The items in this group are related to the MR signal and quantities of the MR sequence used to acquire the signal.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.MS1.001.[j]
Signal
--
Sj
The MR signal (magnitude, phase or complex depending on context) in compartment j.
a.u.
--
Q.MS1.002.[j]
Baseline signal
--
SBL,j
Pre-contrast MR signal (magnitude, phase or complex depending on context) in compartment j before the arrival of indicator at the tissue of interest.
a.u.
--
Q.MS1.003.[j]
Absolute enhancement
--
AEj
The absolute signal change from baseline \(\left\| S_j-S_{BL,j} \right\|\) in compartment j induced by an indicator. In DCE, the enhancement is positive and in DSC, the enhancement is negative.
a.u.
--
Q.MS1.004.[j]
Relative enhancement
--
REj
The relative signal change from baseline \(\left\|\frac{S_j}{S_{BL,j}}-1\right\|\) in compartment j induced by the indicator. In DCE, the enhancement is positive and in DSC, the enhancement is negative.
--
--
Q.MS1.005
Echo time
--
TE
The time between the application of the radiofrequency excitation pulse and the center of the echo.
ms
--
Q.MS1.006
Repetition time
--
TR
The time between the beginning of a pulse sequence and the beginning of a succeeding (essentially identical) pulse sequence.
ms
--
Q.MS1.007
Prescribed excitatory flip angle
--
\(\alpha\)
The prescribed nutation angle of the net magnetization immediately following an excitation RF pulse.
deg
--
Q.MS1.008
Prepulse delay time
Inversion time TI (in case of an inversion recovery sequence)
PD
The time between the middle of a prepulse (e.g. inversion pulse) and the middle of the pulse that reads out the center of k-space.
ms
--
Q.MS1.009
Prepulse flip angle
--
\(\alpha_{p}\)
The nutation angle of the net magnetization immediately following a prepulse.
deg
--
Q.MS1.010
Signal scaling factor
--
S0
A constant scaling factor in a signal model. \(S_0\) typically includes contributions from the receiver gain, the proton density and the coil sensitivities.
--
--
Q.MS1.011
Number of lines to k-space center
--
n
The number of lines to k-space center in the phase encoding direction.
--
--
Q.MS1.012
Total number of k-space lines
--
N
The total number of phase encoding lines for acquiring an image.
--
--
Q.MS1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
The items in this group are related to electromagnetic tissue properties and electromagnetic properties of contrast agents. The abbreviations SE and GE denote spin and gradient echo.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.EL1.001.[j]
Longitudinal relaxation rate
R1 -relaxation rate
\(R_{1,j}\)
Longitudinal relaxation rate in compartment j.
1/s
--
Q.EL1.002.[j]
Native longitudinal relaxation rate
Baseline R1
\(R_{10,j}\)
Longitudinal relaxation rate in compartment j.
1/s
--
Q.EL1.003.[j]
Change in longitudinal relaxation rate
--
\(\Delta R_{1,j}^*\)
Change in longitudinal relaxation rate with respect to \(R_{10,j}\) in compartment j.
1/s
--
Q.EL1.004.[j]
Transverse relaxation rate (SE)
R2-relaxation rate
\(R_{2,j}\)
Natural transverse relaxation rate (observed using a SE) in compartment j.
1/s
--
Q.EL1.005.[j]
Native transverse relaxation rate (SE)
Baseline R2-relaxation rate
\(R_{20,j}\)
Pre-contrast natural transverse relaxation rate (observed using a SE) in compartment j.
1/s
--
Q.EL1.006.[j]
Change in transverse relaxation rate (SE)
--
\(\Delta R_{2,j}\)
Change in natural transverse relaxation rate (observed using a SE) with respect to \(R_{20}\) in compartment j.
1/s
--
Q.EL1.007.[j]
Transverse relaxation rate (GE)
\(R_{2}^*\)-relaxation rate
\(R_{2,j}^*\)
Effective transverse relaxation rate (observed using a GE) in compartment j.
