Effect of Calcium Chloride on Muscle Contraction in Rat Hearts

Description

The purpose of this experiment was to assess the influence of calcium in solution on the contraction of heart muscle in rats. The left auricle of 21 rat hearts was isolated and on several occasions a constant-length strip of tissue was electrically stimulated and dipped into various concentrations of calcium chloride solution, after which the shortening of the strip was accurately measured as the response.

Usage

muscle

Format

This data frame contains the following columns:

Strip

which heart muscle strip was used?

Conc

concentration of calcium chloride solution, in multiples of 2.2 mM.

Length

the change in length (shortening) of the strip, (allegedly) in mm.

Source

Linder, A., Chakravarti, I. M. and Vuagnat, P. (1964) Fitting asymptotic regression curves with different asymptotes. In Contributions to Statistics. Presented to Professor P. C. Mahalanobis on the occasion of his 70th birthday, ed. C. R. Rao, pp. 221–228. Oxford: Pergamon Press.

References

Venables, W. N. and Ripley, B. D. (2002) Modern Applied Statistics with S. Fourth Edition. Springer.

Examples

A <- model.matrix(~ Strip - 1, data=muscle)
rats.nls1 <- nls(log(Length) ~ cbind(A, rho^Conc),
   data = muscle, start = c(rho=0.1), algorithm="plinear")
(B <- coef(rats.nls1))

st <- list(alpha = B[2:22], beta = B[23], rho = B[1])
(rats.nls2 <- nls(log(Length) ~ alpha[Strip] + beta*rho^Conc,
                  data = muscle, start = st))

Muscle <- with(muscle, {
Muscle <- expand.grid(Conc = sort(unique(Conc)), Strip = levels(Strip))
Muscle$Yhat <- predict(rats.nls2, Muscle)
Muscle <- cbind(Muscle, logLength = rep(as.numeric(NA), 126))
ind <- match(paste(Strip, Conc),
            paste(Muscle$Strip, Muscle$Conc))
Muscle$logLength[ind] <- log(Length)
Muscle})

lattice::xyplot(Yhat ~ Conc | Strip, Muscle, as.table = TRUE,
   ylim = range(c(Muscle$Yhat, Muscle$logLength), na.rm = TRUE),
   subscripts = TRUE, xlab = "Calcium Chloride concentration (mM)",
   ylab = "log(Length in mm)", panel =
   function(x, y, subscripts, ...) {
      panel.xyplot(x, Muscle$logLength[subscripts], ...)
      llines(spline(x, y))
   })

Results

R version 3.3.1 (2016-06-21) -- "Bug in Your Hair"
Copyright (C) 2016 The R Foundation for Statistical Computing
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> library(MASS)
> png(filename="/home/ddbj/snapshot/RGM3/R_CC/result/MASS/muscle.Rd_%03d_medium.png", width=480, height=480)
> ### Name: muscle
> ### Title: Effect of Calcium Chloride on Muscle Contraction in Rat Hearts
> ### Aliases: muscle
> ### Keywords: datasets
> 
> ### ** Examples
> 
> A <- model.matrix(~ Strip - 1, data=muscle)
> rats.nls1 <- nls(log(Length) ~ cbind(A, rho^Conc),
+    data = muscle, start = c(rho=0.1), algorithm="plinear")
> (B <- coef(rats.nls1))
          rho .lin.StripS01 .lin.StripS02 .lin.StripS03 .lin.StripS04 
   0.07776401    3.08304824    3.30137838    3.44562531    2.80464434 
.lin.StripS05 .lin.StripS06 .lin.StripS07 .lin.StripS08 .lin.StripS09 
   2.60835015    3.03357725    3.52301734    3.38711844    3.46709396 
.lin.StripS10 .lin.StripS11 .lin.StripS12 .lin.StripS13 .lin.StripS14 
   3.81438456    3.73878664    3.51332581    3.39741115    3.47088608 
.lin.StripS15 .lin.StripS16 .lin.StripS17 .lin.StripS18 .lin.StripS19 
   3.72895847    3.31863862    3.37938673    2.96452195    3.58468686 
.lin.StripS20 .lin.StripS21        .lin22 
   3.39628029    3.36998872   -2.96015460 
> 
> st <- list(alpha = B[2:22], beta = B[23], rho = B[1])
> (rats.nls2 <- nls(log(Length) ~ alpha[Strip] + beta*rho^Conc,
+                   data = muscle, start = st))
Nonlinear regression model
  model: log(Length) ~ alpha[Strip] + beta * rho^Conc
   data: muscle
alpha..lin.StripS01 alpha..lin.StripS02 alpha..lin.StripS03 alpha..lin.StripS04 
            3.08305             3.30138             3.44563             2.80464 
alpha..lin.StripS05 alpha..lin.StripS06 alpha..lin.StripS07 alpha..lin.StripS08 
            2.60835             3.03358             3.52302             3.38712 
alpha..lin.StripS09 alpha..lin.StripS10 alpha..lin.StripS11 alpha..lin.StripS12 
            3.46709             3.81438             3.73879             3.51333 
alpha..lin.StripS13 alpha..lin.StripS14 alpha..lin.StripS15 alpha..lin.StripS16 
            3.39741             3.47089             3.72896             3.31864 
alpha..lin.StripS17 alpha..lin.StripS18 alpha..lin.StripS19 alpha..lin.StripS20 
            3.37939             2.96452             3.58469             3.39628 
alpha..lin.StripS21         beta..lin22             rho.rho 
            3.36999            -2.96015             0.07776 
 residual sum-of-squares: 1.045

Number of iterations to convergence: 0 
Achieved convergence tolerance: 4.923e-06
> 
> Muscle <- with(muscle, {
+ Muscle <- expand.grid(Conc = sort(unique(Conc)), Strip = levels(Strip))
+ Muscle$Yhat <- predict(rats.nls2, Muscle)
+ Muscle <- cbind(Muscle, logLength = rep(as.numeric(NA), 126))
+ ind <- match(paste(Strip, Conc),
+             paste(Muscle$Strip, Muscle$Conc))
+ Muscle$logLength[ind] <- log(Length)
+ Muscle})
> 
> lattice::xyplot(Yhat ~ Conc | Strip, Muscle, as.table = TRUE,
+    ylim = range(c(Muscle$Yhat, Muscle$logLength), na.rm = TRUE),
+    subscripts = TRUE, xlab = "Calcium Chloride concentration (mM)",
+    ylab = "log(Length in mm)", panel =
+    function(x, y, subscripts, ...) {
+       panel.xyplot(x, Muscle$logLength[subscripts], ...)
+       llines(spline(x, y))
+    })
> 
> 
> 
> 
> 
> dev.off()
null device 
          1 
>