STAT 1000: SEMINAR 29Mitchell Thompson III

Reflex Patterns in Postganglionic Neurons Supplying Skin and Skeletal Muscle of the Rat

Hindlimb

OVERVIEWGoal: To determine if the MVC (muscle)and

CVC (skin)neurons can be distinguished functionally based on their reflex patterns?

Reflex analysis of postganglionic Vasoconstrictor neurons to Muscle (MVC) and skin (CVC) elicited through multiple stimuli.

Terms: MVC and CVC classified as postganglionic neurons that innervate blood vessels and are vasoconstrictor in function

MuscleCutaneous

Neuroanatomy

METHODS1. Subjects: 65 female Wistar rats

Selection bias?The investigator aims to prove that the central

organization of the sympathetic nervous system in rats possess a differentiation with respect to function

2. Anesthetics: 3 types used pentorbitone (pentorbital sodium), urethane, and α-chloralose.1.Does this support or damage results?

1. Results are supported because the effects of anesthesia (confounding variable) can be eliminated

SUBJECTS 65 female Wistar rats

59 preparations of spontaneously active MVC (skeletal) neurons

138 preperations of spontaneously active CVC (skin) neurons

What is/are sample size(s)?n1 = 59 n2= 138

SPONTANEOUS ACTIVITY

U AND POOLING A non-parametric test for assessing

whether two samples of observations come from the same distribution The U test (Wilcoxon rank-sum test) is useful

in the same situations as the independent samples Student’s t-test

For distributions sufficiently far from normal Because the spontaneous activity of

neurons under the different anesthetics had a similar distribution (P>0.05) all samples were pooled.

Students’ Distribution A test of the null hypothesis that the means

of two normally distributed populations are equal. Given two data sets, each characterized by its

mean, standard deviation and number of data points, we can use two sample t test to determine whether the means are distinct, provided that the underlying distributions can be assumed to be normal.

All such tests are usually called Student's t tests, though strictly speaking that name should only be used if the variances of the two populations are also assumed to be equal

Reflexes elicited by stimulation of the arterial baroreceptors Arterial baroreceptors: Stimulation of

arterial baroreceptors leads to inhibition of activity in vasoconstrictor neurons innervating resistance vessels.

Quantification of Neural responses: A 20% change of neural activity during the first 30s after stimulation compared with control activity during the 50s preceding stimulation was considered as a response.Paired vs. Two-sample

○ Paired (comparison within sample nx)

Arterial Baroreceptor Stimulation

Two Sample T-Test Equivalent to student’s distribution?

Because variances are assumed to be equals.d.1 ≈ s.d.2

Categorical/ Quantitative VariableNeuron Type (Categorical)

○ MVC (n1= 59) vs. CVC (n2= 138)% Cardiac Rhythmicity (Quantitative)

RequirementsUnknown population σ Difference between means not mean of

differences Sample means normally distributed Independent samples

N ≥ 10n

HYPOTHESISNull Hypothesis: Ho

(a) μ1 – μ2 = 0 (b) μ1 = μ2

(c) μ1 = -μ2

Alternative Hypothesis: Ha(a) μ1 – μ2 ≠ 0 (b) μ1 = μ2

(c) μ1 > μ2

T-Test MVC CR

x bar1= 75; s1= 17; n1= 59CVC CR

x bar2= 44; s2= 20; n2 =138

T-STATISTICFactors that affect t-statistic

Difference between x bar1 and x bar2Large difference Increases | t |Smaller p-value Easier to reject Ho

Sample Sizes n1 and n2Small sizes n1 and n2 Decreases | t |Larger p-value Harder to reject Ho

S.D. s1 and s2 Small s.d. s1 and s2 Increases | t |Smaller p-value Easier to reject Ho

CONCLUSIONStrong (>60% CR)

Weak(40-60% CR)

Absent (<40% CR)

MVC (muscle) Mean =82±12%n= 46 (78%)

Mean = 52 ±4%n= 13 (22%) n= 0 (0%)

CVC (skin) Mean = 76±11%n= 25 (18%)

Mean =51 ±6%n= 46 (33%)

Mean = 28±8%n= 67 (49%)

•T-statistic large?• 11.1…. Big yes!

•P-value small? •P< 0.001 …..Another Big Yes!

•Reject Ho: μ1 – μ2 = 0?• I think you get the picture

•Cardiac Rythmicity is greater in MVC Neurons than CVC neurons; Although CR is less prominent in CVC it is still inhibited by an increase in blood pressure (arterial baroreceptor stimulation)

REFLECTIONS Study Design

Test male rats and compare to females to determine if a significant difference of results exists○ Paired vs. two-sample t-test○ Two-sample

SubjectsNo attempt was made to study neurons w/o

spontaneous activity…recruitment of silent neurons within multiunit preparations… can not be ruled out○ Type I vs. Type II Error?○ Sample size would appear larger than it’s actual value○ Statistic would appear larger (p-value smaller): Type I