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Biomedical subjects

S Kaul

Publications and source records attributed to S Kaul.

At least 343 records · Page 19Linked to original sources
PubMed1989

Effects of successful intravenous reperfusion therapy on regional myocardial function and geometry in humans: a tomographic assessment using two-dimensional echocardiography.

This study tested the hypothesis that reperfusion therapy might provide benefit at two levels: 1) by arresting infarct migration at the endocardial level, such that partial or complete recovery of regional function occurs; and 2) if the former is not achieved, by preventing complete or near complete transmural migration and subsequent infarct expansion. To test this hypothesis, 24 patients who received intravenous streptokinase therapy within 4 h of chest pain were studied prospectively. All patients underwent two-dimensional echocardiography at the time of admission and 1, 2, 3 and 10 days later. The patients also underwent coronary angiography 2 h after completion of streptokinase therapy. Although 18 (75%) of the 24 patients had a patent infarct-related artery, only 8 (45%) of the 18 patients with this finding showed improvement in regional function. Improvement was not evident until 3 to 10 days after streptokinase therapy. In addition to the presence of an open infarct-related artery, the interval between chest pain and onset of streptokinase therapy (2.5 +/- 0.5 versus 3.2 +/- 0.7 h, p = 0.02) differed significantly between patients who did or did not show improved regional function. Of the 15 of 16 patients with no improvement in regional function, 4 showed infarct expansion, and all had a closed infarct-related artery compared with only 2 of the 11 not showing expansion (p = 0.01). In conclusion, intravenous streptokinase given within 4 h of chest pain results in improvement in regional function in about 33% of the patients, presumably by arresting the infarction within the endocardium.(ABSTRACT TRUNCATED AT 250 WORDS)

Coronary Angiography↗
PubMed1989

Assessment of regional myocardial blood flow with myocardial contrast two-dimensional echocardiography.

It was hypothesized that regional myocardial blood flow could be measured using myocardial contrast echocardiography. Accordingly, arterial blood was perfused into the coronary circulation in 16 dogs. In Group 1 dogs (n = 8), blood flow to the cannulated left circumflex artery was controlled with use of a roller pump, whereas in Group 2 dogs (n = 8) blood flow to the left anterior descending coronary artery was controlled by a hydraulic occluder placed around it. Sonicated microbubbles (mean size 4 microns) were used as the contrast agent. In Group 1 dogs the microbubbles were injected subselectively into the left circumflex artery, whereas in Group 2 dogs they were injected selectively into the left main coronary artery and two-dimensional echocardiographic images were recorded. Computer-generated time-intensity curves were derived from these images and variables of these curves correlated with transmural blood flow measured with radiolabeled microspheres. A gamma-variate function (y = Ate-alpha t) best described the curves, and alpha (a variable of curve width) correlated well with transmural blood flow at different flow rates in all Group 1 and Group 2 dogs (mean r = 0.81 and 0.97, respectively). Other variables of the curve width also correlated well with myocardial blood flow, but peak intensity had a poor correlation with myocardial blood flow in both groups of dogs (r = 0.39 and r = 0.63, respectively). When data from all dogs were pooled, Group 1 dogs still showed good correlation between variables of curve width and myocardial blood flow (r = 0.81); Group 2 dogs did not (r = 0.45). The difference between the two sets of dogs was related to the site of contrast agent injection. It is concluded that measurement of the transit time of microbubbles through the myocardium with two-dimensional echocardiography accurately reflects regional myocardial blood flow. Although injection of contrast agent selectively into the left main coronary artery only allows measurement of relative flow, it may be feasible to measure absolute flow by injecting contrast agent subselectively into a coronary artery. Myocardial contrast echocardiography may, therefore, offer the unique opportunity of simultaneously assessing regional myocardial perfusion and function in vivo.

Animals↗
PubMed1989

[Initial experiences with a monoclonal antibody to the progesterone receptor complex].

