The burden of cardiovascular disease attributable to high dietary sodium intake in Australia between 1990 and 2019.

BACKGROUND: Diets high in sodium are associated with adverse cardiovascular outcomes. We aimed to quantify the burden of cardiovascular disease (CVD) attributable to high dietary sodium consumption in the Australian population. METHODS: Using data from the Global Burden of Disease (GBD) 2019, we estimated the age-standardised rates (per 100 000 population) and the total numbers of years lived with a disability (YLDs), years of life lost (YLLs), disability-adjusted life years (DALYs), and deaths for CVD attributable to high sodium (≥1000 mg/day) consumption in the Australian population, by sex and age groups (≥25 years) between 1990 and 2019. The study compared Australian estimates with similar high-income countries (Group of 20 [G20] members). RESULTS: From 1990 to 2019, the age-standardized rates of CVD deaths, DALYs, YLDs, and YLLs per 100 000 population in Australia attributable to high sodium decreased. However, between 2013 and 2019, the total number of CVD deaths increased, and the number of CVD YLDs increased exponentially for both sexes for the whole period between 1990 and 2019. Men had a two-fold higher rate for high sodium CVD burden, compared to females between 1990 to 2019. Individuals aged between 80 and 84 years had the highest rates of CVD burden during the same period; however, older age groups reported the greatest decline in CVD burden compared to young and middle-aged adults in Australia. The age-standardised rates for high sodium attributable CVD consistently contributed more towards DALYs than YLDs in 2019 for both sexes. When compared to G20 countries, Australians displayed the lowest age-standardized rates for CVD deaths, DALYs, YLDs, and YLLs alongside Turkey, France, and the United Kingdom in 2019. CONCLUSION: While age-standardized CVD burden attributable to high sodium consumption decreased for both sexes over the past 30 years, the total number of CVD deaths showed an increase between 2013 and 2019. This study underscores the need for sustained efforts to address the rising absolute number of CVD deaths, especially among men and older people, and emphasizes the importance of continued vigilance in monitoring and implementing strategies to reduce the impact of high sodium consumption on cardiovascular health in Australia.

Association of fat-to-muscle mass ratio with physical activity and dietary protein, carbohydrate, sodium, and fiber intake in a cross-sectional study.

Higher fat-to-muscle mass ratio (FMR) is reported to be a risk factor for various diseases, including type 2 diabetes and cardiovascular diseases, and mortality. Although this association suggests that reducing FMR may help to prevent certain diseases and mortality, the relationship between FMR and lifestyle factors is unclear. Therefore, we performed a cross-sectional study with the aim to elucidate this relationship. This cross-sectional study included 1518 healthy Japanese adults aged 30 to 64 years. We measured FMR in the whole body, arms, legs, and trunk and assessed various lifestyle factors. Then, we performed forced entry multiple regression analyses for FMR with the following variables: sex, age, physical activity, dietary intake, sleep quality, cigarette smoking, stress levels, and body mass index. As a result, whole-body and regional FMRs were correlated with female sex (ß = 0.71); age (ß = 0.06); physical activity (ß = - 0.07); dietary intake of protein (ß = - 0.12), carbohydrate (ß = 0.04), sodium (ß = 0.13), and fiber (ß = - 0.16); and body mass index (ß = 0.70). The results suggest that in the Japanese middle-aged population, low FMR is associated with certain lifestyle factors, i.e. higher physical activity and a diet with higher protein and fiber and lower carbohydrate and sodium, independent of age, sex, and body mass index.

Cardiovascular Disease Burden Attributable to High Sodium Intake in China: A Longitudinal Study from 1990 to 2019.

