Fit theoretical functions to your data waves, such as a line, exponential, polynomial, or Gaussian function. This tab utilizes Igor’s pre-exising Curve Fitting algorithm FuncFit, and is similar to Igor’s Curve Fitting panel (Igor Menu/Analysis/Curve Fitting...), but works within the framework of NeuroMatic.
Add your own fit functions using NeuroMatic fit functions (e.g. NMAlpha, NMSynExp3) as templates.
Fit waves are now created inside Subfolders by default.
>> New stereology Keiding-model fit functions for estimating the 3D diameter distribution from the 2D diameter distribution.
Function – select a function to fit to your data wave (e.g. line, Poly, Gauss, Exp, Sigmoid, Power). The Fit Coefficients Table will appear.
Data Options – set the range (xbgn, xend) over which to perform the curve fit. To fit between graph cursors, place Igor’s cursors A and B on the active wave in the current Channel Graph and check cursors. Alternatively use NeuroMatic’s Channel Graph drag waves (vertical dashed red lines) to set the range. Check weighting to compute weighted fits. Standard deviation values must reside in waves with the same name of the waves to be fit, but with “Stdv_” as the prefix name (e.g. wave “Stdv_RecordA0” that contains standard deviation values for wave “RecordA0”).
Output Options – final fit waves are displayed on top of your data wave in the active Channel Graph. Control their appearance here:
Points – enter the number of points of the final fit wave. Enter “auto” for the default Igor option.
Save – check to save the final fit waves. Waves will be saved in the current NeuroMatic Data Folder with prefix name “Fit_” (e.g. wave “Fit_RecordA0”).
Residuals – check to compute/display fit residuals. Residual waves will be saved in the current NeuroMatic Data Folder with prefix name “Res_” (e.g. wave “Res_RecordA0”).
Graph Now – compute the fit wave based on initial coefficient guesses (wave FT_guess).
Execute – compute the curve fit. Results can be saved to a table.
Fit All – compute the fit to all currently selected channels and waves (7), saving values to a table.
Save – save current fit results to a table.
Plot All – plot all data and fit waves.
Clear – clear current fit results from the output table.
Clear All – clear all output table values.
Auto Fit – check to automatically compute the curve fit when incrementing through your data waves (3).
Print Results – print fit results to Igor’s history window.
Configs – see Configurations for the Fit Tab for more options (MaxIterations, Tolerance, MultiThreads, FitMethod, WeightingWavePrefix).
The Fit Coefficients Table contains the following input/output waves for computing the curve fit:
FT_coef – contains the coefficient result values.
FT_sigma – contains the coefficient sigma (error) values.
FT_guess – contains the coefficient initial guess values (optional).
FT_hold – contains the hold coefficient parameter. Enter 1 to hold a particular coefficient at its initial guess. You must enter a guess value for the parameter.
FT_low – contains the lower limit for coefficient parameter (enter NaN for no limit).
FT_high – contains the upper limit for coefficient parameter (enter NaN for no limit).
A NeuroMatic Channel Graph showing a curve fit (solid red line) of a double exponential function (DblExp_Offset) to the decay phase of an EPSC (black line). Drag waves (dashed red lines) were used to set the time limit parameters xbgn and xend. Results are displayed in the Fit Coefficients table shown above.
The Keiding model for estimating the 3D diameter distribution (F(d)) from the 2D diameter distribution (G(d)). The figure above shows a curve fit of the Keiding model (solid red line) to G(d) of synaptic vesicles in cerebellar mossy fiber terminals (green circles; ET11). Note the absence of measured vesicle diameters less than 25 nm, which are referred to as “lost caps”. The Keiding model accounts for lost caps by setting a lower limit (ɸ) on the cap angle θ (i.e. ɸ ≤ θ ≤ 90°) where θ = sin(d/D), d is the measured 2D diameter and D is the 3D diameter. For the curve fit shown here, the estimated F(d) (dashed red line and red circle) matches the measured F(d) (black line and black circle), and the estimated ɸ (38.4°) matches the average measured ɸ (41.5°). Data is from the PLOS One research article Validation of a stereological method for estimating particle size and density from 2D projections with high accuracy (Figure 6).
The new Kieding-model fit functions NMKeidingGauss, NMKeidingChi and NMKeidingGamma assume either a Gaussian, Chi or Gamma distribution for F(d). The fit parameters for NMKeidingGauss are the mean and standard deviation of the 3D diameter distribution (X0 and STDVx), section thickness (T; should be held constant during the fit, i.e. hold = 1) and cap-angle limit (ɸ, Phi). If you enter the number of particles used to compute G(d) (N), NeuroMatic will compute ɸ-cutoff (PhiCutoff) once the curve fit is finished and warn you if ɸ is likely to be indeterminable. Parameters N and PhiCutoff should also be held during the fit (hold = 1).
Demo and utility functions can be found under NeuroMatic’s Analysis menu:
Igor Menu/NeuroMatic/Analysis/Keiding model for estimating particle size and density
The demo functions replicate key curve fits within the PLOS One research article.
Rothman JS, Borges-Merjane C, Holderith N, Jonas P, Silver RA. Validation of a stereological method for estimating particle size and density from 2D projections with high accuracy. PLoS ONE 2023; 18(3): e0277148. DOI: 10.1371/journal.pone.0277148
Keiding N, Jensen ST, Ranek L. Maximum likelihood estimation of the size distribution of liver cell nuclei from the observed distribution in a plane section. Biometrics 1972 Sep;28(3):813-29 DOI: 10.2307/2528765