dcmri module

dcmri.chain_propagator(t, MTT, dispersion)

dcmri.compartment_propagator(t, MTT)

dcmri.concentrationSPGRESS(S, S0, T10, FA, TR, r1)

Calculates the tracer concentration from a spoiled gradient-echo signal.

Parameters

• S (Signal S(C) at concentration C) –

• S0 (Precontrast signal S(C=0)) –

• FA (Flip angle in degrees) –

• TR (Repetition time TR in msec (=time between two pulses)) –

• T10 (Precontrast T10 in msec) –

• r1 (Relaxivity in Hz/mM) –

Return type

Concentration in mM

dcmri.convolve(u, tc, c, th, h)

dcmri.expconv(T, time, a)

Convolve a 1D-array with a normalised exponential.

expconv() uses an efficient and accurate numerical formula to calculate the convolution, as detailed in the appendix of Flouri et al., Magn Reson Med, 76 (2016), pp. 998-1006.

Note (1): by definition, expconv preserves the area under a(time) Note (2): if T=0, expconv returns a copy of a

Parameters

• a (numpy array) – the 1D array to be convolved.

• time (numpy array) – the time points where the values of ca are defined these do not have to to be equally spaced.

• T (float) – the characteristic time of the the exponential function. time and T must be in the same units.

Return type

a numpy array of the same shape as ca.

Example

coming soon..

dcmri.injection(t, weight, conc, dose1, rate, start1, dose2=None, start2=None)

dose injected per unit time (mM/sec)

dcmri.injection_gv(t, weight, conc, dose, rate, start1, start2=None, dispersion=0.5)

dose injected per unit time (mM/sec)

dcmri.linear(x, x1, x2, y1, y2)

returns a linear function of x that goes through the two points (xi, yi)

dcmri.propagate_2cxm(t, ca, KP, KE, KB)

Calculate the propagators for the individual compartments in the 2CXM

For details and notations see appendix of Sourbron et al. Magn Reson Med 62:672–681 (2009)

Parameters

• t (numpy array) – time points (sec) where the input function is defined

• ca (numpy array) – input function (mmol/mL)

• KP (float) – inverse plasma MTT (sec) = VP/(FP+PS)

• KE (float) – inverse extracellular MTT (sec) = VE/PS

• KB (float) – inverse blood MTT (sec) = VP/FP

Returns

• cp (numpy array) – concentration in the plasma compartment (mmol/mL)

• ce (numpy array) – concentration in the extracellular compartment (mmol/mL)

Examples

coming soon..

dcmri.propagate_chain(t, ci, MTT, dispersion)

dcmri.propagate_compartment(t, c, MTT)

Returns the average concentration at the outlet given the concentration at the inlet

dcmri.propagate_dd(t, c, MTT, TTD)

Propagate concentration through a serial arrangement of a plug flow and a compartment.

Parameters

• TTD (Transit Time Dispersion of the system) – This is the mean transit time of the compartment

• MTT (Mean Transit Time of the system) – This is the sum of delay and MTT of the compartment

Return type

Concentration at the outlet

dcmri.propagate_delay(t, c, delay)

dcmri.propagate_simple_body(t, c_vena_cava, MTTlh, Eint, MTTe, MTTo, TTDo, Eext)

Propagation through a 2-site model of the body.

dcmri.quadratic(x, x1, x2, x3, y1, y2, y3)

returns a quadratic function of x that goes through the three points (xi, yi)

dcmri.residue_chain(t, ci, MTT, dispersion)

Returns the (average) concentration inside the system given the concentration at the inlet

dcmri.residue_compartment(t, c, MTT)

Returns the concentration inside the system given the concentration at the inlet

dcmri.residue_high_flow_2cfm(t, ci, Ktrans, Te, FiTi)

Central compartment i with high flow (Ti=0) and filtration compartment e

dcmri.residue_high_flow_2cfm_varK(t, ci, Ktrans1, Ktrans2, Ktrans3, Te, FiTi)

Central compartment i with high flow (Ti=0) and filtration compartment e

dcmri.residue_high_flow_2cfm_varT(t, ci, Ktrans, Te1, Te2, Te3, FiTi)

Central compartment i with high flow (Ti=0) and filtration compartment e

dcmri.residue_high_flow_2cfm_varlinT(t, ci, Ktrans, Te1, Te2, FiTi)

Central compartment i with high flow (Ti=0) and filtration compartment e

dcmri.residue_high_flow_ccf(t, ci, Ktrans, Te, De, FiTi)

Residue for a compartment i with high flow (Ti=0) and a chain e

dcmri.sample(t, S, ts, dts)

Sample the signal assuming sample times are at the start of the acquisition

dcmri.signalBiExp(TR, R1, S0, A, a, b)

Descriptive bi-exponentional model for SPGRESS sequence.

S = S0 (1 - A e^(-ax) - (1-A) e^(-bx)) with x = TR*R1 0 < A < 1 0 < S 0 < a 0 < b

dcmri.signalSPGRESS(TR, FA, R1, S0)

dcmri.signal_genflash(TR, R1, S0, a, A)

Steady-state model of a spoiled gradient echo but parametrised with cos(FA) instead of FA and generalised to include rate. 0<S0 0<a -1<A<+1

dcmri.signal_hyper(TR, R1, S0, a, b)

Descriptive bi-exponentional model for SPGRESS sequence.

S = S0 (e^(+ax) - e^(-bx)) / (e^(+ax) + e^(-bx)) with x = TR*R1 0 < S 0 < a 0 < b