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Analysis Tools

Peak Finder and Exponential Fit use features that may not be fully supported by browsers that are otherwise compatible with Crawdad. As of summer 2016, the latest versons of Chrome and Opera work well. Safari and Firefox can perform the analyses but may not handle large data sets quickly or display them cleanly. Internet Explorer and Edge have a bug that makes them unable to do the peak and exponential analyses at all.

All browsers should handle the equation calculators equally well.

Equations

To open an equation calculator in a separate window, select a link:

Eq. 1 Ohm’s LawEq. 2 Time ConstantEq. 5 Input Resistance
E =IR
V
A
Ω
τ =RC
s
Ω
F
Rm(Ri + Ro)2 Rinput =
Ω
Ω
Ω
Ω
Eq. 3 Space ConstantEq. 4 Passive SpreadEq. 6 Nernst Potential
λ = Rm Ri +Ro
Ω
Ω
Ω
Vx = Voe -x⁄λ
V
V
[ion]o [ion]i RT ZF Eion = ln
V
mol
mol
Z =
T = 273°K +°C
R = 8.314 J/mol·KF = 96500 C/mol

Saline Calculator

l of
KCl5.4 mM403 mg
NaCl205 mM12 g
CaCl2·2H2O10 mM1.47 g
MgCl2·6H2O2.6 mM529 mg
NaHCO32.3 mM193 mg
dextrose2 mM361 mg
Dextrose is optional.

Peak Finder

If your data acquisition software cannot easily detect spikes in an extracellular recording, the Peak Finder may help. Copy and paste waveform data (columns of time and voltage or, if you enter the sampling rate, just voltage), set window thresholds, and the Peak Finder will find all peaks that fall between the two threshold lines. It provides a list of spike times and heights, along with a histogram of heights. For Lab 2, Nerve Recording, the histogram can show how many spike classes are present. For Lab 7, Stretch Receptor, spike times from the Peak Finder can be automatically sent to the Exponential Fit to show adaptation rates.

Be cautious with large data sets: 60 s of data sampled at 40 kHz is 2.4 million points. If your data acquisition software can reduce the sampling rate when exporting data, try reducing sampling to 10 kHz. Otherwise, go to the Peak Finder’s optional settings and check the Downsample box before pasting in your data. Even with 800,000 points, it can take 15 s for the pasted data to appear in the text box, so be patient.

Open Peak Finder in a new window

Enter data:

samples/sec

Set window:

range to

Peak output:


Histogram:


(1) Paste a column of voltages (or two columns, time and voltage) into the data entry box. The trace will appear to the right. Use mouse wheel or track pad scrolling gestures to zoom in and out of the trace; double-click an axis or trace to restore the initial view. (2) Enter values or drag the threshold lines to set the window for peak finding. Peaks will appear in the peak output box and displayed in the lower left plot. (3) A histogram of spike heights will appear in the histogram box and lower right plot. (4) To recreate the peak or histogram plot, copy the respective data into Peaks.xltx (download template). The trace image can be downloaded in PNG format (with or without peaks) or SVG format (with or without peaks).


ms.
Aim for automatic bins.

Exponential Fit

For Lab 7, Stretch Receptor, you should plot spike rate vs. time and fit an exponential decay curve to your data. Unfortunately, Excel only does exponential fits that decay all the way to zero. The Exponential Fit tool is designed to handle data sets that decline to a non-zero asymptote. Paste in a list of spike times (sent automatically from Peak Finder), and this tool will calculate instantaneous spike rate and plot it against spike time. You can then fit an exponential curve to the rates and copy the resulting data to Excel or other software to plot it.

If you have more specialized software such as MatLab, Mathematica, or Origin, it may do a better job of fitting.

Open Exponential Fit in a new window

Fitting

Enter data here: %

0 points

Output:

 

  

Equation to fit:

A sum of two exponentials may fit data more closely but it is hard to calculate good initial guesses for the parameters. If the calculated guesses do not give good results, try entering your own below.


R∞ = Ro = τ =
Ro′ = τ′ =
Calculated initial guesses:
 

  RMS = Parameter change:
The main Fit button homes in on a fit by adjusting parameters over 10 iterations. RMS error shows how much the fit differs from the data (smaller RMS = closer fit). To iterate another 10 times, press the Fit button again; to iterate once more, press the Iterate button.
Parameter change sets the amount by which parameters change during iterations. Try changing this if you get questionable results.


By default, y values (rate) are plotted and fitted against x values (time). In some cases, you may need to plot and fit rate against point number.

This page simplifies the least-squares algorithm found at http://statpages.info/nonlin.html. Go to that page to fit any arbitrary function you wish to enter.