Units

dcmri uses a standardized system of units for all input and output quantities. The system is internally consistent: as long as data and parameters are entered in these units, all return values will automatically also be in the same units. Hence it is not needed to track units through intermediate computations, which greatly reduces the risk of unit conversion errors in complex analysis pipelines.

Table of units

The following table shows for each quantity the dcmri unit, and wehere relevant also other units that are commonly found in the literature on DC-MRI:

Quantity	dcmri unit	common alternative units
Time	sec	min
Length	cm
Area	cm2
Volume	cm3	mL
Angle	deg	rad
Fluid volume	mL
Weight	kg	g
Amount of indicator	mmol	mol
Concentration	M	mmol/L, mM
Tissue concentration	mmol/cm3	mmol/L, mM
Indicator flux	mmol/sec
MRI relaxation time	sec	msec
MRI relaxation rate	1/sec	1/msec
Magnetization	A/cm	A/m
Contrast agent relaxivity	1/sec*M	1/mM/sec
Perfusion	mL/sec/cm3	mL/100mL/min, 1/sec, mL/sec/mL
Permeability-surface area	mL/sec/cm3	1/sec, 1/min
(Fluid) volume fraction	mL/cm3	mL/100mL, mL/100g, %, dimensionless
Fluid flow	mL/sec

Rationale

We have chosen to deviate from the system of SI units in order to align more closely to the natural units of most of the quantities, and historical conventions in the field. However we have also chosen to deviate from conventions in some places in order the arrive at an internally consistent set of units.

The use of a single systematic system of units minimises the risk of errors due to incorrect conversions between units in code, which are hard to track especially when different functions from different modules are assembled.

It does mean that some of the quantities are not in their natural units - for instance tissue concentrations are typically in the order of 0.001 M and are therefore commonly expressed in units of mM. Equally, contrast agent relaxivities are conventionally expressed in units of 1/mM*sec. In dcmri, concentrations and relaxivities will nevertheless be required and returned in units of M and 1/M*sec, respectively.

It is the responsability of the user to convert any output in more conventional units for publication or presentation purposes. Equally, it is the user’s responsability to convert any input data into dcmri units before applying any of the functions in the package.

Units of volume

Fluid volumes of mL and volumes of cm3 are of course numerically interchangeable. dcmri nevertheless distinguishes explicitly between (tissue) volumes (cm3) or voxel volumes (cm3) and fluid volumes (mL) to avoid confusion in the interpretation of important quantities such as perfusion or concentration.

In the dcmri system of units, perfusion is expressed in mL/sec/cm3. This directly reflects the physical interpretation as volume of blood (mL) delivered per unit of time (sec) to a unit of tissue (cm3). If tissue volumes were to be expressed in units of mL instead of cm3, the units of perfusion would be mL/sec/mL. This looks odd and is often reduced to units of 1/sec, cancelling out the mL’s. In this form the units suggest that perfusion is a rate, which is physically confusing.

The units of mL/sec/cm3 also align more directly to the historical units of perfusion as mL/sec/g. They reflect the original practice of first measuring whole-organ blood flow (mL/min), excising and weighing the organ, and dividing out the weight to arrive at organ perfusion. In an imaging context normalising to weight is awkward as voxel volume is known, but voxel weight is not. Converting to historical units of mL/min/g would require inserting of literature values for tissue density in all models, and keeping track of these throughout computations. This is cumbersome and unnecessary, since conversion to mL/sec/g can always be done at the end of computations on the final output.

The use of cm3 for tissue volumes also ensures that important distinctions such as that between concentration and tissue concentration, are explicit. The term concentration in dcmri documentation is consistently used to designate amounts of indicator (mmol) relative to fluid volumes (mL), whereas the term tissue concentration refers to indicator amounts (mmol) per unit tissue volume (cm3). They are different physical quantities and in an imaging context the distinction is important.

Units in plots

While dcmri rigorously adheres to standard units for all arguments and return values in functions - exceptions are made in plots or other presentations of data and results. Here dcmri will choose the units that are most natural and intuitive in conveying the key messages. For instance concentrations in plots will typically be shown in units of mM.