Today, the immuncytochemical demonstration of estrogen receptors can be regarded as established. Recently, a monoclonal antibody (mab) against the progesterone receptor-complex became commercially available. The antibody Mi 60-10, developed by Milgrom and co-workers, is murine and principally directed against the progesterone receptor of the rabbit, but it also attacks an "epitop" of the human receptor. The Western-Blot analysis shows the antibody having several specific bands against T-47-D cells in the region of 110,000 dalton. To estimate the practical performance of this antibody, 73 primary breastcarcinomas were incubated with both the ER-ICA-Kit and the new "mab". The PAP method was used for visualisation. In a frozen section the mab Mi 60-10 proved as successful as the ER-ICA-Kit. However, in contrast to the ER-ICA-Kit, the mab Mi 60-10 is also successful in locating the receptor, also in formalin-fixed samples embedded in paraffin. This is also the case with blocks, which were stored for several years. In aspirated cytological samples the immunocytochemical demonstration of progesterone was just as successful as that of estrogen and comparable with results on the histological section. A satisfactory validity can be obtained today through the development of highly specific monoclonal antibodies against the progesterone receptor complex, with the complete receptor diagnosis of mammary carcinoma both immunocytochemically in frozen sections and additionally, of progesterone receptors in paraffin wax sections. The only current problems involve the exact quantification of the immunocytochemical results. It is predictable today, that the DCC-method, when compared to the immunocytochemical receptor analysis, will reduce in significance.

Antibodies, Monoclonal↗
PubMed1989

The behavior of sonicated albumin microbubbles within the microcirculation: a basis for their use during myocardial contrast echocardiography.

The purpose of this study was to determine whether the behavior of sonicated albumin microbubbles accurately mimics red blood cell flow in the microcirculation and is thus consistent with their use as in vivo tracers of red blood cell flow during myocardial contrast echocardiography. Accordingly, microbubbles prepared from fluorescein-conjugated albumin and fluorescently labeled red blood cells were injected intravascularly in eight golden hamsters. Their intravascular distribution, velocities, arteriolar-to-venular transit and flux ratios at branch points were determined in the microcirculation of the cheek pouch. Albumin microbubbles (mean diameter, 4.9 +/- 3.6 microns) and red blood cells displayed a similar frequency of distribution across the arteriolar lumen (33% in the central 20% of the arterioles), and their arteriolar velocities were also similar (2.5 +/- 0.7 mm/sec and 2.3 +/- 0.7 mm/sec,p = NS). The mean velocities of microbubbles correlated well with those of red blood cells at baseline and after adenosine application (r = 0.97 and r = 0.89, respectively), as did the calculated maximum velocity (r = 0.98 and r = 0.80, baseline and adenosine, respectively). The velocity profiles across the lumen of the vessels for albumin microbubbles and red blood cells were similar at baseline and after adenosine-induced velocity changes. The flux ratios at branch points also correlated well (r = 0.92, p less than 0.001). Arteriolar-to-venular transit times of albumin microbubbles were similar to those of red blood cells in vessels ranging in size from 22 microns to 45 microns. We conclude that the behavior of albumin microbubbles in the microcirculation mimics that of red blood cells and supports their use as intravascular tracers of red blood cell flow during myocardial contrast echocardiography.

Animals↗
PubMed1989

Cerebrovascular disease in rural Kashmir, India.

We studied the Kuthar Valley in the Anantnag District of south Kashmir (northwestern India) during the year 1986 to ascertain the prevalence and pattern of completed stroke. We detected 91 cases, giving a crude prevalence rate of 143/100,000. However, age-specific prevalence was 41/100,000 in the group aged 15-39 years and 630/100,000 in the group aged greater than or equal to 40 years; 69.23% of the cases were in men. Hypertension was present in 58.24% of the cases, while strokes due to valvular heart disease and puerperium-related strokes were most common in the young. Our study is first of its kind in this part of India.

Adolescent↗
PubMed1989

Reversal of changes of lipid peroxide, xanthine oxidase and superoxide dismutase by cardio-protective drugs in isoproterenol induced myocardial necrosis in rats.

In myocardial necrosis produced by isoproterenol (beta-adrenergic agonist) marked increase in creatine phosphokinase, phospholipase and significant decrease in cardiac glycogen and phospholipid levels were observed. The enhanced levels of lipid peroxides, xanthine oxidase activity and lowering of superoxide dismutase may lead to excessive formation of free radicals resulting in cardiac cell damage. Nifedipine--a calcium antagonist, Propranolol--a beta-blocker and guggulsterone a lipid lowering agent showed marked reversal of these metabolic changes related to ischemia induced by isoproterenol.

