Emanuel Revici used serum potassium and whole blood potassium as metrics in Research in Physiopathology as Basis of Guided Chemotherapy: With Special Application to Cancer. Here we investigate the possibility of using intracellular and extracellular potassium as biomarkers.

References for Revici’s use of Potassium. Some of these will be reproduced below.

Reference Title Notes Page Number
Figure 127 Serum vs Whole Blood K Key graphic 352
Potassium in Cancer 396 - 399
Chapter 4, Note 8 Total Blood Potassium 571 - 573
Chapter 5, Note 2 Potassium 610 - 615
Chapter 6, Note 28 Barometric Influence on Whole Blood K 653

Revici classifies potassium as a cellular level element.

Body Fluids and Electrolytes

Chapter 4 of Clinical Biochemistry: Metabolic and Clinical Aspects, 2e – Sodium, water and potassium
contains the following tables:
Fluid Distribution Electrolyte Concentration

Osmolality expressed as mmol/kg while osmolarity expressed as mmol/L. For the relation of meq and mmol (for Na and K they are the same) see Equivalent (chemistry). For more information about these units see Milliequivalents, Millimoles, and Milliosmoles.

For additional detail see Textbook of Medical Physiology, 9e by Guyton and Hall.
Table 25-2 on page 301 is a more detailed version of Table 4.2 above.

New Human Physiology - Chapter 24 : Body Fluids and Regulation is a good overview including discussion of the resting membrane potential (RMP) and its implications. See the discussions of body potassium and hypo/hyperkalaemia.

Disorders of Potassium Homeostasis: Pathophysiology and Management (see download, sadly the figures are illegible) is a review article with a more in depth discussion.
“States of acidosis and alkalosis affect potassium because it compensates for the movement of protons (hydrogen ions). In acidosis, H+ ions move into cells and, to maintain electrical balance, K+ ions move out into the ECF; and vice-versa in alkalosis. A hyperosmolar ECF environment can promote potassium efflux from the cells leading to depletion of intracellular potassium (and, hence, total body potassium).”
Interesting comments about hypokalemia and alkalosis/acidosis (e.g. different treatments).

Hypokalaemia (Glover, 1999) (full text at Hypokalaemia) has details on hypokalemia treatment and a good discussion of the Nernst potential and its implications. Also has discussion of the impact of pH on ECF K.

Potassium Pitfalls discusses possible causes of inaccurate serum K measurements.

The Measurements

Revici used serum and whole blood potassium as measurements of potassium status.

Serum potassium is a common electrolyte measurement in medical practice and is easily available in a standard CBC.

The whole blood potassium measurement (in this form) is unique to Revici. Details are given in Chapter 4, Note 8

Try calculating the intracellular potassium given Revici’s measurement. See “Further Research” below for details.

Red Blood Cell Potassium seems like the appropriate test to use today. For example:
Potassium, RBC (128241) - Quest Diagnostics STTM RBC Potassium
Metals Red Blood Cell Test
Elemental Analysis, Packed Erythrocytes (RBC’s)
Genova Diagnostics - Nutrient and Toxic Elements

Interpretation

Serum vs Whole Blood K

Revici’s interpretation focuses on the relative level in each compartment and translates this into quantitative excess/deficiency and anaerobic/dysaerobic as shown in Figure 127.

An alternative (but related) interpretation focuses on the physiological manifestations of these.

For quantitative excess/deficiency we create a measure based on the relative quantities of intracellular and extracellular fluid volume.

\[ K_{tot} = 28L \cdot K_{ICF} + 14L \cdot K_{ECF} \] based on the total ICF and ECF volumes.

For the relative imbalance we use the resting membrane voltage (wiki says -9mV for erythrocytes?!) implied by the relative intracellular and extracellular potassium concentrations (the Nernst potential for potassium, \(E_k\)). This is calculated using the Nernst equation. \[ E_k = -V_t \cdot \ln \left( \frac{[K^+]_o}{[K^+]_i} \right) \] where \(V_t = \frac{kT}{q}\)
At body temperature (37C) \(V_t = \) 27mV giving \[ E_k = -27mV \cdot \ln \left( \frac{[K^+]_o}{[K^+]_i} \right) \] with a typical value being ?

