Evaluation of a field deployable, high-throughput RT-LAMP device as an early warning system for COVID-19 through SARS-CoV-2 measurements in wastewater.

Quantification of SARS-CoV-2 RNA copies in wastewater can be used to estimate COVID-19 prevalence in communities. While such results are important for mitigating disease spread, SARS-CoV-2 measurements require sophisticated equipment and trained personnel, for which a centralized laboratory is necessary. This significantly impacts the time to result, defeating its purpose as an early warning detection tool. The objective of this study was to evaluate a field portable device (called MINI) for detecting SARS-CoV-2 viral loads in wastewater using real-time reverse transcriptase loop-mediated isothermal amplification (real-time RT-LAMP). The device was tested using wastewater samples collected from buildings (with 430 to 1430 inhabitants) that had known COVID-19-positive cases. Results show comparable performance of RT-LAMP against reverse transcriptase polymerase chain reaction (RT-qPCR) when detecting SARS-CoV-2 copies in wastewater. Both RT-LAMP and RT-qPCR detected SARS-CoV-2 in wastewater from buildings with at least three positive individuals within a 6-day time frame prior to diagnosis. The large 96-well throughput provided by MINI provided scalability to multi-building detection. The portability of the MINI device enabled decentralized on-site detection, significantly reducing the time to result. The overall findings support the use of RT-LAMP within the MINI configuration as an early detection system for COVID-19 infection using wastewater collected at the building scale.

Skin manifestations of obesity: a comparative study.

BACKGROUND: Obesity is one of the world's biggest health problems nowadays. Little research has been done on the skin diseases that affect obese patients. OBJECTIVE: To study the prevalence of skin manifestations in obese patients compared with a control group of normal-weight patients. METHODS: A total of 76 obese patients [body mass index (BMI) ≥30 kg/m(2) ] and 73 with normal-weight volunteers (BMI 18.5-24.9 kg/m(2) ) were included in the study and had their complete medical history and skin examination evaluated by the same examiner. All patients were investigated for the presence of metabolic syndrome. RESULTS: The dermatoses that showed a statistically significant relationship with obesity, compared with the control group were: striae (P < 0.001), plantar hyperkeratosis (P < 0.001), acrochordons (P = 0.007), intertrigo (P < 0.001), pseudoacanthosis nigricans (P < 0.001), keratosis pilaris (P = 0.006), lymphedema (P = 0.002) and bacterial infections (P = 0.05). The presence of striae, pseudoacanthosis nigricans and bacterial infections were also found to be correlated with the degree of obesity. CONCLUSIONS: Obesity is strongly related to several skin alterations that could be considered as markers of excessive weight. Skin care of obese patients deserves particular attention, not only because of the high prevalence of cutaneous alteration but mainly because many of these disorders are preventable and could be treated, improving patient's quality of life.

[Considerations on photoprotection and skin disorders]. / Photoprotection et maladies cutanées.

Excessive exposure to solar or artificial sources of UV radiation is deleterious to the skin and can cause or worsen several diseases. Detrimental effects of UV radiation exert an important role in the development of skin cancers, cause alterations on the immune response, and act as a trigger or aggravating factor for pigmentary disorders. A group of measures, including education, change of habits, use of physical barriers and sunscreens constitutes a significant part of the treatment of many skin disorders and are valuable preventive tools. This article summarizes the relevant studies addressing these issues, emphasizing the many aspects of photoprotection.

Considerations on photoprotection and skin disorders.

Excessive exposure to solar or artificial sources of UV radiation is deleterious to the skin and can cause or worsen several diseases. Detrimental effects of UV radiation exert an important role in the development of skin cancers, cause alterations on the immune response, and act as a trigger or aggravating factor for pigmentary disorders. A group of measures, including education, change of habits, use of physical barriers and sunscreens constitutes a significant part of the treatment of many skin disorders and are valuable preventive tools. This article summarizes the relevant studies addressing these issues, emphasizing the many aspects of photoprotection.

Beam particle identification and tagging of incompletely stripped heavy beams with HEIST.