1/s
--
Q.EL1.008.[j]
Native transverse relaxation rate (GE)
Baseline \(R_{2}^*\)
\(R_{20,j}^*\)
Pre-contrast effective transverse relaxation rate (observed using a GE) in compartment j.
1/s
--
Q.EL1.009.[j]
Change in transverse relaxation rate (GE)
--
\(\Delta R_{2,j}^*\)
Change in effective transverse relaxation rate (observed using a GE) with respect to \(R_{20}^*\) in compartment j.
1/s
--
Q.EL1.010
Change in a reference transverse relaxation rate
--
\(\overline{\Delta R}_{2,ref}^*\)
Average change in effective transverse relaxation rate in a reference area with no indicator extravasation.
1/s
--
Q.EL1.011.[j]
Molar magnetic susceptibility
--
\(\chi_j\)
Molar magnetic susceptibility in compartment j.
mL/mol
--
Q.EL1.012.[j]
Native molar magnetic susceptibility
Baseline \(\chi\)
\(\chi_{0,j}\)
Pre-contrast molar magnetic susceptibility in compartment j.
mL/mol
--
Q.EL1.013.[j]
Change in molar magnetic susceptibility
--
\(\Delta \chi_j\)
Change in molar magnetic susceptibility with respect to \(\chi_{0}\) in compartment j.
mL/mol
--
Q.EL1.014.[j]
Molar magnetic susceptibility change per unit concentration of indicator
--
\(\delta \chi_j\)
Molar magnetic susceptibility change per unit concentration of indicator in compartment j.
mL/mol/mM
--
Q.EL1.015.[j]
Longitudinal relaxivity
r1 -relaxivity
r1,j
Longitudinal relaxivity in compartment j.
1/s/mM
--
Q.EL1.016.[j]
Transverse relaxivity (SE)
r2 -relaxivity
r2,j
Transverse relaxivity (observed using a SE) in compartment j.
1/s/mM
--
Q.EL1.017
Transverse relaxivity (GE)
r2* -relaxivity
r2*
Transverse relaxivity (observed using a GE) in the voxel.
1/s/mM
--
Q.EL1.018
Longitudinal relaxivity of free indicator
--
r1,f
Longitudinal relaxivity of free (unbound) indicator.
1/s/mM
--
Q.EL1.019
Longitudinal relaxivity of bound indicator
--
r1,b
Longitudinal relaxivity of bound indicator.
1/s/mM
--
Q.EL1.020
Transverse relaxivities of the quadratic model (GE)
--
[k1,k2]
First and second order relaxivities for the quadratic model of the transverse relaxation rate (GE)
[1/s/mM,1/s/mM]
--
Q.EL1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
The items of this group of quantities are either measured or modeled quantities used when pharmacokinetic modeling is applied. This section is split into the subsections indicator kinetic model quantities and AIF model quantities. The latter contains only quantities specific to often used AIF models.
The items of this group of quantities are either measured or modeled quantities used when pharmacokinetic modeling is applied.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.IC1.001.[j]
Indicator concentration
--
Cj
Concentration of indicator molecules in compartment j.
mM
--
Q.IC1.002
Tissue residue function
--
R
Fraction of indicator molecules entering a volume of distribution at time t=0 that are still present at time t.
--
--
Q.IC1.003
Tissue transit time distribution
--
h
Probability distribution of transit times through volume of interest.
--
--
Q.IC1.004
Arterial transit time distribution
--
ha
Probability distribution of transit times through the arterial tree (between AIF location and tissue of interest).
--
--
Q.IC1.005
Tissue impulse response function
IRF
I
Defined by the relationship \(C_t=I\otimes C_{a,p}\) .
1/s
--
Q.IC1.006
General impulse response function
IRF
I
Defined by the relationship \(C_x=I\otimes C_y\) .
