) into a sampling frequency to address safety aspects and other ‘consumer protection’ aspects respectively. This stage requires political ‘buy in’ balancing cost against risk.
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A nomogram for performing the test with Yates's correction could be constructed simply by shifting each "observed" scale half a unit to the left, so that the 1.0, 2.0, 3.0, ... graduations are placed where the values 0.5, 1.5, 2.5, ... appear on the present chart.
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These values are often plotted on the Rumack-Matthew nomogram to determine level of concern. Treatment may include activated charcoal if the person seeks medical help soon after the overdose. Attempting to force the person to vomit is not recommended. If there is a potential for toxicity, the antidote acetylcysteine is recommended.
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Léon Lalanne's "abacus" or "universal computer", 1843 With Philbert Maurice d'Ocagne Lalanne is considered the inventor of the nomogram. The intention was to replace the slide rule. In a paper of 1846 Lalanne contributed to the subject the ideas of anamorphosis and the use of projective transformations. There were applications to the solution of the cubic equation.
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Normal values for peak expiratory flow (PEF), shown on EU scale. Adapted by Clement Clarke for use in EU scale — see Peakflow.com ⇒ Predictive Normal Values (Nomogram, EU scale) Peak expiratory flow (PEF) is the maximal flow (or speed) achieved during the maximally forced expiration initiated at full inspiration, measured in liters per minute or in liters per second.
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LBM is usually estimated using mathematical formulas. Several formulas exist, having different utility for different purposes. For example, the Boer formula is method of choice for LBM estimation to calculate the dose given in contrast CT in obese individuals with BMI between 35 and 40. A nomogram based on height, weight and arm circumference may be used.
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A medical algorithm for assessment and treatment of overweight and obesity. A medical algorithm is any computation, formula, statistical survey, nomogram, or look-up table, useful in healthcare. Medical algorithms include decision tree approaches to healthcare treatment (e.g., if symptoms A, B, and C are evident, then use treatment X) and also less clear-cut tools aimed at reducing or defining uncertainty.
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Activated charcoal can be used to decrease absorption of paracetamol if the person comes to the hospital soon after the overdose. While the antidote, acetylcysteine (also called N-acetylcysteine or NAC), acts as a precursor for glutathione, helping the body regenerate enough to prevent or at least decrease the possible damage to the liver; a liver transplant is often required if damage to the liver becomes severe. NAC was usually given following a treatment nomogram (one for people with risk factors, and one for those without), but the use of the nomogram is no longer recommended as evidence to support the use of risk factors was poor and inconsistent, and many of the risk factors are imprecise and difficult to determine with sufficient certainty in clinical practice. NAC also helps in neutralizing the imidoquinone metabolite of paracetamol.
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Astrup may refer to: an interpolation technique for acid-base measurement, based on pH and the use of the Siggaard-Andersen nomogram to determine the base deficit as an expression of metabolic acidosis and the arterial PCO2 as an expression of respiratory acidosis or alkalosis. Method was a base of blood acid-base balance tests introduced in the first half of the 1950s by Paul Astrup.
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This large, edge-lighted plexiglass combat information center maneuvering board for grease pencils has been used for display of other information. Most maneuvering boards are printed on pads of paper. A maneuvering board is an aid to navigation. It is typically a writing surface with a pre-printed compass rose of polar coordinates about a central point, often including adjacent linear scales, and sometimes a time/speed/distance nomogram.
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Acetylcysteine is the antidote for paracetamol toxicity Acetylcysteine, also called N-acetylcysteine or NAC, works to reduce paracetamol toxicity by replenishing body stores of the antioxidant glutathione. Glutathione reacts with the toxic NAPQI metabolite so that it does not damage cells and can be safely excreted. NAC was usually given following a treatment nomogram (one for patients with risk factors, and one for those without) but the use of the nomogram is no longer recommended as the evidence base to support the use of risk factors was poor and inconsistent and many of the risk factors are imprecise and difficult to determine with sufficient certainty in clinical practice. Cysteamine and methionine have also been used to prevent hepatotoxicity, although studies show that both are associated with more adverse effects than acetylcysteine. Additionally, acetylcysteine has been shown to be a more effective antidote, particularly in patients presenting greater than 8 hours post-ingestion and for those who present with liver failure symptoms.