A challenge preventing successful inverse kinematics measurements with heavy nuclei that are not fully stripped is identifying and tagging the beam particles. For this purpose, the HEavy ISotope Tagger (HEIST) has been developed. HEIST utilizes two micro-channel plate timing detectors to measure the time-of-flight, a multi-sampling ion chamber to measure energy loss, and a high-purity germanium detector to identify isomer decays and calibrate the isotope identification system. HEIST has successfully identified 198Pb and other nearby nuclei at energies of about 75 MeV/A. In the experiment discussed, a typical cut containing 89% of all 198Pb80+ in the beam had a purity of 86%. We examine the issues of charge state contamination. The observed charge state populations of these ions are presented and, using an adjusted beam energy, are well described by the charge state model GLOBAL.

Daily consumption of milk enriched with fish oil, oleic acid, minerals and vitamins reduces cell adhesion molecules in healthy children.

BACKGROUND AND AIMS: Several studies have suggested that polyunsaturated fatty acids, vitamins and minerals have beneficial effects on lipid profile and systemic inflammation in adults. METHODS AND RESULTS: We examined the effects of a daily intake of milk enriched with longchain polyunsaturated fatty acids, oleic acid, carbohydrates, vitamins, minerals and low in saturated fatty acids (SFAs) for 5 months, on several cardiovascular (CVD) risk biomarkers in healthy children aged 8-14 years. In a randomized double-blind placebo-controlled trial, a total of 107 children of both genders were assigned to two study groups: 1) a supplemented group (SG, n=53) who consumed 0.6 L/day of an enriched dairy product, and 2) a control group (CG, n=54) who consumed 0.6 L/day of standard whole milk. Both groups consumed the dairy drinks for 5 months, in addition to their usual diet. Serum levels of adhesion molecules as indices of vascular endothelial cell activation were assessed in both groups at 0 and 5 months as well as white blood cell counts, lipid profile, serum proteins, total serum calcium, 25-OH vitamin D, glucose, insulin and adiponectin. In the enriched dairy drink supplemented group, adhesion molecules E-selectin and ICAM-1 as well as lymphocyte levels decreased while plasma docosahexaenoic acid (DHA) and serum calcium concentrations increased. In the control group, serum total protein, transferrin, total cholesterol, HDL-cholesterol and adiponectin concentrations decreased. CONCLUSION: The consumption of a milk enriched with fish oil, oleic acid, minerals and vitamins reduced indices of endothelial cell activation in the studied group of healthy children.

Effect of melasma on quality of life in a sample of women living in southern Brazil.

BACKGROUND: Melasma can cause a significant effect on individual emotional well-being. Melasma Quality of Life Scale (MELASQoL) is a specific questionnaire elaborated to assess the burden of melasma on patient's quality of life. OBJECTIVE: To evaluate the clinical aspects, severity and the influence of melasma on daily living of a sample of Brazilian women. METHODS: Cross-sectional study that enrolled 85 women with melasma older than 15 years of age. Trained investigators asked 55 questions to collect epidemiological and clinical data. The disease severity was clinically assessed using Melasma Area and Severity Index (MASI). Patients answered the Portuguese version of 10-item MELASQoL scale without coaching. RESULTS: The mean +/- SD age was 41.1 +/- 6.8 years, and the mean +/- SD of MELASQoL score was 37.5 +/- 15.2 (median, 35). Patients with previous psychiatric diagnosis had significantly higher MELASQoL scores (mean, 42.8; SD, 13.6) than patients without this antecedent (mean, 35.4; SD, 15.4; P < 0.05). Patients with less than 8 years of school attendance also had significantly higher MELASQoL score (mean, 44; SD, 16.9) than more graduated ones (mean, 34.4; SD, 13.5; P < 0.05). The mean +/- SD MASI was 10.6 +/- 6.6 (median, 10.2). There was no correlation between MASI and MELASQoL. CONCLUSIONS: This study confirms that MELASQoL-BP is easy to administer, adds important information about the impact of melasma on South American women's life and, finally, contributes to building evidence on the validity, reliability and cultural adaptation of the Portuguese language MELASQoL version.

[Beneficial effects of consumption of a dairy product containing two probiotic strains, Lactobacillus coryniformis CECT5711 and Lactobacillus gasseri CECT5714 in healthy children]. / Efectos beneficiosos en niños sanos del consumo de un producto lácteo que contiene dos cepas probióticas. Lactobacillus coryniformis CECT5711 y Lactobacillus gasseri CECT5714.

