1. Absolute Metabolite Concentrations Gaussian and Lorentzian Functions
on Brain Tissue by
Gaussian and Lorentzian Functions
Amarjeet Bhullar
Bimonthly Meeting on Dec. 5, 2008

2. How to get absolute signal?
Absolute Signal = Raw data - Noise
Raw data = Real Spectrum without any manipulation
Noise = Draw a Baseline using few anchor points on
Spectrum
Noise=Baseline is determined by interpolating
anchor points on spectrums.

3. Absolute Metabolite Concentrations
Create baseline using few anchor points on spectrum.
Find metabolite peaks.
Fit Mathematical function on metabolite peaks.
Integrate peaks between the limits to calculate absolute metabolite concentrations.

4. Mathematical Model: Gaussian Function

5. Integral of Gaussian Function : Error Function
Numerically: Codes developed in C and Mathematica 6.0

6. Integral of Gaussian Function : Gamma Function

7. Mathematical Model: Lorentz Function

8. Integral of Lorentzian Function : ArcTan

9. Difference Between Lorentzian and Gaussian Function

10. Metabolite ratios by Gaussian function
Voxel #32
Gaussian
Cho/Cre
1.58
Cho/NAA
0.34

11. Metabolite ratios by Lorentzian function
Voxel #32
Lorentzian
Cho/Cre
1.54
Cho/NAA
0.33

12. Conclusion: Both mathematical models have produced the same ratios.
Voxel #32
Gaussian
Lorentzian
Average
Cho/Cre
1.58
1.54
1.55
Cho/NAA
0.34
0.33
Both mathematical models have produced
the same ratios.
Suggestions are welcome