BACKGROUND: Overconsumption of sodium has been identified as a key driving factor for diet-related cardiovascular diseases (CVDs). China, being a country bearing a hefty burden of CVD, has a large population with diverse cultural traditions and ethnic beliefs, which complicates the patterns of dietary sodium intake, necessitating a systematic investigation into the profile of the high sodium intake (HSI)-related burden of CVD within its subregions. This study aims to estimate the evolving patterns of HSI-induced CVD burden across China from 1990 to 2019. METHODS: The methodology used in the Global Burden of Disease Study was followed to assess deaths and disability-adjusted life years (DALYs) by age, sex, region, and socio-demographic index (SDI). The estimated annual percentage change (EAPC) was calculated to quantify the secular changes in the age-standardized mortality rate (ASMR) and age-standardized DALY rate (ASDR). RESULTS: In 2019, 0.79 million deaths and 1.93 million DALYs of CVD were attributed to HSI, an increase of 53.91% and 39.39% since 1990, respectively. Nevertheless, a downward trend in ASMR (EAPC: -1.45, 95% CI: -1.55, -1.35) and ASDR (EAPC: -1.61, 95% CI: -1.68, -1.53) was detected over time. ASMR and ASDR were higher for males, individuals aged ≥60 years, and regions with low-middle SDI. A markedly negative association between the EAPC in both ASMR and ASDR and the SDI was found in 2019 (ρ = -0.659, p < 0.001 and ρ = -0.558, p < 0.001, respectively). CONCLUSIONS: The HSI-induced CVD burden is gender-, age-, and socioeconomic-dependent. Integrated and targeted strategies for CVD prevention are anticipated in the future throughout China.

Prediction of 24-Hour Urinary Sodium Excretion Using Machine-Learning Algorithms.

BACKGROUND: Accurate quantification of sodium intake based on self-reported dietary assessments has been a persistent challenge. We aimed to apply machine-learning (ML) algorithms to predict 24-hour urinary sodium excretion from self-reported questionnaire information. METHODS AND RESULTS: We analyzed 3454 participants from the NHS (Nurses' Health Study), NHS-II (Nurses' Health Study II), and HPFS (Health Professionals Follow-Up Study), with repeated measures of 24-hour urinary sodium excretion over 1 year. We used an ensemble approach to predict averaged 24-hour urinary sodium excretion using 36 characteristics. The TOHP-I (Trial of Hypertension Prevention I) was used for the external validation. The final ML algorithms were applied to 167 920 nonhypertensive adults with 30-year follow-up to estimate confounder-adjusted hazard ratio (HR) of incident hypertension for predicted sodium. Averaged 24-hour urinary sodium excretion was better predicted and calibrated with ML compared with the food frequency questionnaire (Spearman correlation coefficient, 0.51 [95% CI, 0.49-0.54] with ML; 0.19 [95% CI, 0.16-0.23] with the food frequency questionnaire; 0.46 [95% CI, 0.42-0.50] in the TOHP-I). However, the prediction heavily depended on body size, and the prediction of energy-adjusted 24-hour sodium excretion was modestly better using ML. ML-predicted sodium was modestly more strongly associated than food frequency questionnaire-based sodium in the NHS-II (HR comparing Q5 versus Q1, 1.48 [95% CI, 1.40-1.56] with ML; 1.04 [95% CI, 0.99-1.08] with the food frequency questionnaire), but no material differences were observed in the NHS or HPFS. CONCLUSIONS: The present ML algorithm improved prediction of participants' absolute 24-hour urinary sodium excretion. The present algorithms may be a generalizable approach for predicting absolute sodium intake but do not substantially reduce the bias stemming from measurement error in disease associations.

Adherence to the Mediterranean Diet, Sodium and Potassium Intake in People at a High Risk of Dementia.

Adequate sodium and potassium intake, along with adherence to the Mediterranean diet (MedDiet), are key factors for preventing hypertension and cerebrovascular diseases. However, data on the consumption of these nutrients within the MedDiet are scarce. This cross-sectional study aims to assess the association between MedDiet adherence and sodium/potassium intake in the MIND-Matosinhos randomized controlled trial, targeting Portuguese adults at a high risk of dementia. Good adherence to the MedDiet was defined using the Portuguese Mediterranean Diet Adherence Screener questionnaire (≥10 points), and both sodium/potassium intakes were estimated from 24-hour urine collections. The association between MedDiet adherence and these nutrients' intake (dichotomized by the median) was quantified by calculating odds ratios (OR) and respective 95% confidence intervals (95% CI) using a logistic regression. A total of 169 individuals (60.9% female; median age: 70 years; range: 36-85 years) were included. Good adherence to the MedDiet was observed among 18.3% of the sample. After adjusting for sex, age, education and using antihypertensive drugs, good MedDiet adherence was associated with higher sodium (OR = 3.11; 95% CI: 1.27-7.65) and potassium intake (OR = 9.74; 95% CI: 3.14-30.26). Increased adherence to the MedDiet may contribute to a higher potassium intake but seems to have limited effects on the adequacy of sodium levels.