Animals↗
PubMed1989

Cardiac sarcolemma enzymes & liver microsomal cytochrome P450 in isoproterenol treated rats.

In the heart sarcolemma and sarcoplasmic reticulum of rat there was significant decrease in cholesterol and phospholipid levels in isoproterenol treated rats. The membrane enzymes lipoprotein lipase and Ca-ATPase decreased due to myocardial necrosis. Lipid peroxide and xanthine oxidase were significantly enhanced, whereas superoxide dismutase was markedly decreased in ischemic heart produced by isoproterenol. Cytochrome P450, b5 and heme were found to be degraded in myocardial cell damage. Guggulsterone showed a marked protective effect on the cardiac enzymes and cyt P450 system against myocardial necrosis induced by isoproterenol.

Animals↗
PubMed1988

Identification of the human papillomavirus type 18 E6 and E6 proteins in nuclear protein fractions from human cervical carcinoma cells grown in the nude mouse or in vitro.

We recently reported the transcription patterns of human papillomavirus (HPV) type 18 sequences in human cervical carcinoma cell lines. The open reading frames (ORFs) E6* and E6 represent the 5'-terminal cistrons in HPV18 mRNAs. ORF E6* was assumed to be specific for HPV types associated with genital carcinomas. To identify the predicted gene product, ORF E6* from a HeLa cDNA clone was expressed as an MS2 fusion protein in Escherichia coli. The C-terminal 23 amino acid residues were chemically synthesized. A panel of monoclonal antibodies was generated, recognizing E6* and E6* plus E6, respectively. In human cervical carcinoma cell lines grown in vitro these monoclonal antibodies specifically immunoprecipitate the putative Mr 17,000 and 18,000 HPV18 E6 proteins in nuclear protein fractions. In a HPV18 DNA containing human cervical carcinoma established in nude mice, these monoclonal antibodies specifically immunoprecipitate a polypeptide with a molecular weight of 6500 as predicted for the HPV18 ORF E6* gene product in a nuclear protein fraction.

Animals↗
PubMed1988

Functional significance of predischarge exercise thallium-201 findings following intravenous streptokinase therapy during acute myocardial infarction.

The purpose of this study was to determine which predischarge exercise thallium-201 imaging pattern(s) best correlate with myocardial salvage following intravenous streptokinase therapy (IVSK). Myocardial salvage was defined as improvement in regional left ventricular function determined by two-dimensional echocardiography between the time of admission and time of discharge in 21 prospectively studied patients receiving IVSK within 4 hours of chest pain. All patients had coronary angiography 2 hours following IVSK. Whereas 16 of the 21 patients (76%) had patent infarct-related vessels, only seven (33%) showed significant improvement in regional function at hospital discharge. Eleven patients demonstrated persistent defects (PD), and five each showed delayed and reverse redistribution. Patients with both delayed and reverse redistribution demonstrated significant improvement in regional left ventricular function score, while those with PD did not (+3.9 +/- 3.3 versus -0.5 +/- 2.9, p = 0.004). All other clinical, exercise, electrocardiographic, scintigraphic, and angiographic variables were similar between all patients, with the exception of the interval between chest pain and the institution of IVSK, which was longer in patients with reverse compared to delayed redistribution (3.5 +/- 0.4 versus 2.2 +/- 0.4 hours, p = 0.001). It is concluded that both delayed and reverse redistribution seen on predischarge exercise thallium-201 imaging are associated with myocardial salvage, defined as serial improvement in regional systolic function. Despite a high infarct vessel patency rate in patients with acute myocardial infarction receiving IVSK within 4 hours of onset of symptoms, only one third demonstrated improvement in regional function that was associated with either delayed or reverse redistribution seen on predischarge exercise thallium-201 imaging.

Adult↗
PubMed1988

Left ventricular dysfunction in excess of the size of infarction: a possible management strategy.

In this report we describe two patients whose left ventricular dysfunction was far in excess of infarct size as evidenced by ECG changes and the magnitude of creatine kinase release. Both patients demonstrated redistribution in myocardial beds remote from the infarct zone on delayed rest thallium 201 images and both had multivessel disease evident on coronary angiography. Both patients experienced relief of symptoms and improvement in regional and global left ventricular function after revascularization surgery. The possible mechanisms of left ventricular dysfunction in myocardial beds remote from the zone of infarction are discussed.

