Kawasaki Formula Research Articles

Which method has the most accurate measurement of daily salt intake?

Sir, Which method has the most accurate measurement of daily salt intake? The recently published paper by Hasandokht et al., entitled “Life style interventions for hypertension treatment among Iranian women in primary health-care settings: Results of a randomized controlled trial,” had this advantage that it was done in Iran[1] that emphasized on the importance of preventive medicine in Iranian population. As the authors mentioned in their study and because the positive correlation between daily salt intake and hypertension is an essential risk factor,[1] it is important to estimate nearly accurate daily sodium intake. However, in their study the amount of dietary salt Intake is based on self-reported food record questionnaires, and this is one of the limitations of their study.[1] We suggested to obtain a morning fasting midstream urine sample from each patient and after freezing, and to send it to the laboratory in an ambient packaging with special boxes for biologic materials.[2] After that the Kawasaki formula is used to calculate 24 h urinary sodium excretion and this estimate is used as equivalent for most accurate salt intake.[2,3] Thus, by this procedure nearly accurate daily sodium intake is achieved and the validity of the studies would be increased. Financial support and sponsorship Nil. Conflicts of interest There are no conflicts of interest.

A virtual Kawasaki–Riemann–Roch formula

Kawasaki's formula is a tool to compute holomorphic Euler characteristics of vector bundles on a compact orbifold X. Let X be an orbispace with perfect obstruction theory which admits an embedding in a smooth orbifold. One can then construct the virtual structure sheaf and the virtual fundamental class of X. In this paper we prove that Kawasaki's formula behaves well " with working virtually" on X in the following sense: if we replace the structure sheaves, tangent and normal bundles in the formula by their virtual counterparts then Kawasaki's formula stays true. Our motivation comes from studying the quantum K-theory of a complex manifold X, with the formula applied to Kontsevich' moduli spaces of genus 0 stable maps to X.

Validation and comparison of three formulae to estimate sodium and potassium excretion from a single morning fasting urine compared to 24-h measures in 11 countries

Although 24-h urinary measure to estimate sodium and potassium excretion is the gold standard, it is not practical for large studies. We compared estimates of 24-h sodium and potassium excretion from a single morning fasting urine (MFU) using three different formulae in healthy individuals. We studied 1083 individuals aged 35-70 years from the general population in 11 countries. A 24-h urine and MFU specimen were obtained from each individual. A subset of 448 individuals repeated the measures after 30-90 days. The Kawasaki, Tanaka, and INTERSALT formulae were used to estimate urinary excretion from a MFU specimen. The intraclass correlation coefficient (ICC) between estimated and measured sodium excretion was higher with Kawasaki (0.71; 95% confidence interval, CI: 0.65-0.76) compared with INTERSALT (0.49; 95% CI: 0.29-0.62) and Tanaka (0.54; 95% CI: 0.42-0.62) formulae (P <0.001). For potassium, the ICC was higher with the Kawasaki (0.55; 95% CI: 0.31-0.69) than the Tanaka (0.36; 95% CI: -0.07 to 0.60; P <0.05) formula (no INTERSALT formula exists for potassium). The degree of bias (vs. the 24-h urine) for sodium was smaller with Kawasaki (+313 mg/day; 95% CI: +182 to +444) compared with INTERSALT (-872 mg/day; 95% CI: -728 to -1016) and Tanaka (-548 mg/day; 95% CI: -408 to -688) formulae (P <0.001 and P = 0.02, respectively). Similarly for potassium, the Kawasaki formula provided the best agreement and least bias. Blood pressure correlated most closely and similarly with the 24-h and Kawasaki estimates for sodium compared with the other two formulae. In a diverse population, the Kawasaki formula is the most valid and least biased method of estimating 24-h sodium excretion from a single MFU and is suitable for population studies.

Low salt intake and changes in serum sodium levels in the combination therapy of low-dose hydrochlorothiazide and angiotensin II receptor blocker

