1 Overview

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
Figure 37, 38, and 39 Oral temperature in cancer 84
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
Chapter 2, Note 2 Distribution of Potassium and Sodium 547

Revici classifies potassium as a cellular level element.

1.1 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.
Alternate Link

1.2 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 electrolyte panel.
This reference states that plasma potassium is 0.5 mEq/L lower than serum potassium:
Clinical Methods: The History, Physical, and Laboratory Examinations. 3rd edition - Chapter 195 Serum Potassium

This reference states that plasma potassium is 0.36 +/- 0.18 mmol/L lower than serum potassium:
Errors in Potassium Measurement: A Laboratory Perspective for the Clinician

The whole blood potassium measurement (in this form) is unique to Revici. Details are given in Chapter 4, Note 8. This section gives a range of 20-60 and an average of 38 for whole blood K.
Note that others in the literature use a 1:3 dilution rather than 1:10.

The intracellular potassium can be calculated given Revici’s measurement. See 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

This reference compares central lab electrolyte measurements to blood gas analyzer. It might be useful as a template for how we would compare different RBC K measurement techniques.
Electrolytes assessed by point-of-care testing - Are the values comparable with results obtained from the central laboratory? - DOI 10.4103/0972-5229.78219 downloaded as 10.4103@0972-5229.78219.pdf

1.3 Interpretation

Serum vs Whole Blood K

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. Page 533 has the actual diagnostic criteria:
Dysaerobic - SK > 4.5 and TBK < 38
Anaerobic - SK < 4.2 and TBK > 40

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)

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)

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)

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)

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.

1.4 Modifying Body Status

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

Jeremy Kaslow Potassium information

2 Further Research

2.1 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, since found (see below)

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 - see below

Hypokalemia Physiological Abnormalities During Cardiopulmonary Bypass - full text

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

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

Determination of potassium in red blood cells using unmeasured volumes of whole blood and combined sodium/potassium-selective membrane electrode measurements - an alternate technique for measuring RBC K

Assessing Cell K Physiology in Hypertensive Patients - Full text
Proposes clinical and research methods of evaluation of cell K physiology in essential hypertension.
He has many more K papers at http://www.researchgate.net/profile/Antonio_Delgado-Almeida

Relation of cellular potassium to other mineral ions in hypertension and diabetes - correlates low RBC K with diabetes and hypertension. Downloaded.

The effect of two different protocols of potassium haemodiafiltration on QT dispersion - QT interval in the context of K and dialysis.
Interesting formula for calculation of \(K_{rbc}\) from \(K_s\), $K_{wb}, and hematocrit.
They calculate membrane potential.

The stability of the potassium concentration in the erythrocytes of individual sheep compared with the variability between different sheep - some good observations.

RED-BLOOD-CELL POTASSIUM AND ALDOSTERONISM

The Concentration Dependence of Active Potassium Transport in the Human Red Blood Cell

Aging and Drug Therapy - Discussion of RBC Potassium and Diuretics (pages 317-318)

Preliminary studies on the relationship of red blood cell potassium concentration and performance - in horses. no plasma/RBC K correlation (?!), interesting references

Skeletal Muscle Resting Membrane Potential in Potassium Deficiency

2.2 Articles I was Unable to Find

See updates, many later downloaded

Studies on total body serum and erythrocyte potassium in patients on maintenance haemodialysis The value of erythrocyte potassium as a measure of body potassium - pre/post dialysis numbers for about 25 people, downloaded
Tissue potassium in chronic dialysis patients - different tissues, downloaded
Red-blood-cell potassium and aldosteronism - short, WBK equation, group RBCK measurements (note SDs), downloaded
Sodium, potassium and water contents in red blood cells from healthy persons
Red blood cell content of water, sodium and potassium in body fluid disturbances
Plasma and red blood cell water and solute - “In several instances correction of hyponatremia was associated with increase in RBC potassium concentration”, note correlation (r = 0.73) between plasma Na and RBC K, discusses dry vs. wet RBC weights, downloaded
Ion and water movements in red blood cells
Potassium depletion in aged patients: an evaluation through red-blood-cell potassium determination - 10.1093/ageing/8.3.190 , WB K equation, some interesting case studies, decreased carbohydrate tolerance, downloaded
Red blood cell potassium and blood pressure in adolescents: a mixture analysis - identifies a bimodal distribution for RBCKi, since found at Libgen/ResearchGate
Serum potassium levels, red-blood-cell potassium and alterations of the repolarization phase of electrocardiography in old subjects - looks like a good place to start for QT interval ideas, 10.1093/ageing/13.5.309 , downloaded
Plasma potassium and erythrocyte potassium content in potassium depletion - Unable to find at all, reference from SANGIORGI 1983 above
The relationship of the electrocardiographic pattern of potassium depletion to the concentration of potassium in red blood cells
Internal potassium balance and the control of the plasma potassium concentration
Serum potassium levels predict blood pressure response to aldosterone antagonists in resistant hypertension - downloaded
High and low serum potassium associated with cardiovascular events in diuretic-treated patients
Factors influencing serum potassium in treated hypertension
Sodium and Potassium in the Pathogenesis of Hypertension - good NEJM review. Downloaded pdf
What is the initial work-up in the diagnosis of hypertension? - see printout
Hypertension in the Elderly