Adult↗
PubMed1988

Superiority of quantitative exercise thallium-201 variables in determining long-term prognosis in ambulatory patients with chest pain: a comparison with cardiac catheterization.

The purpose of this study was to determine the prognostic utility of quantitative exercise thallium-201 imaging and compare it with that of cardiac catheterization in ambulatory patients. Accordingly, long-term (4 to 9 years) follow-up was obtained in 293 patients who underwent both tests for the evaluation of chest pain: 89 had undergone coronary artery bypass graft surgery within 3 months of testing and were excluded from analysis, 119 experienced no cardiac events and 91 had an event (death in 20, nonfatal myocardial infarction in 21 and coronary artery bypass operations performed greater than 3 months after cardiac catheterization in 50). When all variables were analyzed using Cox regression analysis, the quantitatively assessed lung/heart ratio of thallium-201 activity was the most important predictor of a future cardiac event (chi 2 = 40.21). Other significant predictors were the number of diseased vessels (chi 2 = 17.11), patient gender (chi 2 = 9.43) and change in heart rate from rest to exercise (chi 2 = 4.19). Whereas the number of diseased vessels was an important independent predictor of cardiac events, it did not add significantly to the overall ability of the exercise thallium-201 test to predict events. Furthermore, information obtained from thallium-201 imaging alone was marginally superior to that obtained from cardiac catheterization alone (p = 0.04) and significantly superior to that obtained from exercise testing alone (p = 0.02) in determining the occurrence of events. In addition, unlike the exercise thallium-201 test, which could predict the occurrence of all categories of events, catheterization data were not able to predict the occurrence of nonfatal myocardial infarction. The exclusion of bypass surgery and previous myocardial infarction did not alter the results. In conclusion, data from this study demonstrate that exercise thallium-201 imaging may be superior to data from both exercise testing alone and cardiac catheterization data alone for predicting future events in ambulatory patients who have undergone both exercise thallium-201 imaging and catheterization for the evaluation of chest pain.

Adult↗
PubMed1988

Success of internal mammary bypass grafting can be assessed intraoperatively using myocardial contrast echocardiography.

To determine whether the success of internal mammary artery bypass grafting can be assessed intraoperatively using myocardial contrast echocardiography, sonicated Renografin-76 was injected into the aortic root of 11 dogs during the delivery of cardioplegic solution. Studies were performed with the left anterior descending coronary artery patent and totally occluded, and after internal mammary artery bypass grafting distal to the occluded vessel. Flow rate during cardioplegia was constant for all three stages in each experiment. Myocardial contrast echocardiography clearly demonstrated homogeneous myocardial perfusion with the left anterior descending coronary artery patent, lack of perfusion in the left anterior descending artery bed during its occlusion and excellent perfusion of the occluded bed after internal mammary artery bypass grafting distal to the occlusion in 10 of the 11 dogs. In one dog, the bypass graft was technically inadequate and contrast opacification was not noted in the left anterior descending artery bed after internal mammary artery bypass grafting. The exponential function C(t) = Ae-alpha t + Be-beta t was fitted to computer-derived time-intensity curves from the myocardium, where alpha denotes contrast washout and beta denotes contrast appearance. Respective values for alpha and beta (mean + 1 SD) were similar for the patent left anterior descending coronary artery and after internal mammary artery bypass grafting distal to the occluded artery (0.11 +/- 0.10 versus 0.10 +/- 0.10, and 2.5 +/- 2.4 versus 1.1 +/- 0.56). In conclusion, myocardial contrast echocardiography has potential for intraoperative assessment of the adequacy of coronary artery bypass grafting.

Animals↗
PubMed1988

Myocardial contrast echocardiography in humans. II. Assessment of coronary blood flow reserve.