1/s
--
Q.IC1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
In this group commonly used quantities with a physiological meaning are listed.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.PH1.001.[j]
Relative volume fraction
--
vj
The relative volume fraction of compartment j. Only capillary vasculature is considered, thus the c subscript is dropped.
mL/100mL
--
Q.PH1.002
Blood plasma flow
--
Fp
The volume of blood plasma flowing into a unit tissue volume per unit time. The flow inputs and exits the capillary vasculature.
mL/min/100mL
--
Q.PH1.003
Blood flow
Cerebral blood flow (CBF)
Fb
The volume of blood flowing into a unit tissue volume per unit time. The flow inputs and exits the capillary vasculature.
mL/min/100mL
--
Q.PH1.004
Permeability surface area product
Extraction flow (FE)
PS
The volume of tissue plasma that is fully cleared of indicator in a unit of time by a unit tissue volume.
mL/min/100mL
--
Q.PH1.005
Extraction fraction
--
E
The fraction of indicator particles that is extracted from plasma in one pass through the vasculature.
--
--
Q.PH1.006.[j]
Mean transit time
--
MTTj
The average time the indicator spends in compartment j before exchanging into another compartment.
s
--
Q.PH1.007
Arterial delay time
--
Ta
Delay between indicator arrival at the arterial input function location and the voxel or tissue region of interest.
s
--
Q.PH1.008
Volume transfer constant
Transfer constant
Ktrans
The rate of indicator particle delivery from the blood plasma to the extravascular, extracellular volume per unit of tissue volume, per unit arterial plasma concentration.
1/min
--
Q.PH1.009.[j]
Indicator exchange rate
--
kj
Indicator exchange rate constant between two compartments (e.g. \(k_{e \to b}\))
1/s
--
Q.PH1.010.[j]
Water exchange rate
kin, kout
kw,j
Equilibrium water exchange rate between two compartments (e.g. \(k_{w, e \to b}\))
1/s
--
Q.PH1.011
Density
--
\(\rho\)
The density of the tissue of interest.
g/mL
--
Q.PH1.012.[j]
Hematocrit
--
Hctj
The volume percentage of red blood cells in the blood compartment j.
--
--
Q.PH1.013
Hematocrit factor
--
Hctf
Blood flow correction factor accounting for the difference in arterial hematocrit Hcta and capillary hematocrit Hctc.
--
--
Q.PH1.014
Capillary transit time heterogeneity
--
CTTH
Standard deviation of the capillary transit time distribution.
s
--
Q.PH1.015
Maximum oxygen extraction fraction
--
OEFmax
Upper biophysical limit of the proportion of oxygen that can be extracted by tissue.
--
--
Q.PH1.016.[j]
Pre-exchange lifetime of water
--
\(\tau_j\)
The average time water molecules spend in compartment j before exchanging into another compartment.
The water population fraction inside compartment j.
Unitless
--
Q.PH1.018
Filtrate reabsorption fraction
--
\(f\)
The fraction of filtrate lost due to reabsorption.
Unitless
--
Q.PH1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This section contains general physical and mathematical quantities which are used in the context of perfusion image analysis.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.GE1.001
Data grid
--
\([x_1,...,x_n]\)
Sampling points of a data set (typically time or frequency).
variable
--
Q.GE1.002
Data
--
\([f_1,...,f_n]\)
Values of a data set with respect to a data grid. The data set has the value \(f_i\) at data grid point \(x_i\).
variable
--
Q.GE1.003
Index
--
\(i\)
The number of the index of a data or data grid point.
--
--
Q.GE1.004
Time
--
\(t\)
Time
s
--
Q.GE1.005
Time step
--
\(\Delta t\)
Time between two successive data points, e.g. two images (for fixed temporal resolution).
s
--
Q.GE1.006
Frequency
--
\(\nu\)
Frequency
1/s
--
Q.GE1.007
Axial length
--
\(L_{ax}\)
The axial length of a cylindrical object, e.g. a capillary.
\(\mu m\)
--
Q.GE1.008
Axial position
--
\(x_{ax}\)
The spatial position within a cylindrical object, e.g. a capillary. In the case of a capillary x=0 denotes the arterial inlet position and x=Lax the venous outlet position.
