Arterial Input Function¶

Every convolution model requires the plasma concentration curve \(C_p(t)\) delivered to the tissue. ROCKETSHIP measures this curve from arterial voxels in the dynamic series itself, and optionally replaces the measured samples with a fitted analytic form before the tissue models use it.

The arterial input function is the single largest source of systematic error in quantitative DCE-MRI. Because it appears in every model as the input to a convolution, an error in its amplitude propagates directly and proportionally into \(K^{trans}\) for every voxel in the image.

Curve modes¶

The aif_mode option selects where the curve comes from and whether it is fitted.

Mode	Behavior
`fitted`	Take samples from the arterial mask and replace them with a fitted biexponential
`raw`	Take samples from the arterial mask and use them unmodified
`imported`	Load a previously saved curve from `imported_aif_path` and never fit it

Fitting suppresses noise in the input curve, at the cost of imposing a shape the data may not support. The raw mode preserves everything the acquisition measured, including its noise. The imported mode allows a curve measured elsewhere, or a population average built from several subjects, to be substituted.

The fitted model¶

The analytic form is a linear upslope followed by a biexponential decay, constrained to be continuous at the junction:

\[ C_p(t) = \begin{cases} 0 & t < t_{base} \\[2ex] (A + B)\,\dfrac{t - t_{base}}{t_{0} - t_{base}} & t_{base} \le t < t_{0} \\[2ex] A\,e^{-c\,(t - t_{0})} + B\,e^{-d\,(t - t_{0})} & t \ge t_{0} \end{cases} \]

Here \(t_{base}\) is the end of the pre-contrast baseline, \(t_{0}\) is the end of the upslope, and the curve peaks at \(A + B\) where the two segments meet. The two decay rates \(c\) and \(d\) describe first pass washout and the slower recirculation and clearance phase respectively.

Where the curve being fitted is in arbitrary signal intensity units rather than concentration, a constant baseline offset is added to all three segments, so that the ramp climbs from the baseline and the decay relaxes back towards it.

Fit parameters¶

Parameter	Symbol	Role
First decay amplitude	\(A\)	Amplitude of the fast washout term
Second decay amplitude	\(B\)	Amplitude of the slow clearance term
First decay rate	\(c\)	Fast washout rate constant
Second decay rate	\(d\)	Slow clearance rate constant

The four values are configured as vectors in \([A, B, c, d]\) order through the aif_initial_values, aif_lower_limits and aif_upper_limits options. Convergence is controlled by aif_TolFun, aif_TolX, aif_MaxIter and aif_MaxFunEvals.

The two transition times \(t_{base}\) and \(t_{0}\) are not free parameters of this fit. They are resolved beforehand, as described below.

Baseline and injection timing¶

The end of the baseline, \(t_{base}\), determines which frames are averaged to form the pre-contrast signal, and therefore anchors the entire concentration conversion. It is resolved with the following precedence:

An explicit steady_state_end in the run configuration.
A SteadyStateEndTimeIndex field in the JSON sidecar accompanying the arterial mask.
Automatic detection, using the method named by steady_state_auto_method.

The sidecar mechanism is the recommended way to pin a fixed, reproducible baseline for a particular dataset, since it travels with the data rather than with the run configuration. The index it carries counts acquired frames, before any trimming of the analysis window, so it identifies the same physical timepoint however the window is set.

Several automatic detectors are available, differing in how they identify the departure from baseline. The default is a total variation denoising method that locates the first statistically significant upward step. Alternatives include a Sobel edge heuristic, a piecewise constant split, a generalized likelihood ratio change detector, and a full biexponential fit that resolves both transition times simultaneously.

The start of the injection is defined as the resolved end of the baseline; there is no separate option for it. Move it by changing the baseline resolution above.

Robust fitting and peak weighting¶

The bolus peak is frequently the least reliable sample in the curve. It is a single frame, often affected by inflow, partial volume and \(T_2^{*}\) effects at high concentration, and in this model it has full leverage: the model's maximum \(A + B\) can be placed exactly on it. A conventional robust estimator, which identifies outliers by their residuals, therefore cannot detect an inflated peak, because the fit simply interpolates it.

Two independent mechanisms are available:

aif_Robust selects a residual-based robust estimator for the fit: off for ordinary least squares, Bisquare for Tukey biweight iteratively reweighted least squares, or LAR for a soft L1 loss. The default is off.
aif_peak_weight_exponent de-weights the peak sample using the shape of the curve rather than the residuals. The weight is derived from how far the peak stands above the rest of the curve, relative to the next largest sample, raised to this exponent. The default is 2; setting it to 0 disables the mechanism.

Leaving the peak at full weight tends to spend one of the two exponentials reaching that single sample, at the expense of describing the washout, which degrades the fit everywhere else.

Averaging across subjects¶

A population average input function can be built by reading the arterial curves from several completed runs and averaging them. This is useful where individual arterial measurements are unreliable, at the cost of removing genuine between-subject variation in cardiac output and injection dynamics.

Quality control¶

With save_aif_figure enabled, which is the default, the pipeline writes a figure showing the measured samples against the fitted curve, with the resolved baseline end and upslope end marked. Inspect this figure for every run. A poorly resolved baseline, a truncated first pass, or a fit that misses the peak are all immediately visible here and all invalidate every downstream parameter.

Configuration¶

The relevant options are documented in full in the DCE Options reference, under the Stage B AIF fit and acquisition timing sections.