Background: Although a low salt intake and angiotensin II blockade may act to reduce serum sodium (srNa) levels during low-dose diuretic treatment, the effects of these factors on srNa level have not yet been fully clarified. The present study was conducted to examine the association of dietary salt intake with the changes in srNa levels when angiotensin II receptor blocker (ARB) treatment is changed to the combination of ARB plus a low-dose diuretic, Hydrochlorothiazide (HCTZ). Methods: In 88 patients (age 70±12 years old), ARB treatment was switched to the combination drug (the same dosage ARB plus 12.5 mg/day HCTZ). srNa level was measured before and 6 months after administration of this combination drug. The daily salt intake was estimated by the Kawasaki formula using second morning urine. Results: The study subjects were divided into quintile ranges according to the daily salt intake. The reduction in srNa levels by switching to the ARB plus HCTZ treatment was significant in subjects in the lowest quintile Q5 (7.22 g/day or less salt intake), but not in those in Q1-4 (17.78-7.25 g/day salt intake). Increases in serum creatinine and uric acid levels, however, were significantly larger in the former group than in the latter group. ![Figure][1] Conclusions: In the strict low salt intake condition (< 7.2 g/day), the addition of a low-dose diuretic (12.5 mg HCTZ) to ARB treatment causes significant reductions in srNa levels, which might affect blood osmolarity. [1]: pending:yes

Low Salt Intake and Changes in Serum Sodium Levels in the Combination Therapy of Low-Dose Hydrochlorothiazide and Angiotensin II Receptor Blocker

The present study was conducted to examine the association of dietary salt intake with changes in serum sodium (srNa) levels when angiotensin II receptor blocker (ARB) treatment is changed to the combination of ARB plus low-dose diuretic (hydrochlorothiazide [HCTZ]). In 88 patients (age 70 ± 12 years), ARB treatment was switched to the combination therapy (same dosage ARB+12.5mg/day HCTZ). The srNa level was measured before and 6 months after administration of the combination. The daily salt intake was estimated by the Kawasaki formula using second morning urine sample. The study subjects were divided into quintile ranges according to daily salt intake. The reduction in srNa levels by switching to the combination treatment was significant in subjects in the lowest quintile Q5 (≤ 8.9 g/day salt intake), but not in those in Q1-4 (28.1-9.3g/day salt intake). Increases in serum creatinine and uric acid levels were significantly larger in the former group than in the latter group. In elderly Japanese subjects with low salt intake (<8.9 g/day), the addition of a low-dose diuretic (12.5mg HCTZ) to ARB treatment causes significant reduction in srNa levels, which might affect blood osmolarity.

Urinary Sodium and Potassium Excretion and Risk of Cardiovascular Events

The precise relationship between sodium and potassium intake and cardiovascular (CV) risk remains uncertain, especially in patients with CV disease. To determine the association between estimated urinary sodium and potassium excretion (surrogates for intake) and CV events in patients with established CV disease or diabetes mellitus. Observational analyses of 2 cohorts (N = 28,880) included in the ONTARGET and TRANSCEND trials (November 2001-March 2008 from initial recruitment to final follow-up). We estimated 24-hour urinary sodium and potassium excretion from a morning fasting urine sample (Kawasaki formula). We used restricted cubic spline plots to describe the association between sodium and potassium excretion and CV events and mortality, and to identify reference categories for sodium and potassium excretion. We used Cox proportional hazards multivariable models to determine the association of urinary sodium and potassium with CV events and mortality. CV death, myocardial infarction (MI), stroke, and hospitalization for congestive heart failure (CHF). At baseline, the mean (SD) estimated 24-hour excretion for sodium was 4.77 g (1.61); and for potassium was 2.19 g (0.57). After a median follow-up of 56 months, the composite outcome occurred in 4729 (16.4%) participants, including 2057 CV deaths, 1412 with MI, 1282 with stroke, and 1213 with hospitalization for CHF. Compared with the reference group with estimated baseline sodium excretion of 4 to 5.99 g per day (n = 14,156; 6.3% participants with CV death, 4.6% with MI, 4.2% with stroke, and 3.8% admitted to hospital with CHF), higher baseline sodium excretion was associated with an increased risk of CV death (9.7% for 7-8 g/day; hazard ratio [HR], 1.53; 95% CI, 1.26-1.86; and 11.2% for >8 g/day; HR, 1.66; 95% CI, 1.31-2.10), MI (6.8%; HR, 1.48; 95% CI, 1.11-1.98 for >8 g/day), stroke (6.6%; HR, 1.48; 95% CI, 1.09-2.01 for >8 g/day), and hospitalization for CHF (6.5%; HR, 1.51; 1.12-2.05 for >8 g/day). Lower sodium excretion was associated with an increased risk of CV death (8.6%; HR, 1.19; 95% CI, 1.02-1.39 for 2-2.99 g/day; 10.6%; HR, 1.37; 95% CI, 1.09-1.73 for <2 g/day), and hospitalization for CHF (5.2%; HR, 1.23; 95% CI, 1.01-1.49 for 2-2.99 g/day) on multivariable analysis. Compared with an estimated potassium excretion of less than 1.5 g per day (n = 2194; 6.2% with stroke), higher potassium excretion was associated with a reduced risk of stroke (4.7% [HR, 0.77; 95% CI, 0.63-0.94] for 1.5-1.99 g/day; 4.3% [HR, 0.73; 95% CI, 0.59-0.90] for 2-2.49 g/day; 3.9% [HR, 0.71; 95% CI, 0.56-0.91] for 2.5-3 g/day; and 3.5% [HR, 0.68; 95% CI, 0.49-0.92] for >3 g/day) on multivariable analysis. The association between estimated sodium excretion and CV events was J-shaped. Compared with baseline sodium excretion of 4 to 5.99 g per day, sodium excretion of greater than 7 g per day was associated with an increased risk of all CV events, and a sodium excretion of less than 3 g per day was associated with increased risk of CV mortality and hospitalization for CHF. Higher estimated potassium excretion was associated with a reduced risk of stroke.