Blood Pressure and Serum Potassium Levels in Hypertensive Patients Receiving or Not Receiving Antihypertensive Treatment - see download
Effects on blood pressure of reduced dietary sodium and the Dietary Approaches to Stop Hypertension (DASH) diet - see download
Blood pressure and plasma sodium and potassium - no download, notice effect sizes and K:sex interaction
An investigation of the relationship between the concentration of sodium and potassium in erythrocytes and plasma and blood pressure in 270 normal children and adolescents in Wuhan - see download
Serum sodium, potassium, calcium and magnesium and blood pressure in a Dutch population - found Ca most important, no download
Relation of 24-h ambulatory blood pressure with plasma potassium in essential hypertension - see download
Serum potassium is not associated with blood pressure tracking in the Framingham Heart Study - interesting negative result, would like to try reanalyzing data with different methods, see genetics references, see download
Evidence for a gene influencing blood pressure on chromosome 17 - cited by >100 papers, see download
http://snpedia.com/index.php/Blood_pressure

Red blood cell sodium and potassium concentration and blood pressure. The Gubbio Population Study - see download, note gender/age differences

Potassium depletion decreases the number of 3H-ouabain binding sites and the active Na-K transport in skeletal muscle - see download, difference in rate of K depletion in RBC and muscle

2.3 To investigate

Plasma and Red Blood Cell Water and Solute

The Linus Pauling Institute page on potassium is interesting: http://lpi.oregonstate.edu/mic/minerals/potassium
Some notes on potassium: http://hkpp.org/patients/potassium-health

Associations between serum potassium and sodium levels and risk of hypertension: a community-based cohort study - risk with increased serum K ?!

Also see 10/21/14 email “Distribution of RBC and serum K in the population”

LEUCOCYTE ELECTROLYTES IN CARDIAC AND NON-CARDIAC PATIENTS RECEIVING DIURETICS - Notice this is WBC, not RBC. Plot Excel spreadsheet in R (also see PotassiumData.Rmd).

library(car)
## Warning: package 'car' was built under R version 3.2.3
Kdata <- read.csv("Lancet1974.csv")
#kable(Kdata, row.names=FALSE)
scatterplot(K_p ~ K_wbc | Group, data=Kdata, smooth=FALSE, reg.line=FALSE,
            id.n=nrow(Kdata), xlab="WBC K (mEq/L)", ylab="Plasma K (mEq/L)")
##  1 19 29  2 20 30  3 21 31  4 22 32  5 23 33  6 24  7 25  8 26  9 27 10 28 
##  1  1  1  2  2  2  3  3  3  4  4  4  5  5  5  6  6  7  7  8  8  9  9 10 10 
## 11 12 13 14 15 16 17 18 
## 11 12 13 14 15 16 17 18
K_p <- seq(2.7, 5.4, 0.1)
K_wbc <- seq(60, 195, 5)
grd1 <- expand.grid(K_wbc, K_p)
colnames(grd1) <- c("K_wbc", "K_p")
grd1$E_k <- -27 * log(grd1$K_wbc / grd1$K_p) # mV

contourplot(E_k ~ K_wbc * K_p, grd1, cuts=10,
            main="Resting Membrane Potential Due to Potassium (mV)",
            xlab="WBC K (mEq/L)", ylab="Plasma K (mEq/L)",
            xlim=c(64,195), ylim=c(2.7,5.3),
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.2,lty=2)
              panel.abline(v=128,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(Kdata$K_wbc, Kdata$K_p, pch=19, col=Kdata$Group))
ltext(Kdata$K_wbc, Kdata$K_p, labels=Kdata$Patient_number, adj=c(0,0))
trellis.unfocus()

Comparison of the change in the red cell potassium content with the total body balance of potassium during potassium therapy - no pdf, may be useful to correlate RBC with total body

Assessment of body potassium stores

A comparison of leucocyte potassium content with other measurements in potassium depleted rabbits

Changes in erythrocyte contents of potassium, sodium and magnesium and Na, K-pump activity after the administration of potassium and magnesium salts - different effects for different types of K supplementation. Use K-Mg citrate? Downloaded from http://www.bmbmd.research.chula.ac.th/pdf/9.pdf .

2.4 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. downloaded

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

This analysis provides an example of working with a small serum and WBC K dataset.

2.5 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. Also see the more accurate equation which accounts for plasma K.

Updated version from the summary:
Assuming the influence of the serum K on the total blood K is neglible we can estimate the intracellular K from \(K_{TB} = K_{RBC} \cdot Hematocrit\) giving us \(K_{RBC} = K_{TB} \div Hematocrit\) for a typical RBC value of 90.5 corresponding to Revici’s typical total blood value of 38 (given an estimated hematocrit of 42%). This corresponds well with the \(K_{RBC}\) normal values seen (~90).

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.

2.6 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.

2.7 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

Race and sex differences in erythrocyte Na+, K+, and Na+-K+-adenosine triphosphatase - race and sex differences, downloaded

Sex difference in human erythrocyte potassium levels - women higher. downloaded

Seasonal changes in serum and erythrocyte potassium among renal stone formers from northeastern Thailand - no pdf

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
Female mean 4.088, male mean 4.213

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

2.8 Hypothetical Circadian Rhythm Plots

Assume a serum potassium varying as described by a modified version of the equation above and RBC potassium at constant selected values. The idea is to get an idea of the magnitude of the variation. The min/max times don’t seem to match Revici?

example1 <- data.frame(RBC_K=90, time=0:24)
example1$K <- 4.2  + 0.18 * cos(2*pi/24*(example1$time - 10))
example1$E_k <- -27 * log(example1$RBC_K / example1$K) # mV

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(example1$RBC_K, example1$K, pch=19))
#ltext(caseStudy$RBC_K, caseStudy$K, labels=caseStudy$test_date)
trellis.unfocus()
plot(example1$time, example1$E_k)

We see E_k varying between -83.9, -81.6

2.9 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))

# Include more recent data
caseStudy <- rbind.fill(caseStudy,
                   data.frame(test_date=as.Date(c("2014-12-26"), tz="PST"),
                              RBC_K=c(87),
                              K=c(4.5)))