\(\mu m\)
--
Q.GE1.009
Constant value
--
\(k\)
A constant value which can be used e.g. for scaling.
variable
--
Q.GE1.010
Lower threshold
--
\(L\)
The lower value at which the behavior of a function or algorithm changes.
variable
--
Q.GE1.011
Upper threshold
--
\(U\)
The upper value at which the behavior of a function or algorithm changes.
variable
--
Q.GE1.012
Dynamic function
--
\(f(x)\)
A function of an independent variable x (typically time or frequency) with value \(f(x_i)\) at data grid point \(x_i\).
variable
--
Q.GE1.013
Start of range
--
\(x_{start}\)
The start point of the range [\(x_{start}\), \(x_{end}\)].
variable
--
Q.GE1.014
End of range
--
\(x_{end}\)
The end point of the range [\(x_{start}\), \(x_{end}\)].
variable
--
Q.GE1.015
Sample size
--
\(n\)
The number samples within a data set.
variable
--
Q.GE1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
Descriptive parameters describe the shape of a data set sampled at a data grid, but do not offer a direct physiological interpretation.
The data set is often the measured MR signal sampled at specified time points, but it can also be some normalized version of it, or a derived signal such as dynamic concentration time curve or dynamic relaxation rate curve derived from an MR signal.
To keep the inputs of these processes flexible, they are all defined for general data \(f(x_i)\) on a data grid of points \(f(x_i)\) and it is left to the user to specify the data and data grid these processes are applied to (e.g. [Tissue indicator concentration (Q.I.002) , Time (Q.G.004)]).
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.CD1.001
Data value at data grid point
--
\(f(x_i)\)
The data value at the data grid point \(x_i\).
variable
--
Q.CD1.002
Maximum value
--
\(f_{max}\)
The maximum value of given data.
variable
--
Q.CD1.003
Data grid point of maximum value
--
\(x_{max}\)
The data grid point at which the maximum value of a given data set occurs.
variable
--
Q.CD1.004
Minimum value
--
\(f_{min}\)
The minimum value of given data.
variable
--
Q.CD1.005
Data grid point of minimum value
--
\(x_{min}\)
The data grid point at which the minimum value of a given data set occurs.
variable
--
Q.CD1.006
Final data value
--
\(f_{fin}\)
The value of the data at the last data grid point.
variable
--
Q.CD1.007
Final data grid point
--
\(x_{fin}\)
The last point of a given data grid.
variable
--
Q.CD1.008
Maximum deviation from baseline
--
\(\Delta f_{BL, max}\)
The maximum absolute deviation of a given data set from the baseline.
variable
--
Q.CD1.009
Derivative at data grid point \(x_i\)
--
\(\frac{df(x_{i})}{dx}\)
Derivative of a function f with respect to the independent variable x at the data grid point \(x_i\).
variable
--
Q.CD1.010
Time to peak
--
TTP
The time between the bolus arrival time (BAT) and the maximum time point xmax: \(TTP = x_{max} - BAT\) (Remark: this is expressed for time rather than a general data grid, because TTP is an often used parameter in perfusion analysis).
variable
--
Q.CD1.011
Wash-in-slope
--
WIS
The ratio of the difference of the maximum data value \(f_{max}\) and the baseline value \(f_{BL}\) and the time to peak: \(WIS = \frac{f_{max}-f_{BL}}{TTP}\)
\(\frac{variable_{1}}{variable_{2}}\)
--
Q.CD1.012
Wash-out-slope
--
WOS
The ratio of the difference of the maximum data value \(f_{max}\) and the data value at the last data grid point \(f_{fin}\) and difference between the last time point and the time at which the maximum occurs: \(WOS = \frac{f_{max}-f_{fin}}{x_{max}-x_{fin}}\)
\(\frac{variable_{1}}{variable_{2}}\)
--
Q.CD1.013
Area under curve
--
\(AUC_{x_{start}, x_{end}}\)
The integral value of a given dynamic function f (or the numeric approximation for discrete data \([f_{1}, ...f_{n}]\) ) between the data grid points \(x_{1}\) and \(x_{2}\).