Note that this is only an approximation of the actual resting membrane voltage since it ignores the other ions (e.g. Sodium).

Note that Revici explicitly states on page 397 that he is not interested in the ratio of the potassium values.

The working hypothesis is that the Nernst potential for potassium should correspond to a measurement of Revici’s anaerobic/dysaerobic balance. Note that resting potential varies by cell type. It is assumed the RBC is a representative case.

For more information on the Nernst equation see Theory Nernst Equation

Assuming \([K^+]_o\) varies around 4.3 and \([K^+]_i\) varies around 160 we see the following contours for our derived values:

K_o <- seq(2.3, 6.3, 0.1)
K_i <- seq(60, 120, 2)
#K_i <- seq(80, 240, 4)
grd <- expand.grid(K_i, K_o)
colnames(grd) <- c("K_i", "K_o")
grd$K_tot <- 28 * grd$K_i + 14 * grd$K_o # mmol
grd$E_k <- -27 * log(grd$K_i / grd$K_o) # mV

library(lattice)
## Warning: package 'lattice' was built under R version 3.0.3
contourplot(K_tot ~ K_i * K_o, grd, cuts=10,
            main="Total Body Potassium (mmol)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)

plot of chunk unnamed-chunk-1

Based on this it seems sensible to consider quantitative excess or deficiency to be solely a function of the intracellular level. As mentioned elsewhere, ICF volume may affect excess/deficiency.

Also see Figure 29-6 on page 375 of Guyton and Hall.

Remember that the molecular weight of Potassium is 39 g/mol and that people with differing amounts of fat free mass have different ICF volumes (i.e. don’t take the calculated TBK gram values too literally here).

contourplot(E_k ~ K_i * K_o, grd, cuts=10,
            main="Resting Membrane Potential Due to Potassium (mV)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)

plot of chunk unnamed-chunk-2

This measurement adds additional information. To properly evaluate the utility of this we need data which has both intra and extra cellular potassium values. For example, it would be very interesting to have the raw data from the RBC K/blood pressure study below.

Comparing this plot to Revici’s Figure 127 the correct interpretation of \(E_k\) appears to be that lower absolute values of \(E_k\) (less polarized, upper left) are dysaerobic while higher absolute values of \(E_k\) (more polarized, lower right) are anaerobic.

Compare to the ratio.

grd$K_ratio <- grd$K_i / grd$K_o
contourplot(K_ratio ~ K_i * K_o, grd, cuts=10,
            main="Intracellular K to Extracellular K Ratio",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)

plot of chunk unnamed-chunk-3

The ratio is similar to \(E_k\) except for changing the contour spacing. I think \(E_k\) is the appropriate metric to use for now.

Guyton and Hall has a discussion of the normal resting membrance potential in neurons on page 60. It would be interesting to run simulations to see how changing potassium concentrations affect action potential propagation.

Modifying Body Status

Revici gives instructions for therapy on page 615.
Potassium and Therapy

Jeremy Kaslow Potassium information

Further Research

Existing Work with Intracellular Potassium Levels

I would like to find more information about this in the literature.

Red Blood Cell Potassium Therapeutic Implications, the pubmed link shows three papers citing this.
I don’t have full text for this, but the preview shows the following:
K_RBC ranged from 68 to 103 mEq/L with median 86

The sodium, potassium, and water contents of red blood cells of healthy human adults opens by stating:
Intracellular sodium and potassium concentrations in man can only be measured with ease and accuracy in red blood cells (RBC).
They note a variation of RBC potassium with the menstrual cycle (page 1818):
“the average change in potassium concentration from the highest levels (mEq per kg cells) was as follows: day 3, 0; day 10, -2.3; day 19, -2.97; and day 26, - 3.94. These results were not obtained during single cycles.”
No significant variation was observed by time of day.
Observed means: men 88.4 mEq/kg, women 92.4 mEq/kg; SD (both?) 2.86 mEq/kg
Plasma potassium was 4.15 +- 0.32 mEq/kg
“The ratio of intracellular potassium to sodium concentration is about 20% greater in young women than in young men (14.18 to 11.88).”
References 3-9 look like they cover potassium in RBC.

Potassium Depletion in Severe Heart Disease has an interesting discussion of potassium depletion which they ascribe to decreasd ICF volume.
Does the assessment of K depletion/excess above need to account for this (say by using serum Na)?