Na and K Intake from Lunches Served in a Japanese Company Cafeteria and the Estimated Improvement in the Dietary Na/K Ratio Using Low-Na/K Seasonings and Dairy to Prevent Hypertension.

The excessive intake of sodium (Na) and insufficient intake of potassium (K) are major concerns in the prevention of hypertension. Using low-Na/K seasonings (reducing 25% of the NaCl and adding K salt) may improve the dietary Na/K ratio and help prevent hypertension. To devise an intervention study using low-Na/K seasonings at a company cafeteria, we calculated the Na and K contents of the meals served at the cafeteria and estimated changes in the intakes when suitable low-Na/K seasonings were used. We also considered using milk as a good source of K. We used an ingredient list of a company cafeteria and calculated Na and K contents in each dish. The average amounts of NaCl and K per use were 5.04 g and 718 mg, respectively. Seasonings contributed 70.9% of the NaCl. With the use of low-Na/K seasonings, an estimated reduction in NaCl of 0.8 g/day and an estimated increase in K of 308 mg/day was achieved. With an additional serving (200 mL) of milk, NaCl was reduced by 0.57 g/day and K was increased by 610 mg/day, with an overall decrease in the dietary Na/K ratio from 3.20 to 2.40. The use of low-Na/K seasonings and dairy may improve the dietary Na/K ratio among cafeteria users and help prevent hypertension.

Assessing Sodium Intake in Middle-Aged and Older Adults with Elevated Blood Pressure: Validation of Spot Urine Excretion and Dietary Survey-Derived Estimates.

This cross-sectional study evaluated the validity of three alternative methods compared to the gold standard 24-h urine collection for estimating dietary sodium intake, a modifiable risk factor for hypertension, among middle-aged and older adults with elevated blood pressure. These included spot urine collection (using Kawasaki, Tanaka, and INTERSALT equations), 24-h dietary recall, and food frequency questionnaire responses, compared to 24-h urine collection in a subset of 65 participants (aged 50-75 years, 58.5% women, 61.6% hypertensive) from the DePEC-Nutrition trial. The validity of the methods was assessed using bias, the Spearman correlation coefficient (SCC), the intraclass correlation coefficient (ICC), and Bland-Altman analysis. Among the alternative methods, spot urine collection using the Kawasaki equation showed the strongest correlation (SCC 0.238; ICC 0.119, 95% CI -0.079 to 0.323), but it exhibited a significant bias (1414 mg/day, p-value < 0.001) relative to 24-h urine collection. Conversely, dietary surveys had a smaller bias but wider limits of agreement. These findings underscore the complexities of accurately estimating dietary sodium intake using spot urine collection or dietary surveys in this specific population, suggesting that a combination or the refinement of existing methodologies might improve accuracy. Further research with larger samples is necessary to develop more reliable methods for assessing sodium intake in this high-risk group.

No change in 24-h sodium intake estimated from spot urine in Norwegian adults from 2006 to 2019: the population-based Trøndelag Health Study (HUNT).

OBJECTIVE: Monitoring time trends in salt consumption is important for evaluating the impact of salt reduction initiatives on public health outcomes. There has so far not been available data to indicate if salt consumption in Norway has changed during the previous decade. We aimed to assess whether average 24-h salt intake estimated from spot urine samples in the adult population of mid-Norway changed from 2006-2008 to 2017-2019 and to describe variations by sex, age and educational level. DESIGN: Repeated cross-sectional studies. SETTING: The population-based Trøndelag Health Study (HUNT). PARTICIPANTS: In each of two consecutive waves (HUNT3: 2006-2008 and HUNT4: 2017-2019), spot urine samples were collected from 500 men and women aged 25-64 years, in addition to 250 men and women aged 70-79 years in HUNT4. Based on spot urine concentrations of Na, K and creatinine and age, sex and BMI, we estimated 24-h Na intake using the International Cooperative Study on Salt and Blood Pressure (INTERSALT) equation for the Northern European region. RESULTS: Mean (95 % CI) estimated 24-h salt intakes in men were 11·1 (95 % CI 10·8, 11·3) g in HUNT3 and 10·9 (95 % CI 10·6, 11·1) g in HUNT4, P = 0·25. Corresponding values in women were 7·7 (95 % CI 7·5, 7·9) g and 7·7 (95 % CI 7·5, 7·9) g, P = 0·88. Mean estimated salt intake in HUNT4 decreased with increasing age in women, but not in men, and it did not differ significantly across educational level in either sex. CONCLUSIONS: Estimated 24-h salt intake in adult men and women in mid-Norway did not change from 2006-2008 to 2017-2019.

