Gannet will quantify metabolite signals in a number of different ways at various points in the pipeline depending on what reference signals are present and if structural image data are available. It is important to understand what the calculations are for interpretation and reporting.

## GannetFit

MRS_struct.out.vox1.metab.ConcCr is a simple integral ratio of the metabolite and Cr signals:

$C = \frac{I_{M}}{I_{Cr}}$

If a water reference is provided, MRS_struct.out.vox1.metab.ConcIU is also calculated. It is defined as the integral ratio of the metabolite and water signals scaled by a number of global signal scaling factors:

$C_{corr} = \frac{I_{M}}{I_{W}}\cdot \frac{H_{W}}{H_{M}}\cdot \frac{MM}{\kappa}\cdot C_{W}\cdot W_{vis}\cdot \left\{\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]} {\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\right\}$

where:

Parameter Description Default value
$$C_{corr}$$ Metabolite concentration in institutional units -
$$I_{M}$$ Metabolite signal integral -
$$I_{W}$$ Water signal integral -
$$H_{M}$$ Number of 1H protons that give rise to the metabolite signal Metabolite dependent
$$H_{W}$$ Number of 1H protons that give rise to the water signal 2
$$MM$$ Correction factor for the contribution of the co-edited macromolecule signal in the metabolite signal 0.45 for GABA editing and 1 for all other edited metabolites
$$\kappa$$ Editing efficiency Acquisition dependent; 0.5 for GABA editing
$$C_{W}$$ Molal concentration of pure water 55.51 mol/kg
$$W_{vis}$$ Average relative visibility (density) of water in GM and WM 0.65 (1)
$$TE_{W}$$ Echo time of the water reference acquisition Acquisition dependent
$$TR_{W}$$ Repetition time of the water reference acquisition Acquisition dependent
$$TE_{M}$$ Echo time of the metabolite acquisition Acquisition dependent
$$TR_{M}$$ Repetition time of the metabolite acquisition Acquisition dependent
$$T_{2W}$$ Average transverse relaxation time of water in GM and WM 1.100 s (2)
$$T_{2W}$$ Average longitudinal relaxation time of water in GM and WM 0.095 s (2)
$$T_{2M}$$ Transverse relaxation time of metabolite Metabolite dependent; see GannetFit.m and GannetQuantify.m for default values
$$T_{1M}$$ Longitudinal relaxation time of metabolite Metabolite dependent; see GannetFit.m and GannetQuantify.m for default values

## GannetSegment

MRS_struct.out.vox1.metab.ConcIU_CSFcorr:

$C_{CSFcorr} = \frac{I_{M}}{I_{W}}\cdot \frac{H_{W}}{H_{M}}\cdot \frac{MM}{\kappa}\cdot C_{W}\cdot W_{vis}\cdot \left\{\frac{\exp\left(-\frac{TE_{W}}{T_{2W}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W}}\right)\right]} {\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\right\}\cdot \frac{1}{1-f_{CSF}}$

where $$f_{CSF}$$ is the volume fraction of CSF in the MRS voxel.

## GannetQuantify

MRS_struct.out.vox1.metab.ConcIU_TissCorr:

$C_{TissCorr} = \frac{I_{M}}{I_{W}}\cdot \frac{H_{W}}{H_{M}}\cdot \frac{MM}{\kappa}\cdot C_{W}\cdot \left\{\frac{\sum_{i}^{GM,WM,CSF}f_{i}\beta_{i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]} {(1-f_{CSF})\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\right\}$

where:

Parameter Description Default value
$$f_{i}$$ Volume fraction of GM, WM or CSF in the MRS voxel Data dependent
$$\beta_i$$ Relative visibility (density) of water in GM, WM and CSF 0.78, 0.65 and 0.97 (1)
$$T_{2W,i}$$ Transverse relaxation time of water in GM, WM and CSF 0.110, 0.0792 and 0.503 s (2,3)
$$T_{1W,i}$$ Longitudinal relaxation time of water in GM, WM and CSF 1.331, 0.832 and 3.817 s (2,4)

MRS_struct.out.vox1.metab.ConcIU_AlphaTissCorr:

$C_{corr} = \frac{I_{M}}{I_{W}}\cdot \frac{H_{W}}{H_{M}}\cdot \frac{MM}{\kappa}\cdot \left\{\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]} {\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\right\}\cdot \frac{1}{f_{GM}+\alpha{f_{WM}}}$

MRS_struct.out.vox1.metab.ConcIU_AlphaTissCorr_GrpNorm:

$C_{corr} = \frac{I_{M}}{I_{W}}\cdot \frac{H_{W}}{H_{M}}\cdot \frac{MM}{\kappa}\cdot \left\{\frac{\sum_{i}^{GM,WM,CSF}f_{i}C_{W,i}\exp\left(-\frac{TE_{W}}{T_{2W,i}}\right)\left[1-\exp\left(-\frac{TR_{W}}{T_{1W,i}}\right)\right]} {\exp\left(-\frac{TE_{M}}{T_{2M}}\right)\left[1-\exp\left(-\frac{TR_{M}}{T_{1M}}\right)\right]}\right\}\cdot \frac{\mu_{GM}+\alpha{\mu_{WM}}}{(f_{GM}+\alpha{f_{WM}})(\mu_{GM}+{\mu_{WM}})}$

where:

### References

1. Ernst T, Kreis R, Ross BD. Absolute quantitation of water and metabolites in the human brain. I. Compartments and water. Journal of Magnetic Resonance, Series B. 1993;102(1):1-8. doi:10.1006/jmrb.1993.1055

2. Wansapura JP, Holland SK, Dunn RS, Ball WS. NMR relaxation times in the human brain at 3.0 Tesla. Journal of Magnetic Resonance Imaging. 1999;9(4):531-538. doi:10.1002/(SICI)1522-2586(199904)9:4<531::AID-JMRI4>3.0.CO;2-L

3. Piechnik SK, Evans J, Bary LH, Wise RG, Jezzard P. Functional changes in CSF volume estimated using measurement of water T2 relaxation. Magnetic Resonance in Medicine. 2009;61(3):579-586. doi:10.1002/mrm.21897

4. Lu H, Nagae-Poetscher LM, Golay X, Lin D, Pomper M, Zijl PCM van. Routine clinical brain MRI sequences for use at 3.0 Tesla. Journal of Magnetic Resonance Imaging. 2005;22(1):13-22. doi:10.1002/jmri.20356

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