Potassium, Sodium, and Water in Normal Human red Blood Cells
RBCs have an SD of 1.1. Solid content is 334 g/kg. This leads to a substantial difference depending on which units are used (be careful).
meq/kg RBC - mean 89.6, SD 3.6
meq/kg H2O - mean 134.6, SD 5.1 (1.5x above)

The red cell membrane and the transport of sodium and potassium - see download, Also

Red blood cell K+ could be a marker of K+ changes in other cells involved in blood pressure regulation

Hypokalemia Physiological Abnormalities During Cardiopulmonary Bypass - full text

Red-blood-cell potassium as a practical index of potassium status in elderly patients

Potassium depletion in aged patients: an evaluation through red-blood-cell potassium determination

Cardiac Function

Correlating these measures with cardiac function would be useful.

See Revici page 614. Also see page 574.

The Electrocardiogram and Disturbance of Potassium Metabolism mentions intracellular potassium, but I don’t have full text to investigate. Pubmed only shows two citations of this paper, but the related citations look interesting.

What is the optimal serum potassium level in cardiovascular patients? states “Total body potassium is 3,500 mmol, with 98% intracellular.”

Importance of Potassium in Cardiovascular Disease - see download, much on serum K, but nothing on intracellular

Intracellular Potassium from Revici Whole Blood Potassium

Try calculating the intracellular potassium given Revici’s measurement.

Hematocrit is a key component of this. Per Guyton and Hall (9e page 299) for men 0.40 is normal while for women 0.36 is normal and the true hematocrit is 0.96 of the measured hematocrit. Given this I will use 0.38 as a working value.

Revici diluted the whole blood by 1/10, but it looks like this was accounted for in the K_wb = 38 mEq measurement (i.e. we can take that number as given).

Assuming the influence of the serum K on the whole blood K is neglible we can estimate the intracellular K from \(K_{wb} = K_{RBC} \cdot Hematocrit\) giving us \(K_{RBC} = K_{wb} \div Hematocrit\) for a typical value of 100 which seems high but not too far off the K_RBC values given above.

The follow on question is how well do measures of K_RBC correspond to K_i in other cells? This should be investigated in the Existing Work section above.

Circadian Rhythms

If we are using serum K and RBC K as biomarkers it would be helpful to understand if there is any circadian variation. This is especially relevant in the context of circadian variation of Revici’s anaerobic/dysaerobic status.

The sodium, potassium, and water contents of red blood cells of healthy human adults mentions a variation of RBC potassium with the menstrual cycle (page 1818):
“the average change in potassium concentration from the highest levels (mEq per kg cells) was as follows: day 3, 0; day 10, -2.3; day 19, -2.97; and day 26, - 3.94. These results were not obtained during single cycles.” (about a +/- 2% variation)
But no significant RBC K variation was observed by time of day.

Given this we will focus on serum potassium.

Serum Potassium Circadian Rhythm

The medical literature has established that serum potassium has a significant circadian rhythm. Investigate that and try to correlate it with Revici’s anaerobic/dysaerobic circadian variation.

Looking at the “Resting Membrane Potential Due to Potassium (mV)” plot above we see a roughly 5mV change for a 1mmol/L change in serum K. Higher serum K corresponds to more dysaerobic.

Revici mentions of circadian rhythm:
page 151 has some interesting comments about time of day vs. sleep/wake (compare humans and nocturnal rats). 4AM as maximum A and 8-9PM as maximum D
Seasonal variation is discussed on page 153 and on page 297 and 298

“serum potassium variation by time of day” was a good Google search.

Circadian Variation in Human Ventricular Refractoriness a detailed look at multiple metrics in the cardiac context (but for a small number of patients). Also has an evaluation of autonomic NS function. Figure 4 plots hourly serum K. An interesting paper, but not the best choice for establishing a reference for circadian variation of serum K.