\(variable_{1} * variable_{2}\)
--
Q.DC1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This section lists all quantities related to the estimation process of the bolus arrival time of a data curve.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.BA1.001
Bolus arrival time
Onset Time, Lag Time
BAT
The time between the first data grid point and the onset obtained by applying a specified BAT estimation method.
variable
--
Q.BA1.002
Intersection- based BAT estimation parameters
--
[N]
Vector of ordered inputs to the intersection-based BAT estimation process.
--
--
Q.BA1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This section lists all quantities related to the estimation process of the baseline of a data curve.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.BL1.001
Baseline value
--
fBL
The value of a series of data of constant values in the beginning of a data set before the behavior of the data set changes. The baseline value is obtained by applying the baseline estimation process.
variable
--
Q.BL.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This section lists all quantities related to the estimation process of the baseline of a data curve.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.DM1.001
Unit step model parameters
--
[T]
Vector of ordered inputs to the unit step model (M.DM1.001).
[variable units]
--
Q.DM1.002
Linear-quadratic model parameters
--
[BAT, fBL, \(\beta_{1}\), \(\beta_{2}\)]
Vector of ordered inputs to the linear quadratic model (M.DM1.002).
[variable units]
--
Q.DM1.003
Two step linear model parameters
--
[BAT, fBL, b1]
Vector of ordered inputs to the two step linear model (M.DM1.003).
[variable units]
--
Q.DM1.004
Three step linear model parameters
--
[BAT, fBL, \(\beta\), b1, b2]
Vector of ordered inputs to the three step linear model (M.DM1.004).
[variable units]
--
Q.DM1.005
Multi-exponential model parameters
--
[A1, ...An, a1, ...an]
Vector of ordered inputs to the multi-exponential model (M.DM1.005).
[variable units]
--
Q.DM1.006
Gamma-variate model parameters
--
[BAT, \(\alpha\), \(\beta\)]
Vector of ordered inputs to the gamma-variate model (M.DM1.006).
[variable units]
--
Q.DM1.007
Fermi model parameters
--
[F, a, b]
Vector of ordered inputs to the Fermi model (M.DM1.007).
[variable units]
--
Q.DM1.008
Normal distribution model parameters
--
[\(\mu\), \(\sigma\)]
Vector of ordered inputs to normal distribution model (M.DM1.008).
[variable units]
--
Q.DM1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
Leakage correction model parameters are typically ad-hoc correction factors for physical models that are not purely descriptive but are not derived from rigorous physical models, therefore they are not listed in the physiological quantities group.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.LC1.001
Uncontaminated R2* scaling term
--
K1
Scaling constant for the uncontaminated effective transverse relaxation rate in the BSW leakage correction model and Bidirectional leakage correction model.
--
--
Q.LC1.002
Leakage scaling term
--
K2
Scaling constant which reflects the effects of leakage in the BSW leakage correction model and Bidirectional leakage correction model.
1/s
--
Q.LC1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This section is currently work in progress
In this group commonly used quantities to describe uncertainties of the extracted parameters and other statistical properties in the context of perfusion image analysis.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.US1.001
Arithmetic mean (sample)
Average
\(\bar{x}\)
The mean value of a given data sample [x1,...,xn], with sample size n, calculated as \(\bar{x}=\frac{1}{n}\sum_{i=1}^{n}x_i\).
variable
--
Q.US1.002
Geometric mean (sample)
--
\(\bar{x}_{geom}\)
The mean value of a given data sample [x1,...,xn], with sample size n, calculated as \(\bar{x}_{geom}=\sqrt[n]{\prod_{i=1}^{n}x_i}\)
variable
--
Q.US1.003
Variance (sample)
--
s2
Mean squared deviation of the mean of a given data set [x1,...,xn] with sample size n and mean value \(\bar{x}\), calculated as \(s^2=\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}\).