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
## 1  26108 2011-10-12 4.60    77 16.73913   2.817749  78.8   -80 2220.4
## 3  26972 2012-05-01 4.20    79 18.80952   2.934363 117.0   -45 2270.8
## 4  26973 2012-07-27 4.50    87 19.33333   2.961831 117.0   -30 2499.0
## 2  26536 2012-10-15 4.40    84 19.09091   2.949212 153.8   -30 2413.6
## 5  26974 2012-12-05 4.50   100 22.22222   3.101093 156.6   -30 2863.0
## 6  26975 2013-01-25 5.00    88 17.60000   2.867899 117.0   -30 2534.0
## 8      1 2013-03-20 4.35    87       NA         NA    NA    NA 2496.9
## 9      2 2013-06-01 4.10    80       NA         NA    NA    NA 2297.4
## 7  26976 2013-09-12 4.30    89 20.69767   3.030021 105.4   -90 2552.2
## 10     3 2013-11-25 4.10    86       NA         NA    NA    NA 2465.4
## 11    NA 2014-12-26 4.50    87       NA         NA    NA    NA 2499.0
##          E_k
## 1  -76.07923
## 3  -79.22781
## 4  -79.96943
## 2  -79.62873
## 5  -83.72951
## 6  -77.43327
## 8  -80.88477
## 9  -80.21807
## 7  -81.81058
## 10 -82.17073
## 11 -79.96943
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$test_date)
trellis.unfocus()
contourplot(E_k ~ K_i * K_o, grd, cuts=10,
            main="Resting Membrane Potential Due to Potassium (mV)",
            xlab="Intracellular K (mmol/L)",
            ylab="Extracellular K (mmol/L)",
            xlim=c(74,103), ylim=c(4.05,5.05),
            panel = function(...) {
              panel.contourplot(...)
              panel.abline(h=4.5,lty=2)
              panel.abline(v=90,lty=2)
            }, 
            colorkey = FALSE, region = TRUE)
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(caseStudy$RBC_K, caseStudy$K, pch=19))
ltext(caseStudy$RBC_K, caseStudy$K, labels=caseStudy$test_date)
trellis.unfocus()
range(caseStudy$K_tot)
## [1] 2220.4 2863.0
range(caseStudy$E_k)
## [1] -83.72951 -76.07923

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?

Why is this failing now? Disable.

# 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"
     ,xlim=range(caseStudyO$test_date) # Why did this matter?
     )
# plot.ts(caseStudyO$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"))
#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"))
#par(opar)

Plot Total Body Potassium and Membrane Voltage by Date as a 2D scatterplot with date labels as done for serum/RBC K above.

xyplot(E_k ~ K_tot, caseStudy,
       main="Membrane Voltage vs Total Body Potassium",
       xlab="Total Body Potassium (mmol)",
       ylab="Membrane Voltage (mV)",
       #xlim=c(74,103), ylim=c(4.05,5.05)
       )
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(caseStudy$K_tot, caseStudy$E_k, pch=19))
ltext(caseStudy$K_tot, caseStudy$E_k, labels=caseStudy$test_date)
trellis.unfocus()

And with a line connecting the points by time order (sort first).

xyplot(E_k ~ K_tot, caseStudy[order(caseStudy$test_date),], type="l",
       main="Membrane Voltage vs Total Body Potassium",
       xlab="Total Body Potassium (mmol)",
       ylab="Membrane Voltage (mV)",
       #xlim=c(74,103), ylim=c(4.05,5.05)
       )
trellis.focus("panel", 1, 1, highlight=FALSE)
invisible(lpoints(caseStudy$K_tot, caseStudy$E_k, pch=19))
ltext(caseStudy$K_tot, caseStudy$E_k, labels=caseStudy$test_date)
trellis.unfocus()

2.10 Plotting Data Over Time

There are some explorations of this for the 2D case above. Here are some additional ideas (especially for >2D).

Scatter plot matrix with panels of points labeled and connected by time (as above).

Heat maps of test values by time. These can also be clustered (I have examples elsewhere).

2.11 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

2.13 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)

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.

2.15 Potassium and Reaction Time

Investigate the possibility that serum/RBC K influence reaction time by changing nerve conduction velocity. I’m surprised that most of the research below ignores intracellular K.

Mathematical Simulation of Slowing of Cardiac Conduction Velocity by Elevated Extracellular K+ in a Human Atrial Strand - see download
Nerve conduction velocity in man: influence of glucose, somatostatin and electrolytes (<U+FFFD>rskov et al. 1994) - see download, discusses effect of glucose on Na, L, and more
Neuromuscular Disorders in Clinical Practice - page 696, reference 32 might be interesting (not sure if below is related)
Potassium and the excitability properties of normal human motor axons in vivo (Bo<U+00EB>rio et al. 2014) - good discussion and looks like it references most of papers cited by book above. Porphyria reference looks intriguing
Has potassium been prematurely discarded as a contributing factor to the development of uraemic neuropathy? (H. Bostock et al. 2004) - interesting discussion of K and membrane potential

(Sunyer 2005)

2.16 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.

Interesting link at Cell Membrane Potentials

Next few from http://charles_w.tripod.com/arthritis3.html
The relationship between uric acid and potassium in normal subjects - correlates various potassium measures (plasma, total body, total RBC, etc.), total body uric acid correlated 0.84 with TBK
The prediction of muscle potassium from blood electrolytes in potassium depleted rats - unable to find

Effect of prolonged physical exercise on intra-erythrocyte and plasma potassium- could this explain dysaerobic/anaerobic response to exercise? Also see how much aldosterone changed during marathon. downloaded.