The effects of time of venipuncture on variation of serum constituents. Consideration of within-day and day-to-day changes in a group of healthy young men - no full text, but from the abstract:
A unique individual diurnal pattern (subject-hour interaction) was statistically significant for serum potassium.
Statistically significant main effect of month (main effect of day) for the group of subjects was seen for total lipids and potassium
For serum cholesterol, potassium, acid phosphatase, and phosphate ion, the within-day variation was greater than the day-to-day variation occurring over four months

Diurnal variations in serum biochemical and haematological measurements - see page 174 figure
“Our finding of lower values of mean serum potassium in the afternoon compared with the morning has also been shown in other studies, though there seems to be considerable individual variation about this underlying trend. The reasons for this daytime variation in serum potassium are unclear and probably of little clinical importance.”

The effects of age, sex and other factors on blood chemistry in health - Creatinine, urea, glucose, cholesterol, potassium and globulin show a tendency to increase in concentration with age

Factors Contributing to Intra-Individual Variation of Serum Constituents: 1. Within-Day Variation of Serum Constituents in Healthy Subjects - Mean serum K ranged from 5.3 at 08:00 to 4.3 at 14:00
Note that different subjects had different shape/slope of variation (fig 3).

Diurnal Rhythm of Potassium
“There is a net flux of potassium from intracellular fluid to extracellular fluid (mainly blood) in the morning and a reverse net flux later in the day.The net fluxes between these two compartments counterbalance the diurnal rhythm in urinary potassium excretion. The flux appears to be driven by osmotic pressure.”

Circadian Models of Serum Potassium, Sodium, and Calcium Concentrations in Healthy Individuals and Their Application to Cardiac Electrophysiology Simulations at Individual Level - good resource for mathematical models
mean potassium = (M/F mean concentration) + 0.18 * cos(2pi/24(time - 10:07))
(RES: +- 0.18 seems a little low for 24 hour variation based on other references)
see references at end

Rhythmic 24-hour variations of frequently used clinical biochemical parameters in healthy young males–the Bispebjerg study of diurnal variations - source of 0.18 amplitude above

Case Study

Here is example data from a cancer patient case study.

# See RMySQL_example.R
# caseStudy <-
# structure(list(test_date = structure(list(sec = c(0, 0, 0, 0, 
# 0, 0, 0), min = c(0L, 0L, 0L, 0L, 0L, 0L, 0L), hour = c(0L, 0L, 
# 0L, 0L, 0L, 0L, 0L), mday = c(12L, 15L, 1L, 27L, 5L, 25L, 12L
# ), mon = c(9L, 9L, 4L, 6L, 11L, 0L, 8L), year = c(111L, 112L, 
# 112L, 112L, 112L, 113L, 113L), wday = c(3L, 1L, 2L, 5L, 3L, 5L, 
# 4L), yday = c(284L, 288L, 121L, 208L, 339L, 24L, 254L), isdst = c(1L, 
# 1L, 1L, 1L, 0L, 0L, 1L)), .Names = c("sec", "min", "hour", "mday", 
# "mon", "year", "wday", "yday", "isdst"), class = c("POSIXlt", 
# "POSIXt"), tzone = c("", "PST", "PDT")), K = c(4.6, 4.4, 4.2, 
# 4.5, 4.5, 5, 4.3), RBC_K = c(77, 84, 79, 87, 100, 88, 89), K_RATIO = c(16.7391304347826, 
# 19.0909090909091, 18.8095238095238, 19.3333333333333, 22.2222222222222, 
# 17.6, 20.6976744186047), K_LN_RATIO = c(2.81774911835863, 2.9492122579191, 
# 2.9343633271777, 2.96183072187831, 3.10109278921182, 2.86789890204411, 
# 3.03002134703262), mV = c(70.4437279589659, 73.7303064479775, 
# 73.3590831794425, 74.0457680469577, 77.5273197302954, 71.6974725511027, 
# 75.7505336758156), LL = c("78.8", "153.8", "117", "117", "156.6", 
# "117", "105.4"), EQ_CX = c(-80, -30, -45, -30, -30, -30, -90)), .Names = c("test_date", 
# "K", "RBC_K", "K_RATIO", "K_LN_RATIO", "mV", "LL", "EQ_CX"), class = "data.frame", row.names = c(26108L, 
# 26536L, 26972L, 26973L, 26974L, 26975L, 26976L))