OBJECTIVE: In the last decades there has been an increasing interest in the manipulation of intestinal microbiota with probiotics for the prevention and treatment of certain paediatric diseases. In addition, it has been suggested that probiotics could play a role in the development of immune system. Recent studies suggest that the administration of two probiotic strains, Lactobacillus coryniformis CECT5711 and Lactobacillus gasseri CECT5714 improves intestinal function of healthy adults and enhances the immune response. Since there are few studies reporting the use of probiotic in children, the main consumers of these products, the aim of the present study was to analyze the effects of the administration of the mentioned probiotic strains in healthy children. INTERVENTIONS: 30 children (age range 3-12) with no gastrointestinal pathology were included in the study. In addition to their usual diet, during the first 3 weeks they received 200 ml of a conventional yogurt containing Lactobacillus bulgaricus and Streptococcus thermophilus. During the following three weeks this yogurt was substi-tuted for 80 ml of a probiotic product (Max Defensas, Puleva Food S.L.) containing the same amounts of Streptococcus thermophilus and the L. bulgaricus was substituted by a mixture of the target probiotic strains: L. coryniformis CECT5711 and L. gasseri CECT5714. Samples of faeces and saliva were taken at the beginning of the protocol, at week 3 and at the end of the study. Intestinal microbiota, faecal citotoxicity and the inhibition of Salmonella cholerasusis ssp. cholerasuis adhesion to intestinal mucins by the faeces were analyzed. Finally, IgA concentration was determined in the faecal and saliva samples. RESULTS: Tolerance of the probiotic product was good in all the children included in the study. An increase in faecal lactobacilli counts was shown at the end of the experimental protocol (P < 0,05). In addition citotoxicity of faecal samples was significantly (p < 0.05) reduced after probiotic consumption. The inhibition of S. cholerasuis adhesion to intestinal mucins was significantly higher (P < 0.05) for faecal waters from children in week 6 compared to samples form week 0 and 3. Probiotic consumption was also shown to increase IgA concentration in faeces and saliva (P < 0.05). CONCLUSIONS: The consumption of a probiotic product containing L. coryniformis CECT5711 and L. gasseri CECT5714 improves intestinal flora of healthy children, enhancing the defence against gastrointestinal aggressions and infections both by inhibiting pathogen adhesion to intestinal mucins and enhancing the immune function.

Laparoscopic excision of a retroperitoneal cystic lymphangioma in an elderly patient.

A 68-year-old male patient was referred to our hospital due to protrusion and pain in the right iliac fossa. On physical examination a palpable oval tumor was found. Ultrasonography and computed tomography revealed a cystic mass in right iliac fossa. The tumor was successfully excised laparoscopically and histologically diagnosed as cystic lymphangioma. Retroperitoneal cystic lymphangiomas are rare lesions, most often seen in pediatric patients. Surgical excision is the treatment of choice because of its potential to grow and develop complications, especially due to mass effect. The laparoscopic approach is a safe and effective alternative for treatment of retroperitoneal cystic lymphangioma in the elderly.

[Intake of an iron-supplemented milk formula as a preventive measure to avoid low iron status in 1-3 year-olds]. / Ingesta de una fórmula láctea suplementada con hierro como medida preventiva del déficit de hierro en niños de 1 a 3 años de edad.

OBJECTIVE: Low iron status is a well known risk factor for iron deficiency anemia in infants and young children. The aim of the present study was to evaluate the influence of an iron-fortified toddler formula on iron status in 1-3 year-olds. PATIENTS AND METHODS: Thirty-three healthy infants and young children were assigned to two groups that received 500 mL/day of and iron-fortified toddler formula or 500 mL/day of unmodified cow's milk for 4 months. Allocation was random and double-blind. Daily dietary intake was calculated by dietary evaluation, and iron nutritional status was assessed (hemoglobin, hematocrit, mean corpuscular volume, mean corpuscular hemoglobin, mean corpuscular hemoglobin concentration, serum iron, ferritin, and transferrin). RESULTS: At enrollment, no anemia was found in either group, although hemoglobin concentration and hematocrit were significantly lower in the toddler formula group than in the unmodified cow's milk group. However, these differences disappeared at the end of the intervention period. After 4 months, the toddler formula group showed significantly higher serum ferritin and lower serum transferrin concentrations than the cow's milk group. CONCLUSION: Intake of iron-supplemented toddler formula for 4 months in 1-3 year-olds is more effective in maintaining iron nutritional status than cow's milk.