Method for the Diagnosis and Treatment of Conditions Involving Aberrant Erythrocyte Potassium Levels- patent by Antonio Delgado Almeida

Serum and intracellular levels of ionized sodium, potassium, and magnesium in type 2 diabetic subjects - Numbers differ about 4mV for T2D (dysaerobic). no pdf. 10.4103/2231-0738.153796 , see printout, interesting glucose/electrolyte correlations for diabetics

Mitochondrial Membrane Potential: A Novel Biomarker of Oxidative Environmental Stress - downloaded

Evaluating the validity of blood-based membrane potential changes for the identification of bipolar disorder I (Thiruvengadam and Chandrasekaran 2007) - see Thiruvengadam below, downloaded

Leukocyte transmembrane potential in bipolar illness- downloaded [The Na,K-ATPase hypothesis for bipolar illness](http://www.ncbi.nlm.nih.gov/pubmed/77[@El_Mallakh_1995]1-d") - figure 1 relating membrane potential and mood is interesting. downloaded
Figure 1

Erythrocyte membrane sodium potassium adenosine triphosphatase activity in affective disorders. - downloaded
Meta-analysis of erythrocyte Na,K-ATPase activity in bipolar illness - downloaded
Intraerythrocyte sodium and potassium in manic-depressive illness - no pdf

Mineral metabolism, mania, and melancholia- downloaded. See related citations. *Note discussion of membrane potential and K ratio!* also useful discussion of NA and ICW/ECW [The Body Cell Mass and its Supporting Environment](http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1515383/) - book review for book containing some of the data above. [Worldcat - Stanford and UCSF have copies](https://www.worldcat.org/title/body-cell-mass-and-its-supporting-environment-body-composition-in-health-and-disease/oclc/1241711&referer=brief_results) [Studies of electrolyte changes](http://bjp.rcpsych.org/content/119/548[@SHAW_1971]114") - downloaded
Changes in erythrocyte sodium and potassium on recovery from a depressive illness- downloaded [Potassium and Water Distribution in Depression](http://bjp.rcpsych.org/content/112/484[@SHAW_1966]269") - has Kin and Kout data, downloaded
Changes in Sodium, Potassium and Body Fluid Spaces in Depression and Dementia- downloaded [Mineral Metabolism in Affective Disorders](http://bjp.rcpsych.org/content/111/481/1133.full-text.pdf+[@COPPEN_1965]133") (aka Coppen, 1965) - downloaded
Mineral metabolism in mania` (aka Coppen, 1966) - downloaded
Mineral Metabolism in Melancholia - downloaded
DM Shaw?

A novel membrane potential-sensitive fluorescent dye improves cell-based assays for ion channels` - on libgen but unable to download?

Effect of lithium and sodium valproate ions on resting membrane potentials in neurons: an hypothesis` - interesting speculation (hyperpolarization and bipolar). Downloaded. Mentions “Krupp, M.A., Sweet, N.J. et al., 1997. Physicians Handbook. Lange Medical Publications, Los Altos, CA.” as a source of K data (also Coppen 1966).
Figure 3

Deficient erythrocyte NaK-ATPase activity in different affective states in bipolar affective disorder and normalization by lithium therapy

Comparative study of erythrocyte and muscle potassium - no pdf. In German. Also see
Electrolyte changes in the plasma, erythrocytes, and in the skeletal muscle in patients with chronic liver diseases - no pdf. In Czech.
Correlation between concentrations of magnesium, zinc, and potassium in plasma, erythrocytes and muscles - Has both whole blood and RBC K measurements. downloaded
Table IV Human cardiac muscle magnesium and potassium concentrations: can skeletal muscle, mononuclear blood cells, erythrocyte and plasma concentrations provide a surrogate measure` - RBC K not useful? downloaded
The relation between extra- and intracellular electrolytes in patients with hypokalemia and/or diuretic treatment - downloaded
Resting transmembrane potential difference of skeletal muscle in normal subjects and severely ill patients - differences due to Na not K! interesting discussion and figure 4, in table IV what gives charge balance if both Na and K are high? notice SDs, downloaded
Skeletal muscle resting membrane potential in potassium deficiency - rat and dog, downloaded (also above?)

Study of membrane potential in T lymphocytes subpopulations using flow cytometry` - downloaded

2.17 Body Water

Interrelations Between Total Exchangeable Sodium, Potassium, Body Water, and Serum Sodium and Potassium Concentrations in Hyponatremic and Normonatremic Heart Disease - downloaded

Relationship between red cell volume, body cell mass, and serum potassium in potassium deficiency - See figure for correlations between RBC/serum/muscle K. downloaded
Figure 1 Figure 2 Their scatter plots give perhaps the best idea I have of a typical serum/RBC K correspondence.
I wish I had their raw data since it looks like there are data points missing in some of the debilitated plots (high in both serum and RBC K). Unlikely to find data since the paper was from 1969 and it looks like the lead author passed away some time ago: http://www.rosalindfranklin.edu/cms/Surgery/WilliamSchumer.aspx

2.19 Aging and Drug Therapy (book)

This book has some interesting material on RBC Potassium. One of the editors (and lead author of the most relevant chapter) is Italian. Given this and the Gubbio Study is there more interest in RBC K in the Italian research community than elsewhere?

Google Books
Amazon

I purchased a copy from BWB June 2015.

Two chapters look most relevant to the Potassium work.

2.19.1 Disorders of Fluid and Electrolyte Metabolism in the Elderly

DOI: 10.1007/978-1-4613-2791-2_15, has references!

Pages 155-174. The author is A. Borghetti and he (?) is also Italian. I believe this is the appropriate Pubmed author search
The book was published in 1984 and here is a paper from 1986: Altered Cellular Calcium Control in Blood Cells in Primary Hypertension

I believe this is the author: Alberico Borghetti

Pages 158-159 (not available in Google Book preview) discuss potassium physiology.