# Another version with additional data from Doctors Data RBC K and Labcorp Serum K
caseStudy <-
structure(list(X = c(26108L, 26536L, 26972L, 26973L, 26974L, 
26975L, 26976L, 1L, 2L, 3L), test_date = structure(c(1L, 4L, 
2L, 3L, 5L, 6L, 9L, 7L, 8L, 10L), .Label = c("2011-10-12", "2012-05-01", 
"2012-07-27", "2012-10-15", "2012-12-05", "2013-01-25", "2013-03-20", 
"2013-06-01", "2013-09-12", "2013-11-25"), class = "factor"), 
    K = c(4.6, 4.4, 4.2, 4.5, 4.5, 5, 4.3, 4.35, 4.1, 4.1), RBC_K = c(77L, 
    84L, 79L, 87L, 100L, 88L, 89L, 87L, 80L, 86L), K_RATIO = c(16.7391304347826, 
    19.0909090909091, 18.8095238095238, 19.3333333333333, 22.2222222222222, 
    17.6, 20.6976744186047, NA, NA, NA), K_LN_RATIO = c(2.81774911835863, 
    2.9492122579191, 2.9343633271777, 2.96183072187831, 3.10109278921182, 
    2.86789890204411, 3.03002134703262, NA, NA, NA), mV = c(70.4437279589659, 
    73.7303064479775, 73.3590831794425, 74.0457680469577, 77.5273197302954, 
    71.6974725511027, 75.7505336758156, NA, NA, NA), LL = c(78.8, 
    153.8, 117, 117, 156.6, 117, 105.4, NA, NA, NA), EQ_CX = c(-80L, 
    -30L, -45L, -30L, -30L, -30L, -90L, NA, NA, NA)), .Names = c("X", 
"test_date", "K", "RBC_K", "K_RATIO", "K_LN_RATIO", "mV", "LL", 
"EQ_CX"), class = "data.frame", row.names = c(NA, -10L))

caseStudy$K_tot <- 28 * caseStudy$RBC_K + 14 * caseStudy$K # mmol
caseStudy$E_k <- -27 * log(caseStudy$RBC_K / caseStudy$K) # mV
caseStudy$mV <- NULL
caseStudy[order(caseStudy$test_date),]
##        X  test_date    K RBC_K K_RATIO K_LN_RATIO    LL EQ_CX K_tot    E_k
## 1  26108 2011-10-12 4.60    77   16.74      2.818  78.8   -80  2220 -76.08
## 3  26972 2012-05-01 4.20    79   18.81      2.934 117.0   -45  2271 -79.23
## 4  26973 2012-07-27 4.50    87   19.33      2.962 117.0   -30  2499 -79.97
## 2  26536 2012-10-15 4.40    84   19.09      2.949 153.8   -30  2414 -79.63
## 5  26974 2012-12-05 4.50   100   22.22      3.101 156.6   -30  2863 -83.73
## 6  26975 2013-01-25 5.00    88   17.60      2.868 117.0   -30  2534 -77.43
## 8      1 2013-03-20 4.35    87      NA         NA    NA    NA  2497 -80.88
## 9      2 2013-06-01 4.10    80      NA         NA    NA    NA  2297 -80.22
## 7  26976 2013-09-12 4.30    89   20.70      3.030 105.4   -90  2552 -81.81
## 10     3 2013-11-25 4.10    86      NA         NA    NA    NA  2465 -82.17
contourplot(K_tot ~ K_i * K_o, grd, cuts=10,
            main="Total Body Potassium (mmol)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            xlim=c(74,103), ylim=c(4.05,5.05),
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(caseStudy$RBC_K, caseStudy$K, pch=19))
ltext(caseStudy$RBC_K, caseStudy$K, labels=caseStudy$test_date)
trellis.unfocus()

plot of chunk unnamed-chunk-4

contourplot(E_k ~ K_i * K_o, grd, cuts=10,
            main="Resting Membrane Potential Due to Potassium (mV)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            xlim=c(74,103), ylim=c(4.05,5.05),
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(caseStudy$RBC_K, caseStudy$K, pch=19))
ltext(caseStudy$RBC_K, caseStudy$K, labels=caseStudy$test_date)
trellis.unfocus()

plot of chunk unnamed-chunk-4

range(caseStudy$K_tot)
## [1] 2220 2863
range(caseStudy$E_k)
## [1] -83.73 -76.08

Display as a time series. Try both the raw K/RBCK data and the K_tot/E_k data.

