.. _constants:

Constants
=========

The following constants are hardcoded into FSL-MRS and are used in the quantisation module.

Water to tetramethylsilane (TMS) chemical shift ::
    
    H2O_PPM_TO_TMS     = 4.65

Gyromagnetic ratio of proton::

    H1_gamma           = 42.576     # MHz/tesla

Concentration scaling parameters
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Tissue water density [0]_::

    TISSUE_WATER_DENSITY = {'GM':0.78,'WM':0.65,'CSF':0.97} 

Molecular mass of water::

    H2O_MOLECULAR_MASS = 18.01528   # g/mol

Molality of pure water::

    H2O_MOLALITY = 55.51E3    # mmol/kg     

Number of protons in water::

    H2O_PROTONS = 2

The integrated water signal is referenced to a single reference basis.
There are three defaults defined in FSL-MRS, and each are tried in the order listed here.
Each possible reference is equivalent to a predetermined number of protons and has associated integration limits.
There are::

    WATER_SCALING_METAB = ['Cr', 'PCr', 'NAA']
    WATER_SCALING_METAB_PROTONS = [5, 5, 3]
    WATER_SCALING_DEFAULT_LIMITS = [(2, 5), (2, 5), (1.8, 2.2)]

Relaxation parameters
*********************
Values are derived from a survey of the literature. References listed below. Values for metabolites are derived from an average of NAA, Cr and Cho peaks.

T1 (all values in seconds)
__________________________
.. csv-table::
    :header: "Field strength (T)", "Water: WM", "Water: GM", "Water: CSF" , "Metabolites" 
    :widths: 10, 10, 10, 10, 10

    1.5,	    0.63,	1.19,	3.90,	1.24
    3,	        0.97,	1.50,	4.47,	1.29
    7,	        1.21,	2.05,	4.43,	1.43
    References,	"1-6, 16",	"1-6, 16",	"4, 17",	    "2, 7-9, 17"

T2 (all values in ms)
__________________________
.. csv-table::
    :header: "Field strength (T)", "Water: WM", "Water: GM", "Water: CSF" , "Metabolites" 
    :widths: 10, 10, 10, 10, 10

    1.5,	    80,	      83,	2000,	279
    3,	        73,	      88,	2030,	194 
    7,	        55,	      50,	1050,	131
    References,	"1-3, 10-11, 19",	"1-3, 10-11, 19",	"12, -", "7-9, 13-15, 20"

Code definitions::

    STANDARD_T1 = {
    '1.5T': {'H2O_WM': 0.630,  # Ref: 16
             'H2O_GM': 1.185,  # Ref: 16
             'H2O_CSF': 3.90,  # Ref: 17
             'METAB': 1.238},  # Ref: 18
    '3T': {'H2O_WM': 0.97,  # Ref: 1-6
           'H2O_GM': 1.50,  # Ref: 1-6
           'H2O_CSF': 4.47,  # Ref: 4
           'METAB': 1.29},  # Ref: 2, 7-9
    '7T': {'H2O_WM': 1.21,  # Ref: 1-6
           'H2O_GM': 2.05,  # Ref: 1-6
           'H2O_CSF': 4.43,  # Ref: 4
           'METAB': 1.43}}  # Ref: 2, 7-9

    STANDARD_T2 = {
        '1.5T': {'H2O_WM': 0.080,  # Ref: 19
                'H2O_GM': 0.083,  # Ref: 19
                'H2O_CSF': 2.000,  # Approximate
                'METAB': 0.279},  # Ref: 20
        '3T': {'H2O_WM': 0.073,  # Ref: 1,3,10-11
            'H2O_GM': 0.088,  # Ref: 1,3,10-11
            'H2O_CSF': 2.030,  # Ref: 12
            'METAB': 0.194},  # Ref: 7-9,13-15
        '7T': {'H2O_WM': 0.055,  # Ref: 1,3,10-11
            'H2O_GM': 0.050,  # Ref: 1,3,10-11
            'H2O_CSF': 1.050,  # Ref: 12
            'METAB': 0.131}}  # Ref: 7-9,13-15


References
----------

.. [0] Kreis R, Ernst T, Ross BD. Absolute quantitation of water and metabolites in the human brain. II. Metabolite concentrations. J Magn Reson B. 1993;102:9-19.
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