Identification and characterization of novel angiotensin-converting enzyme inhibitors obtained from goat milk.

The aim of the present study was to identify and characterize new inhibitory peptides of angiotensin I-converting enzyme (ACE) from goat milk and to analyze the effect of long-term intake of a goat milk hydrolysate-supplemented (GP-hyd) diet on the development of hypertension in spontaneously hypertensive rats (SHR). Three new inhibitory peptides for ACE (TGPIPN, SLPQ, and SQPK) were isolated. The inhibitory concentration 50% (IC50) values of individual peptides were 316, 330, and 354 micromol/L, respectively. Only TGPIPN was found to pass intact a monolayer of Caco-2 cells in small amounts. The SHR fed for 12 wk a diet (GP-hyd) enriched in a hydrolysate containing these peptides (estimated intake of TGPIPN was 230 mg/kg per d) showed lower (approximately 15 mmHg) systolic blood pressure than animals fed a control diet. The ACE activities in the aorta, left ventricle, and kidney were significantly decreased in the GP-hyd group compared with those of the control group and were similar to those found in SHR fed captopril (130 mg/kg per d). Impaired endothelium-dependent relaxation to acetylcholine by aortic rings from SHR was improved in those fed the GP-hyd diet. The left ventricle weight and kidney weight index were significantly reduced in the GP-hyd group and captopril groups. Moreover, long-term treatment of SHR with a diet enriched in goat milk hydrolysate, or captopril, attenuated the development of hypertension, cardiac and renal hypertrophy, and endothelial dysfunction. These effects might be related to the in vivo inhibitory effects of the hydrolysate on tissue ACE activity.

[Cardiovascular effects of omega-3-fatty acids and alternatives to increase their intake]. / Efectos cardiovasculares de los ácidos grasos omega-3 y alternativas para incrementar su ingesta.

Cardiovascular diseases are the main mortality cause in Europe, the USA and a great extent of Asia. There are several risk factors associated with cardiovascular diseases, such as increased total cholesterol, homocysteine and triglycerides, hypertension, diabetes, and reduced levels of HDL-cholesterol. Many of these risk factors are diet influenced. In spite of the great amount of foods enriched with n-3 fatty acids available at the market, the knowledge about the effects produced by regular intake of these foods still is a challenge in the majority of cases. It appears that intake of foods enriches with n-3 polyunsatured fatty acids is an option that may be effective in reducing risk factors for diseases, by substituting supplements without modifying consumer's alimentary habits. Also shown are the outcomes from a nutritional study undergone with a functional milk-bases food that contains n-3 fatty acids, oleic acid and vitamins.

Glutamine supplementation further enhances exercise-induced plasma IL-6.

Exercise stimulates the production and release of interleukin-6 (IL-6) from skeletal muscle. Glutamine is also synthesized in skeletal muscle and is involved in protein synthesis within this tissue. During exercise, plasma levels of glutamine decline, and this may affect the concentration of plasma IL-6 via a decrease in IL-6 synthesis and release from muscle. We hypothesized that glutamine supplementation would attenuate the exercise-induced decrease in plasma glutamine concentration and, thus, further enhance levels of plasma IL-6. Eight healthy men participated in a randomized, double-blind, crossover study in which they performed 2 h of cycle ergometry at 75% of peak O2 uptake. They received glutamine, glutamine-rich protein, or placebo supplementation at intervals during and 2 h after exercise. Exercise induced an 11-fold increase in plasma IL-6, which was further enhanced by glutamine (18-fold) and glutamine-rich protein (14-fold) supplementation, administered at doses that attenuated the exercise-induced decrease in plasma glutamine concentration.

Effect of glutamine and protein supplementation on exercise-induced decreases in salivary IgA.