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The inputs are displayed in a real time format via a computer generated Nomogram presenting an individual and an overall predictive index of likelihood ratios establishing evidence for or against a diagnosis. Results are likewise presented in a normalized, relative Standard score, T-score, Z-Score, and Percentile rank format for comparison to the non-clinical reference group. The Nomographic display of the individual and cumulative inputs are evaluated stepwise via the calculation of likelihood ratios applied incrementally with a Fagan's Nomogram, (Fagan TJ; 1975) to produce an overall predictive index beginning with a calculated base rate, and combining the results of the other measures, in either an additive or subtractive manner, to provide a post-test probability. When these components are used in conjunction with clinical judgment they have proven to be highly effective for consideration of diagnosis, in highlighting and documenting a need for further evaluation or actions, and may allow the clinician to evaluate their own diagnostic practices and effectiveness over time.
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The Naranjo algorithm, Naranjo Scale, or Naranjo Nomogram is a questionnaire designed by Naranjo et al. for determining the likelihood of whether an ADR (adverse drug reaction) is actually due to the drug rather than the result of other factors. Probability is assigned via a score termed definite, probable, possible or doubtful. Values obtained from this algorithm are often used in peer reviews to verify the validity of author's conclusions regarding adverse drug reactions.
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An Animated Drive Line Schematic & A Rotational Speeds Nomogram File:ZF 9HP Animated Schematic Drive Line & Nomogram.gif These ordinates are positioned on the abscissa in strict accordance with the proportions of the sun gears' teeth numbers relative to those of their rings. Consequently, the output ratios on the ordinate C4 (carrier of the last planetary gearset RS4) follows closely to those of the actual transmission. Note that elements A and F are labelled interchanged (cf.
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The result is read off the unknown scale at the point where the line intersects that scale. The scales include 'tick marks' to indicate exact number locations, and they may also include labeled reference values. These scales may be linear, logarithmic, or have some more complex relationship. The sample isopleth shown in red on the nomogram at the top of this article calculates the value of T when S = 7.30 and R = 1.17.
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Food risk assessment nomogram Although nomograms represent mathematical relationships, not all are mathematically derived. The following one was developed graphically to achieve appropriate end results that could readily be defined by the product of their relationships in subjective units rather than numerically. The use of non- parallel axes enabled the non-linear relationships to be incorporated into the model. The numbers in square boxes denote the axes requiring input after appropriate assessment.
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Methods of objectively corroborating that a BWER is associated with a mesocyclone is done by using a weather radar with Doppler effect to obtain the precipitations velocities. This have been available operationally in United States since 1997 with the NEXRAD network.Kenneth Falk and William Parker. ROTATIONAL SHEAR NOMOGRAM FOR TORNADOES. Retrieved on 2008-03-08. When using the lightning detection system, lightning holes (uncovered in 2004) correspond to where a BWER would be seen on radar.
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The user does not have to know how to solve algebraic equations, look up data in tables, use a slide rule, or substitute numbers into equations to obtain results. The user does not even need to know the underlying equation the nomogram represents. In addition, nomograms naturally incorporate implicit or explicit domain knowledge into their design. For example, to create larger nomograms for greater accuracy the nomographer usually includes only scale ranges that are reasonable and of interest to the problem.
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Since materials differ in their Biot numbers, the time it takes for the material to quench, or the Fourier number, varies in practice. In steel, the quenching temperature range is generally from 600 °C to 200 °C. To control the quenching time and to select suitable quenching media, it is necessary to determine the Fourier number from the desired quenching time, the relative temperature drop, and the relevant Biot number. Usually, the correct figures are read from a standard nomogram.
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The result is obtained by laying a straightedge across the known values on the scales and reading the unknown value from where it crosses the scale for that variable. The virtual or drawn line created by the straightedge is called an index line or isopleth. Nomograms flourished in many different contexts for roughly 75 years because they allowed quick and accurate computations before the age of pocket calculators. Results from a nomogram are obtained very quickly and reliably by simply drawing one or more lines.
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Use of a timed serum paracetamol level plotted on the nomogram appears to be the best marker indicating the potential for liver injury. A paracetamol level drawn in the first four hours after ingestion may underestimate the amount in the system because paracetamol may still be in the process of being absorbed from the gastrointestinal tract. Therefore, a serum level taken before 4 hours is not recommended. Clinical or biochemical evidence of liver toxicity may develop in one to four days, although, in severe cases, it may be evident in 12 hours.