variable2
--
Q.US1.004
Standard deviation (sample)
--
s
The standard deviation of the mean value of a given data set [x1,...,xn] with sample size n and mean value \(\bar{x}\) , calculated as \(s^2=\sqrt{\frac{\sum_{i=1}^{n}(x_i-\bar{x})^2}{n-1}}\).
variable
--
Q.US1.005
Median value (sample)
--
xmedian
Centermost point \(x_{\frac{n+1}{2}}\) of ordered data points \(\left[x_{1}\leq x_{2}...\leq x_{n-1}\leq x_{n}\right]\) for an odd number of samples or the average of the two centermost points \(\frac{x_{n/2}+x_{n/2+1}}{2}\) for an even number of samples.
variable
--
Q.US1.006
Coefficient of variation (sample)
--
CV
The standard deviation (sample) s of a given data set divided by the mean value (sample) \(\bar{x}\) same dataset (only applicable to ratio scaled variables), calculated as \(CV=\frac{s}{\bar{x}}\)
variable
--
Q.US1.007
Mean (population)
--
\(\mu _{x}\)
The mean is a parameter used to characterize the center of a population distribution of the quantity x. (Remark: For simplicity the subscript x can be omitted.)
variable
--
Q.US1.008
Standard error of the mean
Standard error
SEM
The SEM quantifies how precisely the population mean \(\mu _{x}\) is estimated from the sample mean. \(\bar{x}\) of a sample of size n : \(SEM = \frac{s}{\sqrt{n}}\)
variable
--
Q.US1.009
Variance (population)
--
\(\sigma_{x}^2\)
The variance is a parameter used to characterize the amount of variation or dispersion of a population distribution of the quantity x. (Remark: For simplicity the subscript x can be omitted.)
variable2
--
Q.US1.010
Standard deviation (population)
--
\(\sigma_{x}\)
The standard deviation is a parameter used to characterize the amount of variation or dispersion of a population distribution of the quantity x. (Remark: For simplicity the subscript x can be omitted.)
variable
--
Q.US1.011
Estimated variance (population)
--
\(\hat{\sigma_x^2}\)
The estimated variance of a population distribution of the quantity x.
variable
--
Q.US1.012
Estimated covariance
--
\(\hat{\sigma_{xy}^2}\)
The estimated covariance of two quantities x and y.
variable
--
Q.US1.013
Range
--
r
The range of a dataset \(\left[ x_1, ..., x_n \right]\) is given as \(r = \left[ x_{min}, x_{max} \right]\)
variable
--
Q.US1.014
Interquartal range
--
IQR
The interquartile range of a data set \(\left[ x_1, ..., x_n \right]\) is determined by dividing the ordered data into 4 equally sized groups with \(\geq 25\%\) of values \(\leq Q_1\) and \(\geq 75\%\) of values \(\leq Q_3\) and calculating \(IQR=Q_3-Q_1\).
variable
--
Q.US1.015
Gamma-quantile value
--
\(\gamma\)
The number \(0 \leq \gamma \leq 1\) defining the \(\gamma\)-quantile.
--
--
Q.US1.016
Gamma-quantile
\(\left( \gamma * 100\% \right)^{th}\) percentile
\(f_\gamma\)
For \(0 \leq \gamma \leq 1\), \(f_\gamma\) is the \(\gamma\)-quantile of a distribution if \(\gamma * 100\%\) of the values (distributed according to f) lie below \(f_\gamma\) and \((1-\gamma) * 100\%\) of the values lie above it.
--
--
Q.US1.017
Percentile range
--
PR
The difference between two \(\gamma\)-quantiles \(f_{\gamma_1} - f_{\gamma_2}\).
--
--
Q.US1.018
Confidence interval probability
--
\(\alpha\)
The probability \((1-\alpha)\%\) with which a confidence interval covers a population parameter.