There is discussion of the inadequacy of plasma K as an indicator of K status.

Figure 3 provides a nomogram relating serum K to K % depletion or excess at various pH. This graphic is from reference 2
Interpretation of the serum potassium concentration
This is one of six papers by the lead author concerning potassium
These two papers are freely available:
The effect in humans of extracellular pH change on the relationship between serum potassium concentration and intracellular potassium
The effect of acute respiratory acidosis on the internal equilibrium of potassium - experiments on dogs, discussion of Ke/Ki ratio changing in acidosis
I was unable to find these papers:
Interpretation of the serum potassium concentration in patients with acid-base imbalance
Failure of change in extracellular volume to alter plasma potassium concentration
Serum potassium concentration as a guide to potassium need

Figure 4 and Table 2 describe the variation of muscle magnesium with plasma and muscle potassium. This is from reference 4 which is a French paper I have been unable to find (1979, lead author A. Montanari, A. Birghetti is a coauthor): Effets du potassium et des proteines cellulaires sur le magnesium musculaire chez des patients atteints de troubles hydro-electrolytiques
The bottom line is they recommend supplementing Mg with K for K deficiency.

There is some discussion of potassium variation with age. Figure 11 on page 166 is modified from
Average potassium concentration of the human body as a function of age
Some more references
Total-body potassium in health: effects of age, sex, height, and fat
Water and electrolyte content of human skeletal muscle. Variations with age

Pages 171-173 (not available in Google Book preview) discuss potassium disorders.
Some discussion of hypo/hyperkalemia treatment.

I was unable to find reference 18 (which appears to discuss effects of Ke/Ki ratio changes):
Rhabdomyolysis and effects of potassium deficiency on muscle structure and function
but here are some other papers by the author:
On the mechanism of rhabdomyolysis in potassium depletion - dog experiments, freely available
Diuretic-induced hypokalemia

Chapter references are on pages 173-174.

2.19.2 Diuretic Therapy in Old Patients

DOI: 10.1007/978-1-4613-2791-2_26, has references!

Pages 311-325. The lead author is G. Barbagallo Sangiorgi (Italian book co-editor). I believe this is the appropriate Pubmed author search
One of his papers is mentioned above: Serum potassium levels, red-blood-cell potassium and alterations of the repolarization phase of electrocardiography in old subjects

I believe this is the author: Giuseppe Barbagallo Sangiorgi

Table 1 on page 316 has a good list of ECG changes related to potassium depletion.

Discussion of potassium depletion on pages 316-318.
Total body K in hypertensive patients during prolonged diuretic therapy - “On average a fall of 1 meq. per litre in plasma-potassium concentration was associated with a reduction of about 20% in the total-body potassium, but there was considerable variation. When the plasma-potassium concentration was 3·5 meq. per litre or more, the total-body potassium was not usually reduced by more than 10%.”
22 Total body and serum K during prolonged thiazide therapy for essential hypertension - downloaded, title actually potassium not K?
Body sodium and potassium; inter-related trends in alimentary, renal and cardiovascular disease; lack of correlation between body stores and plasma concentration
Serum-potassium levels as an index of body content
Effect of disease on erythrocyte and plasma potassium concentrations

They focus on RBC K with a discussion on pages 317-318. Quite a few references are given.
Red-blood-cell potassium as a practical index of potassium status in elderly patients
Red-blood-cell potassium and hand-grip strength in healthy elderly people - 10.1093/ageing/5.2.116, no correlation, downloaded as 10.1093@ageing@5.2.116.pdf , note figure 1 normal dist, but many exclusions
37: Potassium depletion in aged patients: an evaluation through red-blood-cell potassium determination - downloaded
The partition of potassium between the serum and corpuscles in health and disease - 1934
Red blood cell potassium as a measure of body potassium in thiazide-treated patients with essential hyper tension
Down with plastma: Intracellular chemical pathology studies by autoanalysis of cells of solid tissues, erythrocytes and leucocytes - downloaded
A comparison of leucocyte potassium content with other measurements in potassium-depleted rabbits
Studies on total body serum and erythrocyte potassium in patients on maintenance haemodialysis. The value of erythrocyte potassium status in elderly patients - http://dx.doi.org/10.1159/000179825
Sodium and potassium movements in human red cells - downloaded, shows glucose dependence
The permeability of human erythrocytes to sodium and potassium
Are potassium supplements for the elderly necessary? - also http://ageing.oxfordjournals.org/content/7/3/165

Unable to find
47: Aspetti di farmacoterapia cardiologica nell’anziano

22, 37, and 47 are their work and I wish I could find those papers.

Potassium and decreased carbohydrate tolerance discussed on page 318
Glycogen, glucose tolerance and tissue metabolism in potassium-deficient rats - downloaded, interesting rat glucose tolerance curve
Effect of potassium deficiency on carbohydrate metabolism
Glucose tolerance and insulin responsiveness in experimental potassium depletion
Hypertension, the potassium ion and impaired carbohydrate tolerance
Also note unpublished data from 37 mentioned.

Chapter references are on pages 321-324.

Lord & Bralley discussion of Potassium in Laboratory Evaluations for Integrative and Functional Medicine - includes potassium repletion dosing
also see references ~261-276. Check out Michael’s copy?

Is red-cell potassium a prognostic indicator? - see more below

Potassium and magnesium depletion in patients with cirrhosis on maintenance diuretic regimens

Our present knowledge of potassium in physiological and pathological processes - downloaded

2.20 Role of Potassium in Preventive Cardiovascular Medicine (book)

This book looks highly relevant to Potassium work. Ordered a copy from Amazon/BWB June 2015.
Google Books
Amazon

Expand this section once I have the book.