Development and preliminary validation of a prediction formula of sodium and sodium-to-potassium ratio based on multiple regression using 24-h urines.

Accurate measurement of sodium intake in the diet is challenging, and epidemiological studies can be hampered by the attenuation of associations due to measurement error in sodium intake. A prediction formula for habitual 24-h urine sodium excretion and sodium-to-potassium ratio might lead to more reliable conclusions. Five 24-h urinary samples and two Food Frequency Questionnaires (FFQs) were conducted among 244 Japanese participants aged 35-80 years. We conducted multivariate linear regression analysis with urinary excretion as dependent variables and eating behaviour and food frequency as independent variables. Empirical weights of sodium excretion and sodium-to-potassium ratio were extracted. Preliminary validity was also assessed by randomly dividing the subjects into development and validation groups based on the correlation coefficient between estimates by the prediction formula and urinary excretion. Taste preference, soy sauce use at the table, frequency of pickled vegetables intake and number of bowls of miso soup were extracted as determinants of sodium excretion. Correlation coefficients between the estimates and urinary excretion for men and women were 0.42 and 0.43, respectively, for sodium and 0.49 and 0.50, respectively, for sodium-to-potassium ratio. This prediction formula may provide more accurate estimation of sodium intake and sodium-to-potassium ratio than the food composition approach.

Association between Urinary Sodium Excretion and Body Fat in School-Aged Children: Insights from the ARIA Study.

Childhood obesity has been associated with increased sodium intake. Nonetheless, evidence linking sodium intake to Body Mass Index (BMI) and Body Fat Mass Percentage (%BF) remains limited, especially in the pediatric age group. Therefore, this study aims to investigate whether there is an association between 24 h urinary sodium excretion with BMI and %BF in a sample group of children from the ARIA study. This cross-sectional analysis included 303 children aged 7 to 12 from across 20 public schools in Porto, Portugal. Weight and %BF were assessed using the Tanita™ BC-418 Segmental Body Analyzer. Children's Total Energy Intake (TEI) was estimated through a single 24 h Recall Questionnaire, and urinary sodium and potassium excretion was estimated by a 24 h urine collection. The association of %BF and BMI with 24 h sodium excretion was estimated by a binary logistic regression adjusted for sex, age, physical activity, total energy intake, parental education, and 24 h urinary excreted potassium. There was a significant positive association between higher levels of urinary sodium excretion and higher %BF values, even after adjusting for confounders. However, the same was not observed for BMI. Our findings suggest that higher sodium intake is associated with higher values of %BF among children, regardless of TEI and potassium intake.

Sodium and Human Health: What Can Be Done to Improve Sodium Balance beyond Food Processing?

Sodium plays a key role in the regulation of water balance and is also important in food formulation due to its contribution to the taste and use in the preservation of many foods. Excessive intake of any essential nutrient is problematic and this seems to be particularly the case for sodium since a high intake makes it the nutrient most strongly associated with mortality. Sodium intake has been the object of recommendations by public health agencies such as the WHO and this has resulted in efforts by the food industry to reduce the sodium content of packaged foods, although there is still room for improvement. The recent literature also emphasizes the need for other strategies, e.g., regulations and education, to promote adequate sodium intake. In the present paper, we also describe the potential benefits of a global healthy lifestyle that considers healthy eating but also physical activity habits that improve body functionality and may help to attenuate the detrimental effects of high sodium intake on body composition and cardiometabolic health. In conclusion, a reduction in sodium intake, an improvement in body functioning, and educational interventions promoting healthy eating behaviours seem to be essential for the optimal regulation of sodium balance.

Hypotensive drugs mitigate the high-sodium diet-induced pro-inflammatory activation of mouse macrophages in vivo.