For some reason these plots display correctly from the CLI but not from knitr. Lattice was complicated and ggplot2 does not support two Y axes so punting for now.

The CLI correctly spaces the X axis by actual date, but knitr has the points at equal intervals (and here does not give the dates on the axis).

See an R time series quick fix for more on R time series.

First a simple knitr test case. Why does this not display with red points and lines?

# For more than two Y axes see
# http://www.r-bloggers.com/multiple-y-axis-in-a-r-plot/

# First order the data
caseStudyO <- caseStudy[order(caseStudy$test_date),]

# # Try using a time series
# ts1 <- ts(caseStudyO$test_date, caseStudyO$K)

# Should really reset parameters when done here (but code did not work right)
#opar <- par()
par(mar=c(5,4,4,5)+.1)
plot.default(caseStudyO$test_date, caseStudyO$K, main="Serum and RBC Potassium by Date",
     xlab="Date", ylab="Serum Potassium", col="red", type="b")
# plot.ts(caseStudyO$test_date, caseStudyO$K, main="Serum and RBC Potassium by Date",
#      xlab="Date", ylab="Serum Potassium", col="red")
# ts.plot(caseStudyO$test_date, caseStudyO$K, main="Serum and RBC Potassium by Date",
#      xlab="Date", ylab="Serum Potassium", col="red")
abline(h=4.5, col="red", lty=2)
par(new=TRUE)
plot.default(caseStudyO$test_date, caseStudyO$RBC_K,
     xlab="", ylab="",col="blue" , type="b", xaxt="n", yaxt="n")
abline(h=90, col="blue", lty=2)
axis(4)
mtext("RBC Potassium",side=4,line=3)
legend("topleft",col=c("red","blue"),lty=1,legend=c("K","RBC K"))

plot of chunk unnamed-chunk-7

#par(opar)

par(mar=c(5,4,4,5)+.1)
plot.default(caseStudyO$test_date, caseStudyO$E_k, main="Total Body Potassium and Membrane Voltage by Date",
     xlab="Date", ylab="Membrane Voltage (mV)", col="red", type="b")
#abline(h=4.5, col="red", lty=2)
par(new=TRUE)
plot.default(caseStudyO$test_date, caseStudyO$K_tot,
     xlab="", ylab="",col="blue" , type="b", xaxt="n", yaxt="n")
#abline(h=90, col="blue", lty=2)
axis(4)
mtext("Total Body Potassium",side=4,line=3)
legend("topright",col=c("red","blue"),lty=1,legend=c("E_k","K_tot"))

plot of chunk unnamed-chunk-7

#par(opar)

Total Body Potassium Measurement

There is literature on other techniques to measure total body potassium (TBK). I have not looked into this enough to see if it relates to the ideas above. In particular, does this have implications for the assessment of excess/deficiency in people with varying body composition?

Total Body Potassium (TBK) - overview.
BODY POTASSIUM MEASUREMENTS WITH A TOTAL-BODY COUNTER - some interesting comments about metabolic balance on page 258.
A New Total Body Potassium Method to Estimate Total Body Skeletal Muscle Mass in Children
Comparison of total body potassium with other techniques for measuring lean body mass in men and women with AIDS wasting
Total body potassium and body fat: relevance to aging
Whole-body and exchangeable potassium measurements in normal elderly subjects - see download
Total-body potassium in health: effects of age, sex, height, and fat - no full text
Body composition. Prediction of normal body potassium, body water and body fat in adults on the basis of body height, body weight and age - no full text. They found TBW relevant and discussed intra/extra cellular water.
PREDICTION OF TOTAL BODY POTASSIUM FROM ANTHROPOMETRIC MEASUREMENTS - see download

The prediction of muscle potassium from blood electrolytes in potassium depleted rats - no full text, see Kindle reference in Potassium Nutrition : In Heart Disease, Rheumatoid Arthritis, Gout, Diabetes, and Metabolic Shock
The consequences of potassium depletion - see download

http://www.lef.org/prod_hp/abstracts/potassiumabs.html

Chloride Ion

Take a look at the impact of the chloride ion (in particular serum chloride) on membrane potential. Based on a suggestion by Lynne August.