Postexercise immune impairment has been linked to exercise-induced decrease in plasma glutamine concentration. This study examined the possibility of abolishing the exercise-induced decrease in salivary IgA through glutamine supplementation during and after intense exercise. Eleven athletes performed cycle ergometer exercise for 2 h at 75% of maximal oxygen uptake on 3 separate days. Glutamine (a total of 17.5 g), protein (a total of 68.5 g/6.2 g protein-bound glutamine), and placebo supplements were given during and up to 2 h after exercise. Unstimulated, timed saliva samples were obtained before exercise and 20 min, 140 min, 4 h, and 22 h postexercise. The exercise protocol induced a decrease in salivary IgA (IgA concentration, IgA output, and IgA relative to total protein). The plasma concentration of glutamine was decreased by 15% 2 h postexercise in the placebo group, whereas this decline was abolished by both glutamine and protein supplements. None of the supplements, however, was able to abolish the decline in salivary IgA. This study does not support that postexercise decrease in salivary IgA is related to plasma glutamine concentrations.

Effect of dietary nucleotides and orotate on the blood levels of prostacyclin (PGI2) and thromboxane (TXA2) in the weanling rat.

Dietary nucleotides affect the maintenance of immune responses, tissue repair and polyunsaturated fatty acid metabolism. Orotate, a pyrimidine nucleotide precursor, induces fatty livers by impairing VLDL hepatic secretion. The aim of this study was to evaluate the changes in the blood levels of fatty acids and prostacyclin (PGI2) and thromboxane (TXA2) in the weanling rat caused by the dietary intake of nucleotides and orotate. Three groups of rats at weaning were fed a control diet, an orotate supplemented diet (O-50) and a nucleotide supplemented diet (N-50) during 4 weeks, respectively. Absolute values of plasma polyunsaturated fatty acids greater than 18 carbon atoms of the n-6 and n-3 series were increased in the N-50 group and decreased in O-50 with regard to the control. However, the relative fatty acid composition of plasma lipid fractions was mostly unaffected. Plasma 6-keto-PGF1 alpha showed a trend to be increased in N-50 and serum TXB2 was significantly increased in that group. Both eicosanoids were unchanged by dietary orotate intake. These results may be explained because of the increased plasma 20:4n-6 found in rats fed a supplemented nucleotide diet. Thus, nucleotides present in foods appear to modulate PUFA conversion and eicosanoids synthesis in early life.

A rapid gas-liquid chromatography method for the determination of lactulose and mannitol in urine: clinical application in studies of intestinal permeability.

OBJECTIVE: The purpose of this study was to develop a gas-liquid chromatography method for the determination of the urinary excretion of two nonmetabolizable sugars (lactulose and mannitol) to estimate the intestinal permeability. METHODS: Two internal standards (alpha-methyl-D-glucopyranosyde and sucrose) were added to the urine samples prior to derivatization with the aid of a solution of pyridine, [N, O-bis (trimethylsilyl)]-acetamide and chlorotrimethylsilan. Sample preparation was simpler and faster than in other previous methods and the four sugars were resolved within 27 min. RESULTS: The inclusion of internal standards reduced the coefficient of variation from 9.44% to 4.78%. The method provided better sensitivity, range of analysis, and linearity than a previously published HPLC method reducing variances in the recovery of lactulose and mannitol added to urine. The clinical application of this method was tested in preterm infants fed human milk or cow's milk based formula and in breast fed term infants. CONCLUSION: The method described here for the determination of urinary lactulose and mannitol is more rapid, simpler, and more accurate than other previously published methods.

n-3 Fatty acids plus oleic acid and vitamin supplemented milk consumption reduces total and LDL cholesterol, homocysteine and levels of endothelial adhesion molecules in healthy humans.

BACKGROUND AND AIMS: Numerous studies suggest n -3 polyunsaturated fatty acids (n -3 PUFA) and oleic acid intake have beneficial effects on health including risk reduction of coronary heart disease. The purpose of this study was to evaluate the effect of a commercially available skimmed milk supplemented with n -3 PUFA, oleic acid, and vitamins E, B(6), and folic acid (Puleva Omega3) on risk factors for cardiovascular disease. (CVD). METHODS: Thirty volunteers were given 500 ml/day of semi-skimmed milk for 4 weeks and then 500 ml/day of the n -3 enriched milk for 8 further weeks. Plasma and LDL lipoproteins were obtained from volunteers at the beginning of the study (T(pre)), and at 4, 8 and 12 weeks. RESULTS: The consumption of n -3 enriched milk produced a significant decrease in plasma concentration of total and LDL cholesterol accompanied by a reduction in plasma levels of homocysteine. Plasma and LDL oxidability and vitamin E concentration remained unchanged throughout the study. A significant reduction in plasma levels of vascular cell adhesion molecule 1, and an increase in plasma concentration of folic acid were also observed. CONCLUSION: Daily intake of n -3 PUFA and oleic acid supplemented skimmed milk plus folic acid and B-type vitamins has favourable effects on risk factors for CVD.