The hypothesis that myocardial contrast echocardiography could be used to simultaneously assess coronary blood flow reserve and the size of the perfusion bed supplied by a coronary artery was examined in nine patients and six dogs. All patients were undergoing cardiac catheterization and had single vessel coronary artery disease (greater than or equal to 85% stenosis of either the proximal left anterior descending or the left circumflex coronary artery); the six dogs had a critical stenosis of the left circumflex coronary artery. Three milliliters of sonicated Renografin-76 (mean microbubble size 6 micron) was injected into the left main coronary artery before and after intracoronary administration of papavarine, 6 to 9 mg. The beds supplied by the normal and stenotic vessels could not be differentiated during contrast echocardiography before injection of papavarine. However, after papavarine, the normal vascular bed showed significantly more contrast enhancement than did the bed supplied by the stenotic artery. This disparity in contrast enhancement made it possible to delineate the size of the bed perfused by the stenotic vessels. When quantitative analysis of the time-intensity curves obtained from the echocardiograms was performed in the dogs, the absolute values for the area under the curve, peak contrast intensity and curve width did not correlate with absolute blood flows measured with radiolabeled microspheres. However, the ratios of the areas under the curves derived from the two vascular beds before and after papavarine correlated well with the ratios of blood flows between the two beds during the same stages (r2 = 0.73 by linear regression and r2 = 0.85 by an exponential function). In comparison, the ratios of peak amplitudes and curve widths before and after papavarine had poor correlations with ratios of flows from the two beds (r2 = 0.18 and 0.02, respectively). In conclusion, myocardial contrast echocardiography can be used to simultaneously assess coronary blood flow reserve and the size of the perfusion bed supplied by a stenotic vessel.

Aged↗
PubMed1988

Myocardial contrast echocardiography without significant hemodynamic effects or reactive hyperemia: a major advantage in the imaging of regional myocardial perfusion.

All agents used for myocardial contrast echocardiography to date produce adverse hemodynamic effects and alter coronary blood flow. It was hypothesized that because 5% human albumin, when sonicated for use as a contrast agent, is neither hyperosmolar nor a calcium chelator, it would not have significant effects on coronary blood flow, left ventricular function or systemic hemodynamics. Albumin microbubbles of two distinct sizes (mean size 2.9 and 5.8 micron) were produced and compared with nonsonicated albumin, nonsonicated Renografin, sonicated Renografin and hand-agitated Renografin for their effects on hemodynamics, coronary blood flow and regional left ventricular systolic thickening in 15 open chest anesthetized dogs. None of the albumin solutions significantly altered left atrial, left ventricular systolic and end-diastolic and mean aortic pressures. These agents did not cause a coronary hyperemic response or alter left ventricular systolic thickening, but slightly lowered the peak positive left ventricular maximal rate of rise in pressure (dP/dt) (-4.1 +/- 5.4%, p less than 0.01). In contrast, all the Renografin solutions caused significant changes in all these variables (p less than 0.02). In six dogs. albumin solutions did not alter these variables even in the presence of critical coronary stenosis. The contrast opacification produced by 5.8 micron albumin microbubbles was equivalent to that produced by sonicated Renografin. Compared with an equivalent amount of saline and nonsonicated albumin solutions, 10 ml of sonicated albumin did not produce any evidence of infarction, embolization or hemorrhage in the myocardium, brain or kidneys of rabbits.(ABSTRACT TRUNCATED AT 250 WORDS)

Animals↗
PubMed1988

Prognostic utility of the exercise thallium-201 test in ambulatory patients with chest pain: comparison with cardiac catheterization.

The goal of this study was to determine the prognostic utility of the exercise thallium-201 stress test in ambulatory patients with chest pain who were also referred for cardiac catheterization. Accordingly, 4 to 8 year (mean +/- 1SD, 4.6 +/- 2.6 years) follow-up data were obtained for all but one of 383 patients who underwent both exercise thallium-201 stress testing and cardiac catheterization from 1978 to 1981. Eighty-three patients had a revascularization procedure performed within 3 months of testing and were excluded from analysis. Of the remaining 299 patients, 210 had no events and 89 had events (41 deaths, nine nonfatal myocardial infarctions, and 39 revascularization procedures greater than or equal to 3 months after testing). When all clinical, exercise, thallium-201, and catheterization variables were analyzed by Cox regression analysis, the number of diseased vessels (when defined as greater than or equal to 50% luminal diameter narrowing) was the single most important predictor of future cardiac events (chi 2 = 38.1) followed by the number of segments demonstrating redistribution on delayed thallium-201 images (chi 2 = 16.3), except in the case of nonfatal myocardial infarction, for which redistribution was the most important predictor of future events. When coronary artery disease was defined as 70% or greater luminal diameter narrowing, the number of diseased vessels significantly (p less than .01) lost its power to predict events (chi 2 = 14.5). Other variables found to independently predict future events included change in heart rate from rest to exercise (chi 2 = 13.0), ST segment depression on exercise (chi 2 = 13.0), occurrence of ventricular arrhythmias on exercise (chi 2 = 5.9), and beta-blocker therapy (chi 2 = 4.3). The exclusion of myocardial revascularization procedures as an event did not change the results significantly. Although the number of diseased vessels was the single most important determinant of future events, the exercise thallium-201 stress test when considered as a whole (which included the number of segments demonstrating redistribution on delayed thallium-201 images, change in heart rate from rest to exercise, ST segment depression on the electrocardiogram, and ventricular premature beats on exercise) was equally powerful (chi 2 = 41.6). Combination of both catheterization and exercise thallium-201 data was superior to either alone (chi 2 = 57.5) for determining future events. Exercise stress test alone (without thallium-201 data) was inferior to the exercise thallium-201 stress test or cardiac catheterization for predicting future events (chi 2 = 30.6).(ABSTRACT TRUNCATED AT 400 WORDS)