To include the chloride ion in the membrane potential we start with the Goldman-Hodgkin-Katz (aka GHK or Goldman) Equation. Also see the wiki Goldman Equation and this simulator.

\[ V_m = V_t \cdot \ln \left( \frac{p_K[K^+]_o + p_{Na}[Na^+]_o + p_{Cl}[Cl^-]_i}{p_K[K^+]_i + p_{Na}[Na^+]_i + p_{Cl}[Cl^-]_o} \right) \]

Notice the difference for Cl compartments due to the different charge.

For a typical neuron at rest, p_K : p_Na : p_Cl = 1 : 0.05 : 0.45. In contrast, approximate relative permeability values at the peak of a typical neuronal action potential are p_K : p_Na : p_Cl = 1 : 12 : 0.45. (from first link above)

From Guyton and Hall Textbook of Medical Physiology, 9e, page 575, we have concentrations for a neuron of:
\([Na^+]_o = \) 142 mEq/L
\([K^+]_o = \) 4.5 mEq/L
\([Cl^+]_o = \) 107 mEq/L
\([Na^+]_i = \) 14 mEq/L
\([K^+]_i = \) 120 mEq/L
\([Cl^+]_i = \) 8 mEq/L
By looking at both the permeabilities and the concentrations we can get an idea of the relative contributions of each ion/compartment.

# Make clear that RT/F is the same as V_t = kT/q above
# R <- 8.314
# T <- 37 + 273.15
# F <- 96485
# R * T / F
Na_o <- 142; K_o <- 4.5; Cl_o <- 107; Na_i <- 14; K_i <- 120; Cl_i <- 8
p_Na <- 0.05; p_K <- 1; p_Cl <- 0.45
Na_ow <- 10; K_ow <- 1.8; Cl_ow <- 10; K_iw <- 45

In the numerator we have contributions of:
Na = 7.1, K = 4.5, Cl = 3.6
In the denominator we have contributions of:
Na = 0.7, K = 120, Cl = 48.15

Combining this with our knowledge of how much these components typically vary (expressed as width of the reference range, where available):
\([Na^+]_{ow} = \) 10 mEq/L
\([K^+]_{ow} = \) 1.8 mEq/L
\([Cl^+]_{ow} = \) 10 mEq/L
\([Na^+]_{iw} = \) ? mEq/L
\([K^+]_{iw} = \) 45 mEq/L (estimated by using percentages from DD RBCK mean/range)
\([Cl^+]_{iw} = \) ? mEq/L

In the numerator we have variation of:
Na = 0.5, K = 1.8
In the denominator we have variation of:
K = 45, Cl = 4.5

This makes a compelling case for the importance of \([K^+]_i\) in the denominator (remember \(p_{Na}\) is small). Therefore the variation of serum Cl has a small impact.
The numerator is less clear cut. Especially since we don’t know much about \([Cl^-]_i\)

Based on this I conclude it is necessary to look at the other ions to get a good estimate of the actual membrane voltage.
But, for now I think it is reasonable to use potassium only to look at variation (track serum sodium and chloride ongoing to check if this should change).

It may be reasonable to add average values for the other ions in an effort to show a more realistic variation of the membrance voltage with K concentrations.
Try that here.

grd$E_k2 <- 27 * log((p_K * grd$K_o + p_Na*Na_o + p_Cl*Cl_i) /
                       (p_K * grd$K_i + p_Na*Na_i + p_Cl*Cl_o)) # mV

contourplot(E_k2 ~ K_i * K_o, grd, cuts=10,
            main="Resting Membrane Potential Variation Due to Potassium (mV)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)

plot of chunk unnamed-chunk-9

Note the membrane potential values still do not correspond to the true values. Part of this is due to the RBC K mean (90) being different from the neuron \([K^+]_i\) given above as 120.

Also notice the dramatic change in the range of membrane potential values.

For now I think it is appropriate to stick with \(E_k\) as defined above for our metric.

To Follow Up

Investigate circadian variation of serum potassium. Does it correspond to Revici circadian variation?

Potassium Nutrition: In Heart Disease, Rheumatoid Arthritis, Gout, Diabetes, and Metabolic Shock might be worth a look ($4 Kindle)
I think it discusses differing variation in ICF K concentration in RBC and muscle.
Author’s website - this looks a bit crankish, but I suspect there is some valuable information there and in the book.

Test link to Modifying Body Status header