Nowadays, there is an increasing emphasis on the need to alleviate the chronic inflammatory response to effectively treat hypertension. However, there are still gaps in our understanding on how to achieve this. Therefore, research on interaction of antihypertensive drugs with the immune system is extremely interesting, since their therapeutic effect could partly result from amelioration of hypertension-related inflammation, in which macrophages seem to play a pivotal role. Thus, current comprehensive studies have investigated the impact of repeatedly administered hypotensive drugs (captopril, olmesartan, propranolol, carvedilol, amlodipine, verapamil) on macrophage functions in the innate and adaptive immunity, as well as if drug-induced effects are affected by a high-sodium diet (HSD), one of the key environmental risk factors of hypertension. Although the assayed medications increased the generation of reactive oxygen and nitrogen intermediates by macrophages from standard fed donors, they reversed HSD-induced enhancing effects on macrophage oxidative burst and secretion of pro-inflammatory cytokines. On the other hand, some drugs increased macrophage phagocytic activity and the expression of surface markers involved in antigen presentation, which translated into enhanced macrophage ability to activate B cells for antibody production. Moreover, the assayed medications augmented macrophage function and the effector phase of contact hypersensitivity reaction, but suppressed the sensitization phase of cell-mediated hypersensitivity under HSD conditions. Our current findings contribute to the recognition of mechanisms, by which excessive sodium intake affects macrophage immune activity in hypertensive individuals, and provide evidence that the assayed medications mitigate most of the HSD-induced adverse effects, suggesting their additional protective therapeutic activity.

Dietary sodium and fluid intake in heart failure. A clinical consensus statement of the Heart Failure Association of the ESC.

Sodium and fluid restriction has traditionally been advocated in patients with heart failure (HF) due to their sodium and water avid state. However, most evidence regarding the altered sodium handling, fluid homeostasis and congestion-related signs and symptoms in patients with HF originates from untreated patient cohorts and physiological investigations. Recent data challenge the beneficial role of dietary sodium and fluid restriction in HF. Consequently, the European Society of Cardiology HF guidelines have gradually downgraded these recommendations over time, now advising for the limitation of salt intake to no more than 5 g/day in patients with HF, while contemplating fluid restriction of 1.5-2 L/day only in selected patients. Therefore, the objective of this clinical consensus statement is to provide advice on fluid and sodium intake in patients with acute and chronic HF, based on contemporary evidence and expert opinion.

Global guidelines recommendations for dietary sodium and potassium intake.

Non-communicable diseases (NCDs) cause a significant global health challenge, with unhealthy diets identified as a major risk factor. Sodium and potassium, which are essential minerals for human health, play important roles in various bodily functions, and an imbalance in their intake can have significant health implications, particularly concerning hypertension and cardiovascular diseases. This review compiles dietary sodium and potassium intake recommendations from prominent global health organizations and compares global guidelines to Japan's Dietary Reference Intake (DRI) guidelines. Sodium and potassium intake guidelines from organizations such as the World Health Organization (WHO), American College of Cardiology (ACC) and American Heart Association (AHA), Dietary Guidelines for Americans (DGA), European Food Safety Authority (EFSA), and DRI for Japanese exhibit variations. Compared to other Asian countries, Japan's historically higher sodium goal aligns with Southeast Asia where traditional preserved foods contribute to high sodium intake. Contrarily, Japan's lower potassium goal contrasts with other countries in Asia promoting a diet rich in fruits and vegetables. The ongoing effort by Japan to align with global recommendations reflects a gradation approach considering social habits. While harmonizing international efforts is essential, appreciating regional diversities is paramount through tailoring guidelines to cultural and dietary habit practices. Implementing context-specific guidelines informed by scientific research can contribute to global efforts in promoting healthy diets and reducing the burden of NCDs. Global guidelines that recommended the daily dietary intake goal for sodium and potassium exhibit variations. These disparities are influenced by diverse factors, including cultural dietary habits, socioeconomic status, health priorities, and available scientific research. Each population should follow the recommendations of their region.

Sex-specific associations between sodium and potassium intake and overall and cause-specific mortality: a large prospective U.S. cohort study, systematic review, and updated meta-analysis of cohort studies.