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Nomograms are typically used in applications where the level of accuracy they offer is sufficient and useful. Alternatively, a nomogram can be used to check an answer obtained from another, more exact but possibly error-prone calculation. Other types of graphical calculators such as intercept charts, trilinear diagrams and hexagonal charts are sometimes called nomograms. Other such examples include the Smith chart, a graphical calculator used in electronics and systems analysis, thermodynamic diagrams and tephigrams, used to plot the vertical structure of the atmosphere and perform calculations on its stability and humidity content.
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Shortly after the end of the Second World War the establishment developed the MEXE method as a means of quickly assessing the carrying capacity of arch bridges, particularly for military traffic. The method was developed by Alfred Pippard of Imperial College, London. The bridge's span, arch thickness and depth of fill were input into an equation or nomogram to determine a provisional acceptable axle loading. This was then modified by a number of additional factors to determine a maximum permissible loading, which could be used to assess which military vehicles could use the bridge.
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The standard method of determining chemotherapy dosage is based on calculated body surface area (BSA). The BSA is usually calculated with a mathematical formula or a nomogram, using the recipient's weight and height, rather than by direct measurement of body area. This formula was originally derived in a 1916 study and attempted to translate medicinal doses established with laboratory animals to equivalent doses for humans. The study only included nine human subjects. When chemotherapy was introduced in the 1950s, the BSA formula was adopted as the official standard for chemotherapy dosing for lack of a better option.
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The field of nomography was invented in 1884 by the French engineer Philbert Maurice d'Ocagne (1862–1938) and used extensively for many years to provide engineers with fast graphical calculations of complicated formulas to a practical precision. Nomograms use a parallel coordinate system invented by d'Ocagne rather than standard Cartesian coordinates. A nomogram consists of a set of n scales, one for each variable in an equation. Knowing the values of n-1 variables, the value of the unknown variable can be found, or by fixing the values of some variables, the relationship between the unfixed ones can be studied.
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Food risk assessment nomogram #Dose- Response Analysis, is determining the relationship between dose and the type of adverse response and/or probability or the incidence of effect (dose- response assessment). The complexity of this step in many contexts derives mainly from the need to extrapolate results from experimental animals (e.g. mouse, rat) to humans, and/or from high to lower doses, including from high acute occupational levels to low chronic environmental levels. In addition, the differences between individuals due to genetics or other factors mean that the hazard may be higher for particular groups, called susceptible populations.
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The example uses a three-year minimum frequency for each, though with the high risk end of the scales different for the two aspects, giving different frequencies for the two, but both subject to an overall minimum sampling of every food for all aspects at least once every three years. This risk assessment nomogram was developed by the UK Public Analyst Service with funding from the UK Food Standards Agency for use as a tool to guide the appropriate frequency of sampling and analysis of food for official food control purposes, intended to be used to assess all potential problems with all foods, although not yet adopted.
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The isopleth crosses the scale for T at just under 4.65; a larger figure printed in high resolution on paper would yield T = 4.64 to three-digit precision. Note that any variable can be calculated from values of the other two, a feature of nomograms that is particularly useful for equations in which a variable cannot be algebraically isolated from the other variables. Straight scales are useful for relatively simple calculations, but for more complex calculations the use of simple or elaborate curved scales may be required. Nomograms for more than three variables can be constructed by incorporating a grid of scales for two of the variables, or by concatenating individual nomograms of fewer numbers of variables into a compound nomogram.
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Born Elizabeth Frances Thorndike in New York City and known as Frances, her parents were Elizabeth (Moulton) Thorndike and Edward L. Thorndike, an educational psychologist who taught at Teachers College, Columbia University. Frances was educated at Horace Mann School in New York and at Drum Hill High School in Peekskill. She graduated from Vassar College in 1922 and earned her master's degree in mathematics from Columbia University in 1925. In a 1926 paper, she first published a two-dimensional diagram of the Poisson distribution that is now named the Thorndike nomogram after her. She worked for several years as an engineering assistant at American Telephone and Telegraph Company (1922–24, 1925–27) before becoming an instructor of physics at Vassar (1927–28).
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