--
--
Q.US1.019
Confidence interval
--
CI
The interval which contains a population parameters with a probability of \((1-\alpha)\%\).
--
--
Q.US1.020
Signal to noise ratio
--
SNR
The mean value (sample) of a given data set \(\bar{x}\) divided by the standard deviation (sample) s from the same dataset: \(\frac{\bar{x}}{s}\)
--
--
Q.US1.021
Contrast to noise ratio
--
CNR
The absolute deviation of a given data value \(f_1\) from another data value \(f_2\), divided by the standard deviation s (noise), all from the same data set: \(\frac{\left\| f_1 - f_2 \right\|}{s}\)
--
--
Q.US1.022
Contrast ratio
--
CR
The absolute deviation of a given data value \(f_1\) from another data value \(f_2\), divided by the sum of the two data values: \(\frac{\left\| f_1 - f_2 \right\|}{f_1 + f_2}\)
--
--
Q.US1.023
Sum of squared errors
--
SSE
\(SSE = \sum_{i=0}^{N}\left[ f(t_i) - f_{model}(t_i)\right]^2\), where N is the number of samples, \(f(t_i)\) measured value and \(f_{model}(t_i)\) is the modeled value. This is valid for linear and non-linear least-squares optimization.
variable
--
Q.US1.024
Goodness-of-fit parameter
--
\(\chi^2\)
\(\chi^2 = \frac{SSE}{\sigma_N^2}\), where \(\sigma_N^2\) is the random noise variance. This is valid for linear and non-linear least-squares optimization.
--
--
Q.US1.025
Degrees of freedom
--
df
\(N-p\), where N is the number of samples and p is the number of quantities to be determined e.g. model parameters.
--
--
Q.US1.026
Akaike-information-criterion
--
AIC
\(AIC = 2p + Nln(SSE)\), where p is the number of model parameters, N is the number of samples. This is valid for linear and non-linear least-squares optimization.
--
--
Q.US1.027
Jacobian matrix
--
J
J is a matrix of the first derivatives of a function f(x) with respect to the parameters \(p_1,...,p_n\): \(J_{ij}(x) = \left[ \frac{df_j(x)}{dp_i} \right]\)
variable
--
Q.US1.028
Hessian matrix
--
H
H is a matrix of the second derivatives of a function f(x) with respect to the parameters \(p_1,...,p_n\): \(H_{ij}(x) = \frac{\partial^2f(x)}{\partial p_i \partial p_j}\)
variable
--
Q.US1.029
Covariance matrix
--
Cov
\(Cov = (J^T \cdot J)^{-1} \cdot \frac{SSE}{df}\)
variable
--
Q.US1.030
Cramer Rao lower bound
--
CRLB
Lower bound on the variance of any unbiased estimator.
variable
--
Q.US1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
A vector of the known quantities of a forward model. Select from section Q.
[variable units]
--
Q.AI1.002
Model parameters
--
MP
A vector of the quantities to be determined by the analytical inversion of a forward model. Select from section Q.
[variable units]
--
Q.AI1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
In this group, quantities related to optimization methods are listed. In this version, only least squares optimization methods are considered. Approaches that use e.g. maximum likelihood estimation, bayesian inference, machine learning will be taken into account in future versions of the lexicon.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.OP1.001
Model parameters
--
\(\phi\), MP
A vector of quantities which are the variable of the model fitting process. Select from section Q.
[variable units]
--
Q.OP1.002
Static model parameters
--
\(\theta\), SMP
A vector of the quantities of the forward model to be fitted which are not in the scope of the optimization. Select from section Q.
[variable units]
--
Q.OP1.003
Estimated model parameter
--
\(\hat{\phi}\), EMP
A vector (in the same order as model parameters, indicated with “^”) of the estimated model parameters resulting from the optimization process.
[variable units]
--
Q.OP1.004
Cost value
--
C
The scalar or vectorial value of a specified cost function.