BACKGROUND: The impact of sodium intake on cardiovascular disease (CVD) health and mortality has been studied for decades, including the well-established association with blood pressure. However, non-linear patterns, dose-response associations, and sex differences in the relationship between sodium and potassium intakes and overall and cause-specific mortality remain to be elucidated and a comprehensive examination is lacking. Our study objective was to determine whether intake of sodium and potassium and the sodium-potassium ratio are associated with overall and cause-specific mortality in men and women. METHODS: We conducted a prospective analysis of 237,036 men and 179,068 women in the National Institutes of Health-AARP Diet and Health Study. Multivariable-adjusted Cox proportional hazard regression models were utilized to calculate hazard ratios. A systematic review and meta-analysis of cohort studies was also conducted. RESULTS: During 6,009,748 person-years of follow-up, there were 77,614 deaths, 49,297 among men and 28,317 among women. Adjusting for other risk factors, we found a significant positive association between higher sodium intake (≥ 2,000 mg/d) and increased overall and CVD mortality (overall mortality, fifth versus lowest quintile, men and women HRs = 1.06 and 1.10, Pnonlinearity < 0.0001; CVD mortality, fifth versus lowest quintile, HRs = 1.07 and 1.21, Pnonlinearity = 0.0002 and 0.01). Higher potassium intake and a lower sodium-potassium ratio were associated with a reduced mortality, with women showing stronger associations (overall mortality, fifth versus lowest quintile, HRs for potassium = 0.96 and 0.82, and HRs for the sodium-potassium ratio = 1.09 and 1.23, for men and women, respectively; Pnonlinearity < 0.05 and both P for interaction ≤ 0.0006). The overall mortality associations with intake of sodium, potassium and the sodium-potassium ratio were generally similar across population risk factor subgroups with the exception that the inverse potassium-mortality association was stronger in men with lower body mass index or fruit consumption (Pinteraction < 0.0004). The updated meta-analysis of cohort studies based on 42 risk estimates, 2,085,904 participants, and 80,085 CVD events yielded very similar results (highest versus lowest sodium categories, pooled relative risk for CVD events = 1.13, 95% CI: 1.06-1.20; Pnonlinearity < 0.001). CONCLUSIONS: Our study demonstrates significant positive associations between daily sodium intake (within the range of sodium intake between 2,000 and 7,500 mg/d), the sodium-potassium ratio, and risk of CVD and overall mortality, with women having stronger sodium-potassium ratio-mortality associations than men, and with the meta-analysis providing compelling support for the CVD associations. These data may suggest decreasing sodium intake and increasing potassium intake as means to improve health and longevity, and our data pointing to a sex difference in the potassium-mortality and sodium-potassium ratio-mortality relationships provide additional evidence relevant to current dietary guidelines for the general adult population. SYSTEMATIC REVIEW REGISTRATION: PROSPERO Identifier: CRD42022331618.

Effect of High Sodium Intake on Gut Tight Junctions' Structure and Permeability to Bacterial Toxins in a Rat Model of Chronic Kidney Disease.

INTRODUCTION: Uremic toxicity changes the gut structure and permeability, allowing bacterial toxins to translocate from the lumen to the blood during chronic kidney failure (CKD). Clinical fluid overload and tissue edema without uremia have similar effects but have not been adequately demonstrated and analyzed in CKD. AIMS: To investigate the effect of sodium intake on the plasma concentration of gut-derived uremic toxins, indoxyl sulfate (IS), and p-cresyl sulfate (pCS) and the expression of genes and proteins of epithelial gut tight junctions in a rat model of CKD. METHODS: Sham-operated (control group, CG) and five-sixths nephrectomized (5/6Nx) Sprague-Dawley rats were randomly assigned to low (LNa), normal (NNa), or high sodium (HNa) diets., Animals were then sacrificed at 8 and 12 weeks and analyzed for IS and pCS plasma concentrations, as well as for gene and protein expression of thigh junction proteins, and transmission electron microscopy (TEM) in colon fragments. RESULTS: The HNa 5/6Nx groups had higher concentrations of IS and pCS than CG, NNa, and LNa at eight and twelve weeks. Furthermore, HNa 5/6Nx groups had reduced expression of the claudin-4 gene and protein than CG, NNa, and LNa. HNa had reduced occludin gene expression compared to CG. Occludin protein expression was more reduced in HNa than in CG, NNa, and LNa. The gut epithelial tight junctions appear dilated in HNa compared to NNa and LNa in TEM. CONCLUSION: Dietary sodium intake and fluid overload have a significant role in gut epithelial permeability in the CKD model.