3 Alagu Thiruvengadam

Alagu Thiruvengadam has done substantial work with membrane potential in the context of Bipolar Disorder (BD) and Attention Deficit Hyperactivity Disorder (ADHD) and is working on creating a testing product through his company PsychNostics.

This work addresses membrane potential through a different approach. Rather than using intracellular and extracellular potassium to compute membrane potential they directly measure membrane potential with a fluorescent dye.

3.2 Books

Focus on Bipolar Disorder Research - Google Books excerpt
“the membrane potential would depolarize with the addition of lithium”

3.4 PsychNostics

Medical diagnostics company in Maryland. Website: http://psychnostics.com/

Appears to be related to (same address) Free State Diagnostics which is the assignee for the earlier patents.
Also see:
http://www.marylandcorporates.com/corp/363993.html
http://patents.justia.com/assignee/free-state-diagnostics-llc

Membrane Potential Ratio (MPR™) Test for BD and ADHD
Note the statement that they have investigated both WBC and RBC membrane potential.

4 More Papers July 14, 2015

Added here to avoid disturbing line numbers of diffs above.

Red Blood Cell Potassium Therapeutic Implications - Uses hematocrit to estimate \(K_W\), good references, downloaded
> Krbc was quite variable and even in the same patients values of 82 and 99 mEq/liter were found on successive days. No correlation was found between simultaneous KRBc and Ks.

Notes on the determination and distribution of sodium and potassium in cells and serum of normal human blood - 8 complete sets of measurements on page 432, downloaded

Equilibration of Potassium in Blood and Tissues - good discussion of distribution of potassium in the body (see Table 1), downloaded

References from Role of Potassium in Preventive Cardiovascular Medicine - page 53 “long-term hypokalemia is associated with depolarization of the membrane potential of skeletal muscle cells from the usual resting level of -86 mV to -50 to -55 mY”, downloaded book and have paper copy
A comparative and regional study of potassium induced relaxation in vascular smooth muscle - downloaded
Cell potential and the sodium-potassium pump in vascular smooth muscle - not found, reference 159 from Preventive Cardiology looked interesting
Heart Cell Communication in Health and Disease - downloaded
Basic Cardiac Electrophysiology for the Clinician- downloaded
Above led to Cardiac pacemaker potentials at different extra- and intracellular K concentration (downloaded) and The effect of extracellular potassium on the intracellular potassium ion activity and transmembrane potentials of beating canine cardiac Purkinje fibers (downloaded)
Physiology and Pharmacology of the Heart - not found, only $4
Potassium and ventricular arrhythmias - good table of effects (e.g. on EKG), downloaded
Diuretics, serum and intracellular electrolyte levels, and arrhythmias in hypertensive men
Potassium: Its Biologic Significance - in particular see “Extra- and intracellular potassium and magnesium. diuretics. and arrhythmias”, other books in series for Sodium and Magnesium

Analysis of human serum and whole blood for mineral content by ICP-MS and ICP-OES: development of a mineralomics method` - downloaded as nihms603989.pdf
metallomics and minearlomics look like useful search terms
Also see supplmental material (intraday results) in NIHMS603989-supplement-12011_2014_33_MOESM1_ESM.pdf

The influence of the metabolism of human erythrocytes on their potassium content - 1941, downloaded as 10.0000@www.jbc.org@141@2@579.pdf

Magnesium, Potassium and Zinc Deficiency in Subjects with Type II Diabetes Mellitus - downloaded as 10.0000@www.researchgate.net@19954312.pdf
Note difference between behavior of K in RBC vs. skeletal muscle in T2DM!

Magnesium and potassium status in healthy subjects as assessed by analysis of magnesium and potassium in skeletal muscle biopsies and magnesium in mononuclear cells

Intra-erythrocyte cation concentrations in relation to the C1797T b-adducin polymorphism in a general population - downloaded as 07-09-P.pdf
Some RBC K distribution information.

Sex difference in human erythrocyte potassium levels - downloaded as 10.1038@icb.1981.31.pdf brief

Studies on erythrocyte magnesium and potassium levels in childhood schizophrenia and growth

Potassium, RBC, Quest Test Code 128241

Advanced Therapy In Hypertension And Vascular Disease - Delgado pp.291-296
See downloaded CV Curriculum Vitae of Antonio Delgado-Almeida.pdf

Basis for a Major Genetic Alteration in Essential Hypertension: Inherited Defect in RBC-K Function and Oxygen transport - Downloaded as Bases for a Major Genetic Defect in Essential Hypertension_Online Poster Circulation 2013.ppt

Improving RBC K Transport and Hemoglobin-O2 Binding by Amiloride: A Novel Therapeutic Approach for Reversion of Angina and Myocardial Ischemia in Coronary Heart Diseases - downloaded as art00010.pdf

Improving red blood cell K-uptake and its impact on O(2)/CO(2) exchange, and NO-generation in microvascular CHD: a novel therapeutic approach - downloaded as 10.0000@www.researchgate.net@46577058.pdf 10.2174/157489012803832801

Effect of increased potassium intake on cardiovascular risk factors and disease: systematic review and meta-analyses downloaded as bmj.f1378.full.pdf
See Delgado response Re: Effect of increased potassium intake on cardiovascular risk factors and disease: systematic review and meta-analyses - downloaded as Low Potassium Intake or Impaired Potassium Uptake_BMJ 24, April 2013.doc

Intracellular Potassium or Intramolecular Potassium-binding and Dependent Function. TM’s 2nd world drug discovery online conference downloaded as Intracellular Vs Intramolecular Potassium_2nd World drug discovery Conference(1)_2012.ppt
Good overview of his work.