Cardiac Catheterization↗
PubMed1988

Effect of fish oil concentrate on lipoprotein composition in NIDDM.

Non-insulin-dependent diabetes mellitus (NIDDM) is associated with elevated very-low-density lipoprotein (VLDL) triglyceride concentrations and abnormalities of low-density lipoprotein (LDL) composition. Because fish oil supplementation may favorably affect lipid and lipoprotein concentrations in nondiabetic subjects, we determined the effect of fish oil concentrate on plasma lipids and lipoprotein composition in patients with NIDDM. Dietary-supplementation 1-mo periods of 4.0 and 7.5 g of omega-3 fatty acids in fish oil were compared with a placebo of 12 g safflower oil by use of a single-blind crossover design. Medications, including antidiabetic therapy, were continued through the study. Compared with safflower oil treatment, fish oil supplementation resulted in a significant reduction of total plasma triglycerides of 24% at the 4-g dose and a larger reduction of 39% at the 7.5-g dose. These decreases were due to similar reductions in VLDL triglycerides. LDL cholesterol levels were mildly elevated, but a larger 20% increase in LDL apolipoprotein B (apoB) concentration was observed. During supplementation with the fish oil concentrate, the LDL cholesterol-to-apoB ratio was significantly reduced when compared with pretreatment values, but not when compared with safflower oil treatment. High-density lipoprotein (HDL) cholesterol and plasma apoA1 levels were not significantly changed during fish oil treatment. At the 7.5-g dose, fasting glucose and glycohemoglobin levels increased by 20 and 12%, respectively, but were unchanged at the lower level of supplementation. Thus, in NIDDM patients, dietary supplementation with omega-3 fatty acids induces a reduction in total plasma and VLDL triglyceride levels.(ABSTRACT TRUNCATED AT 250 WORDS)

Adult↗
PubMed1988

Increased exercise thallium-201 lung uptake: a noninvasive prognostic index in two-vessel coronary artery disease.

To determine the physiologic impact of two-vessel coronary artery disease and its effect on prognosis, a series of clinical, angiographic, exercise and quantitative thallium-201 (Tl-201) imaging parameters were analyzed in 85 consecutive two-vessel coronary artery disease patients followed for 52 +/- 27 months after coronary angiography and Tl-201 scintigraphy. End points were cardiac death (n = 3), myocardial infarction (n = 6) and coronary bypass graft surgery more than three months after testing (n = 16). Using Cox Hazards survival analysis, early cardiac events were not predicted by: myocardial infarction or anginal history; resting left ventricular function; exercise blood pressure response; angina or severity of ECG ST segment depression (mm); Tl-201 defect size; redistribution or clearance; angiographic patterns; or the presence of proximal left anterior descending disease. Significant predictors of adverse cardiac events were: increased exercise lung to heart Tl-201 ratio (0.59 +/- 0.12 versus 0.46 +/- 0.1; P less than 0.0001); ECG lead extent of ST segment depression (P less than 0.03); and exercise heart rate response (P less than 0.047). Event-free survival for patients with normal and abnormally increased lung to heart Tl-201 ratios at 48 months was 76% versus 63% (P less than 0.003). It was concluded that two-vessel coronary artery disease survival correlates with exercise Tl-201 uptake which reflects exercise induced left ventricular dysfunction.

Actuarial Analysis↗