Derivation of Ohm's law in a deterministic mechanical model.

We study the Lorentz gas in small external electric and magnetic fields, with the particle kinetic energy held fixed by a Gaussian ``thermostat.'' Starting from any smooth initial density, a unique stationary, ergodic measure is approached for times t\ensuremath{\rightarrow}\ensuremath{\infty}. The steady-state electric current J(B,E) is given by a Kawasaki formula and the entropy production J\ensuremath{\cdot}E/T, with T the ``temperature,'' is equal to both the asymptotic decay rate of the Gibbs entropy and minus the sum of the Lyapunov exponents. The Einstein and Kubo formulas hold, i.e., J(B,E)=\ensuremath{\sigma}(B)\ensuremath{\cdot}E + higher order terms, with the diffusion matrix D(B) at E=0 given by ${\mathit{k}}_{\mathit{B}}$T times the symmetric part \ensuremath{\sigma}\ifmmode \tilde{}\else \~{}\fi{}(B) of the conductivity matrix.

Steady-state electrical conduction in the periodic Lorentz gas

We study nonequilibrium steady states in the Lorentz gas of periodic scatterers when an external field is applied and the particle kinetic energy is held fixed by a ``thermostat'' constructed according to Gauss' principle of least constraint (a model problem previously studied numerically by Moran and Hoover). The resulting dynamics is reversible and deterministic, but does not preserve Liouville measure. For a sufficiently small field, we prove the following results: (1) existence of a unique stationary, ergodic measure obtained by forward evolution of initial absolutely continuous distributions, for which the Pesin entropy formula and Young's expression for the fractal dimension are valid; (2) exact identity of the steady-state thermodyamic entropy production, the asymptotic decay of the Gibbs entropy for the time-evolved distribution, and minus the sum of the Lyapunov exponents; (3) an explicit expression for the full nonlinear current response (Kawasaki formula); and (4) validity of linear response theory and Ohm's transport law, including the Einstein relation between conductivity and diffusion matrices. Results (2) and (4) yield also a direct relation between Lyapunov exponents and zero-field transport (=diffusion) coefficients. Although we restrict ourselves here to dimension $d=2,$ the results carry over to higher dimensions and to some other physical situations: e.g. with additional external magnetic fields. The proofs use a well-developed theory of small perturbations of hyperbolic dynamical systems and the method of Markov sieves, an approximation of Markov partitions. In our context we discuss also the van Kampen objection to linear response theory, which, we point out, overlooks the ``structural stability'' of strongly hyperbolic flows.

Experimental Confirmation of the Kawasaki-Einstein-Stokes Formula; Measurement of Small Correlation Lengths

The Kawasaki formula $D=\frac{\mathrm{kT}}{6\ensuremath{\pi}\ensuremath{\eta}\ensuremath{\xi}}$ is experimentally verified using the measured values in a cyclohexane-aniline critical mixture near ${T}_{c}$. Its application in a wide range of temperatures above ${T}_{c}$, where the viscosity is known, is completely verified by the measurements of the diffusion coefficient $D$ and allows a direct determination of the correlation length $\ensuremath{\xi}$ in a domain where no other optical method is suitable. We show that the power law $\ensuremath{\xi}=\ensuremath{\xi}{(\ensuremath{\epsilon})}^{\ensuremath{\nu}}$ is followed up to 40\ifmmode^\circ\else\textdegree\fi{} from ${T}_{c}$.