Neither glutamine nor arginine supplementation of diets increase glutamine body stores in healthy growing rats.

The aim of the work was to resolve whether glutamine and arginine supplemented diets affect plasma and tissue (muscle, liver and intestinal mucosa) glutamine concentrations, as well as glutaminase and glutamine synthetase specific activities. The trial was performed in growing rats fed 10% protein diets for 3 weeks. Protein sources were: whey proteins (W); whey proteins+free glutamine (WG); whey proteins+arginine (WA); and casein+wheat protein hydrolysate+acid whey (39:39:22), as source containing protein-bound glutamine (CGW). Rats fed the control diet (6.4% glutamine) (W) showed comparable glutamine body stores to those of rats fed the WG diet. In fact, glutamine sup- plementation down-regulated the hepatic glutamine synthetic capacity of growing rats (W/WG: 6.8+/-0.3 vs 6.0+/-0.2 nmol/min/mg protein). Arginine supplementation of the diet (up to 9% of the protein content) resulted in a decrease in plasma and tissue glutamine concentrations (W/WA: plasma, 1218+/-51 vs 1031+/-48 micromol/L; liver 7.5+/-0.4 vs 6.5+/-0.2 micromol/g; muscle: 5.7+/-0.2 vs 4.0+/-0.2 micromol/g). These data suggest that glutamine supplementation of the diet does not increase plasma and tissue glutamine concentrations in healthy growing rats, while the addition of arginine to the diet decreases glutamine body stores.

Plasma glutamine response to enteral administration of glutamine in human volunteers (free glutamine versus protein-bound glutamine).

The goal of the present work was to compare the plasma glutamine response to exogenous glutamine administration in human volunteers; glutamine was provided as a free amino acid, bound to proteins, or in the form of peptides. Plasma glutamine concentrations were measured in eight human volunteers at 30, 60, 90, 120, and 240 min after receiving a drink containing 30 g of protein from one of the five different proteins tested (sodium caseinate, sodium caseinate + free glutamine, carob germ flour, carob protein concentrate, and carob protein hydrolysate). Peak plasma glutamine concentrations were 42% higher than postabsorptive basal values when exogenous glutamine was administered in the form of free glutamine added to caseinate (925.9 +/- 67.7 versus 651.3 +/- 44.0 micromol/L, respectively). In contrast, when glutamine was offered 100% bound to proteins (carob proteins), peak plasma glutamine concentration increased only between 18% and 23% from basal values, possibly because of the lower digestibility of carob proteins versus that of caseinate + free glutamine, to a different glutamine utilization at the gut level, or to a different response in endogenous glutamine kinetics to enteral administration of glutamine, depending on the molecular form of the glutamine source (free or protein bound).

Effect of glutamine supplementation of the diet on tissue protein synthesis rate of glucocorticoid-treated rats.

Although glutamine status in the critically ill patient can be improved by nutritional means, the most effective way of effecting such supplementation has received little attention. We evaluated two different ways of supplementing clinical nutrition products with glutamine, either with free glutamine or by providing a glutamine-rich protein source, in acute glucocorticoid-treated (intraperitoneal dexamethasone, 120 mg/kg) rats. During the recovery period, the animals received isonitrogenous and isoenergetic diets containing either casein, mixed whey proteins with or without glutamine, or carob protein plus essential amino acids. Plasma and tissue amino acids and glutathione as well as tissue protein synthesis were measured. Dexamethasone treatment lowered weight gain, muscle glutamine, and muscle and jejunal protein synthetic rate. Muscle protein synthesis was increased (from 15.9% to 24.2%/d) only when glutamine was included in the diet as a free amino acid. This increase paralleled a rise in plasma glutamine. We speculate that glutamine provided in dietary protein is extensively metabolized by the splanchnic tissues and does not influence peripheral glutamine status to the same extent as glutamine provided in a free amino acid form. However, both forms of glutamine supplementation were equally effective in increasing protein synthesis in the jejunum (by 25%). This is likely the main benefit of glutamine supplementation of enteral nutrition formulas.