An Integrated View of Potassium Homeostasis - downloaded as 10.1056@nejmra1313341.pdf

Narrative Review: Evolving Concepts in Potassium Homeostasis and Hypokalemia - downloaded as greenlee.pdf

Intracellular Potassium: New Concept on the Physiology and Pathophysiology of Potassium - Delgado-Almeida 1986 thesis. From his CV (ask him for copy?):
QV277D4533, 1986: 1-71. Health Science Central Library, University of Carabobo (Spanish)

http://www.snpedia.com/index.php/Rs5443
Association of GNB3 C825T polymorphism with plasma electrolyte balance and susceptibility to hypertension

Textbook of Natural Medicine - Potassium - page 203 (in my 2e pp. 213-214)
Good short overview. Has references (already above, but some I have not found full paper)

Is red-cell potassium a prognostic indicator? - downloaded as chp%3A10.1007%2F978-94-009-8048-8_36.pdf, brief chapter in context of cardiac bypass from book Towards Safer Cardiac Surgery

Red-blood-cell potassium as a practical index of potassium status in elderly patients - haven’t been able to find this, looks like a good reference. todo
Pay download available at http://ageing.oxfordjournals.org/content/5/1/24.abstract
Was able to find usin(BAHEMUKA and HODKINSON 1976).24“)` Downloaded as bahemuka1976 practical.pdf
Worth spending more time on its references.
They measure RBCK from whole blood K (3x dilute), serum K, and hematocrit with a detailed methods section.
The 140 normal patients had a RBCK of 99.7 ? 4.0 mmol/1 of red cells giving a 95 percent range of 91.7-107.6 mmol/1. Serum potassium was 4.1 ? 0.5 mmol/1 and showed no significant correlation with RBCK (r = 0.063).
They also give results for treatment with Digitalis and/or diuretics (+ K supp), and ‘abnormals’ with K depletion.
Table IV compares different methods for RBC K measurement in literature.

Red Blood Cell Potassium Therapeutic Implications, the pubmed link shows three papers citing this. Was able to find usin(Singer et al. 1964)007“)` Downloaded as 10.1001@jama.1964.03060140030007.pdf
it seems that the KRKC changes occur slowly. A probable explanation is that the red blood cell fining does not act as a simple semipermeable membrane. It has been previously reported that, when exogenous potassium is added to serum, at least 48 hours are required for it to appear in the red cell.20 (ref below)
KRBc concentration must be influenced by multiple factors and its value as an indicator of intracellular potassium is limited to certain and more stable circumstances. KRBc may possibly be of great importance in chronic diseases or treatment in which early detection of adverse changes in body potassium is necessary, as well as in states of abnormal acid-base balance where the serum potassium values can be distorted.

2 The relationship of the electrocardiographic pattern of potassium depletion to the concentration of potassium in red blood cells` - can’t find PDF (even with DOI)
Microfilm at SJSU?
Notice intriguing statement in preview concerning reference 9 by Kuhns and the ratio of intracellular to extracellular potassium. Turns out this is in German. See below.

3 Effect of disease on erythrocyte and plasma potassium concentrations` - can’t find PDF (even with DOI) See also

Internal potassium balance and the control of the plasma potassium concentration

20 The permeability of human erythrocytes to sodium and potassium - downloaded as J Gen Physiol-1952-Solomon-57-110.pdf
54 page paper. See Table III for some plasma/RBC K measurements.

POTASSIUM TRANSPORT IN HUMAN ERYTHROCYTES: EVIDENCE FOR A THREE COMPARTMENT SYSTEM - downloaded as 10.1085@jgp.38.3.371.pdf

Red Cell Membrane Transport in Health and Disease - 10.1007/978-3-662-05181-8
downloaded as [Cees_W._M._Haest__(auth.),__Professor_Dr.Ingolf(BookZZ.org).pdf
700+ page book!
page 592 genetics, hypertension , and membrane transport - Na+-K+-2Cl cotransporter NKCC1/2

Dietary Potassium Intake and Grip Strength in Older People - downloaded as 10.1159@000245343.pdf
Hypokalaemia in the Elderly - DOI 10.1159/000245172 no pdf

The relation of total body potassium to height, weight, and age in normal adults - downloaded as J Clin Pathol-1972-Boddy-512-7.pdf data for 50 each M/F

The effect of hypokalaemia and of Digoxin therapy on red cell sodium and potassium content (some clinical aspects) - DOI 10.3109/00365517409114191, downloaded as 10.3109@00365517409114191.pdf

Statistical Investigation of Correlations Between Serum Potassium Levels and Electrocardiographic Findings in Patients on Intermittent Hemodialysis Therapy - downloaded as Circulation-1970-FROHNERT-667-76.pdf DOI 10.1161/01.CIR.41.4.667
Prefers serum to intracellular (tested both).
Gives regression equations for electrocardiograph variables on serum potassium.
Some references looking at the K ratio follow (was unable to followup on any of them).
“Although evidence has accumulated that hypokalemic ECG changes correlate better with the ratio of intracellular to extracellular potassium,29-31 hyperkalemic ECG patterns seem to be related well to serum potassium level alone.”