[variable units]
--
Q.OP1.005
Cost value minimum
--
\(C_{opt}\)
The minimum cost value as returned by an optimizer. This can be a local or global minimum.
[variable units]
--
Q.OP1.006
Initial model parameters
--
\(\phi_{init}\)
Vector of the starting values of the search for the model parameters.
[variable units]
--
Q.OP1.007
Model parameter lower bounds
--
\(\phi_{LB}\)
Vector of the lower bounds for the search for the model parameters.
[variable units]
--
Q.OP1.008
Model parameter upper bounds
--
\(\phi_{UB}\)
Vector of the upper bounds for the search for the model parameters.
[variable units]
--
Q.OP1.009
Data weights
--
\(\omega\)
Vector of weights on the measured values during the optimization process.
--
--
Q.OP1.010
Maximum number of iterations
--
\(N_{it, max}\)
Largest number of steps taken in an iterative optimization.
-
--
Q.OP1.011
Convergence threshold
--
e
Convergence threshold on the optimizer.
--
--
Q.OP1.012
Linear coefficients matrix
--
A
A matrix with elements Aij with which a function linear in the model parameters can be expressed as \(f(\phi;x_i)= \sum_{j=1}^{m}A_{ij}\phi_j\). The \(A_{ij}\) contain the data grid and the static model parameters.
--
--
Q.OP1.013
Regularization parameter
--
\(\lambda\)
A parameter which determines the weight of the regularization in an optimization.
--
--
Q.OP1.014
Normalized regularization parameter
--
\(\hat{\lambda}\)
The regularization parameter is expressed relative to the largest singular value \(\sigma_1\) of a SVD: \(\hat{\lambda}=\frac{\lambda}{\sigma_1}\) .
--
--
Q.OP1.015
Fixed \(\lambda\) value
--
\(\lambda_{fixed}\)
A fixed value, e.g. a literature value, assumed as regularization parameter.
--
--
Q.OP1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
The items of this group are quantities which are required to describe arterial input function estimation methods.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.AE1.001
k-means-cluster-algorithm-parameters
--
[k]
Vector of ordered inputs to the k-means AIF detection algorithm.
[variable units]
--
Q.AE1.002
Fuzzy-c-means-cluster-algorithm-parameters
--
[m, \(\epsilon\), c, Pc, ci]
Vector of ordered inputs to the fuzzy-c-means AIF detection algorithm.
[variable units]
--
Q.AE1.003
Partial-volume corrected
--
PVE
If the value of this flag is 1, partial volume effects are accounted for. Otherwise, or if not specified, no partial volume effect correction was done.
--
--
Q.AE1.004
Dual Bolus
--
DB
The full-dose AIF is reconstructed from pre-bolus injection with a smaller dose. If the value of this flag is 1, a dual bolus approach is used. Otherwise, or if not specified, no dual bolus approach is used.
A factor that scales signal or indicator concentrations measured in a partial volume affected artery such that partial volume effects are removed. Usually this is estimated by deconvolving arterial and venous signals or indicator concentrations.
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.
This group contains quantities related to the process of image segmentation.
Code
OSIPI name
Alternative names
Notation
Description
OSIPI units
Reference
Q.SE1.001
Binary mask
--
Mask
Binary mask of segmented region of interest.
--
--
Q.SE1.002
Binary AIF mask
--
AIF mask
Binary mask of a vessel in which the arterial input function is estimated.
--
--
Q.SE1.003
Binary ROI mask
--
ROI mask
Binary mask of a tissue region of interest.
--
--
Q.SE1.004
Seeds
--
[seeds]
Vector of ordered voxel coordinates of seed points for seed based segmentation (e.g. region growing segmentation).
--
--
Q.SE1.005
Number of k–means clusters
--
Nk-means
Number of clusters in the k-means clustering algorithm.
--
--
Q.SE1.999
Quantity not listed
--
--
This is a custom free-text item, which can be used if a quantity of interest is not listed. Please state a literature reference and request the item to be added to the lexicon for future usage.