29 KUHNs K: uber den Einfluss des Kalium-Ions auf
Elektrokardiogramm und Herzsystolendauer. Z
Kreislaufforsch 44: 4, 1955
Effect of potassium ion on electrocardiogram and on duration of cardiac systole (Pubmed translation)
Klaus Kuhns’ thesis (German)
What about this book? http://www.amazon.de/Die-St%C3%B6rungen-Wasser-Elektrolytstoffwechsels-Schwab/dp/toc/B0000BNMQT
What about Extra, intracellular potassium levels, blood pressure and ECG (translated from German) - DOI 10.1007/BF02119985 downloaded as 10.1007@bf02119985.pdf page 6 interesting plot of pH vs. K page 27 English summary, on dogs, no intracellular?, cites Kuhns

30 Electrocardiographic changes related to disturbances in potassium metabolism - Lancet 1953 by Burchell, but can’t find. 1953 Jun;73(6):235-8
Is this actually the Minnesota The Journal-lancet?
Worldcat claims SJPL has.
Looks like SJPL collection is incomplete: http://catalog.sjlibrary.org/record=b1529556~S1
UCSF seems to have http://ucsfcat.library.ucsf.edu/record=b1198039~S0 Hathi Trust has pre-1923 online

31 Removal of excess body potassium by hemodialysis - Worldcat claims UCSC, SJPL (microfilm), and UCSF have.

Intra- and Extracellular Potassium Activities, Acetylcholine and Resting Potential in Guinea Pig Atria - downloaded as Circulation Research-1984-Baumgarten-65-73.pdf discussion of Ek and relation to membrane potential.

Effects of Potassium on Blood Pressure Regulation - DOI 10.1097/00005344-198400061-00035 no pdf, negative result but discusses intraleukocytic concentration of potassium

Internal Potassium Balance and the Control of the Plasma Potassium Concentration - DOI 10.1097/00005792-198109000-00002 no pdf

Adrenergic Control of Serum Potassium - DOI 10.1056/NEJM198312083092308 downloaded as 10.1056@nejm198312083092308.pdf

Regulation of Potassium Homeostasis - downloaded as CJN.08580813.full.pdf review article

Hypertension, the Potassium Ion and Impaired Carbohydrate Tolerance - DOI 10.1056/NEJM196511182732106 Downloaded as 10.1056@nejm196511182732106.pdf

Hemoglobin A1c: Hemoglobin Risk Factor or Biomarker of Erythrocyte Function - Antonio Rafael Delgado- Almeida, downloaded as Replies to Hemoglobin A1c Is Associated With Increased Risk of Incident Coronary Heart Disease Among Apparently Healthy, Nondiabetic Men and Women.pdf
also Hemoglobin A1c_Hemoglobin Fraction or Biomarker of Erythrocyte Function_June 11, 2013.pdf

Introduction to DynaPulse Technology in Clinical Practice: From Riva-Rocci Concept to the Noninvasive Central Aortic and Cardiovascular Hemodynamics - downloaded as Introduction to DynaPulse Technology in Clinical Practice.Feb. 6, 2013.ppt
Antonio R. Delgado-Almeida

RBC-K dependent ATP synthesis and O2% saturation might prevent and reverse contrast induced nephropathy_April 30, 2015.doc - downloaded as RBC-K dependent ATP synthesis and O2% saturation might prevent and reverse contrast induced nephropathy_April 30, 2015.doc

Assessing Cell K Physiology in Hypertensive Patients: A New Clinical and Methodologic Approach - DOI 10.1016/j.amjhyper.2005.09.013 downloaded as 10.1016@j.amjhyper.2005.09.013.pdf

ASSESSMENT OF CELL K PHYSIOLOGY IN THE CLINICAL LABORATORY AND PRACTICE -

Reinterpreting sodium-potassium data in salt-sensitivity hypertension: a prospective debate - DOI 10.1161/01.HYP.0000154194.49725.b7 downloaded as 10.1161@01.HYP.0000154194.49725.b7.pdf

JACC Assessment of Potassium Homeostasis and Vascular Function in the Management of Essential Hypertension -

Red blood cell K+ could be a marker of K+ changes in other cells involved in blood pressure regulation - DOI 10.1038/sj.jhh.1001527 downloaded as 10.1038@sj.jhh.1001527.pdf
Has both plasma and RBC K along with BP. Would be interesting to look at membrane potential on this data!

DYSRRHYTHMIAS AND ECG CHANGES IN SEVERE HYPERKALEMIA (HYPERK) AND HYPOKALEMIA (HYPOK): DEPEDENCY ON PLASMA IONIZED CALCIUM (ICA) AND RED BLOOD CELL POTASSIUM (KI) CONTENT - DOI 10.1097/00003246-200212001-00262 no pdf
See preview - looks like RBCK most important for low serum K?
Figure

G009: Early signs of insulin resistance in normotensive offspring of hypertensives with low RBC K content - DOI 10.1016/S0895-7061(99)80211-8 downloaded as 10.1016@s0895-7061(99)80211-8.pdf notice RBCK, plasma K, and glucose correlations; poster session

L007 Low RBC K (Ki): A possible intermediate phenotype for essential hypertension - DOI 10.1016/S0895-7061(97)91430-8 downloaded as 10.1016@s0895-7061(97)91430-8.pdf poster session

G011: Insulin and membrane function of erythrocytes in essential hypertension -an electron paramagnetic resonance investigation - DOI 10.1016/S0895-7061(99)80213-1 downloaded as 10.1016@s0895-7061(99)80213-1.pdf poster (same page as G009 above), membrane fluidity lower in hypertension

Test link to Modifying Body Status header

File originally created: Thursday, August 28, 2014
File kniSun Jan 10 20:08:30 2016ate()`

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Singer, Mark M., H. Richard Hoff, Solomon Fisch, and Arthur C. DeGraff. 1964. “Red Blood Cell Potassium.” JAMA 187 (1). American Medical Association (AMA). doi:10.1001/jama.1964.03060140030007.

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Thiruvengadam, Alagu P., and Krish Chandrasekaran. 2007. “Evaluating the Validity of Blood-Based Membrane Potential Changes for the Identification of Bipolar Disorder I.” Journal of Affective Disorders 100 (1-3). Elsevier BV: 75–82. doi:10.1016/j.jad.2006.09.036.