.. _co_correct_top:
Cardiac Output Measurement and Correction
=========================================
.. contents::
:depth: 1
:local:
:backlinks: top
Cardiac Output Measurement and Correction Tool
----------------------------------------------
The **Cardiac Output Measurement and Correction** tool (under the
**Dynamic Analysis** group) enables constrained signal-to-concentration
conversion based on the subject’s cardiac output (CO). This operation
limits the errors in the contrast concentration in the blood,
which is often required in DCE MRI model analysis, but is
challenging to measure accurately.
The MRI signal in the blood may be affected by multiple issues,
such as the inflow artifact, limited temporal resolution,
partial volume effects, and image inhomogeneity, among others.
In compartmental model analysis of DCE MRI data, the errors in
the arterial input function (AIF) are the main source of errors
in model parameters. For example, the Tofts-Kety model
(`Tofts 1999 PMID: 10508281 `__)
parameters K\ :sup:`trans` and ve scale nearly proportionally with the AIF,
and the AIF errors propagate into the parameters errors in a similar way.
The inflow artifact arises when unsaturated spins (which have not seen
the excitation pulse) in flowing blood move into the imaging slab and
result in artificially high signal intensity of blood (higher than
in a stationary tissue with the same T\ :sub:`10` value as blood).
The inflow artifact may cause up to 100% errors in K\ :sup:`trans` along
the length of the vessel when a fixed T\ :sub:`10` value is used to convert
the blood to concentration.
The CO-based correction tool limits the errors that arise from
the inaccurate baseline signal in blood.
.. _aifcorrect_basics:
CO-Based Correction Basics
--------------------------
The constrained conversion method is a post-correction method
that constrains the are under the first pass of the arterial
concentration based on the Stewart-Hamilton principle.
The Stewart-Hamilton principle relates the injected dose of contrast
(in mmol), the subject’s cardiac output (CO, L/min), and the area under
the curve (AUC, mmol/L x min) of the first pass peak of the arterial curve:.
.. math::
:label: stew-ham
\text{AUC} = \frac{\text{Dose}}{\text{CO}}.
This equation constrains the magnitude of the first pass peak
of the blood concentration for a known contrast dose and CO.
If the blood concentration fails to satisfy Eq. :eq:`stew-ham`,
the baseline of the corresponding blood signal can be altered
so that .
In its initial implementation, this method was shown to reduce
the variations of the AIF variations and kidney parameters in repeated
measurements in the same patients
(`Zhang 2009 PMID: 19711414 `__).
The CO-based correction makes several **assumptions**:
- The arterial signal S(t) consists of the bolus curve S\ :sub:`b`\ (t) shifted
by an additive baseline S\ :sub:`0`;
- The errors in the arterial concentration are caused
by (i) incorrect baseline OR (ii) by incorrect flip angle;
- These errors are reduced by replacing the original baseline S\ :sub:`0`
with the corrected baseline signal S\ :sub:`0c`, for which
the AUC of the first peak satisfies the Stewart-Hamilton principle
(Eq. :eq:`stew-ham`).
- The corrected signal is obtained by shifting the bolus curve to the corrected
baseline: S\ :sub:`c`\ (t) = S\ :sub:`0c` + S\ :sub:`b`\ (t).
:red:`(Alternatively, only the baseline signal can be adjusted OR
the flip angle can be corrected.)`
- After S\ :sub:`c`\ (t) is converted to concentration, it yields
the corrected blood curve C\ :sub:`c`\ (t).
.. _aifcorrect_algorithm:
CO-Based Correction Algorithm
-----------------------------
The algorithm takes the blood signal S(t) as the input, for which
the bolus arrival time (BAT), the baseline signal S\ :sub:`0`,
the recirculation time (RCT) are determined. RCT is the time point after
the first pass peak and before the start of the recirculation peak.
.. _co_algorithm:
.. figure:: ../images/co_diagram.png
:alt: CO-based correction algorithm diagram
:scale: 50%
:align: center
:figclass: align-center
CO-based correction algorithm diagram.
Next, the baseline is iteratively shifted in increments within the range:
S\ :sub:`k`\ (t) = S\ :sub:`b`\ (t) + :math:`{\Delta}` x k, where k = [-N, N]
and :math:`{\Delta}` = S\ :sub:`0`\ /2N by default.
At each iteration, the signal S\ :sub:`k`\ (t) is converted to concentration
C\ :sub:`k`\ (t). The first pass peak (defined as the part of C\ :sub:`k`\ (t)
between BAT and RCT) is fitted with gamma variate function and the AUC\ :sub:`k`
under the first pass is determined.
This AUC\ :sub:`k` and the injected contrast dose (in millimoles) are used
to estimate cardiac output CO\ :sub:`k` based on Stewart-Hamilton principle
(Eq. :eq:`stew-ham`).
After all iterations are completed, the curve C\ :sub:`k`\ (t) that minimizes
the difference between the estimated CO\ :sub:`k` and the actual CO value
provided by the user. This concentration is returned as the corrected
concentration C\ :sub:`c`\ (t).
.. _aifcorrect_co_estimates:
CO Estimates
~~~~~~~~~~~~
The CO required for the constrained conversion can be measured by
several different methods, which include noninvasive (Doppler ultrasound,
echocardiography, cardiac MRI, modified carbon dioxide Fick method),
and invasive (oxygen Fick method, lithium dilution)
(see `Physiology, Cardiac Index `__).
The agreement among the measurements made by these methods is modest
(`Maeder 2015 PMID: 25728504 `__).
Alternatively, the CO (in L/min) may be estimated as
.. math::
:label: co_ci_bsa
\text{CO} = \text{CI} \times \text{BSA},
where CI (L/min/m\ :sup:`2`\) is the cardiac index
and BSA (m\ :sup:`2`\) is the body surface area.
For practical purposes, the cardiac index may be assumed to be constant
in relatively healthy subjects. Studies have shown that CI *at rest* in subjects
*without severe heart disease* does not significantly vary with age, sex, body mass
index, overweight, and fitness
(`Wolsk 2017 PMID: 28017352 `__).
A small decrease of CI with age was observed
in some studies, but it was not found in all studies
(`Cioccari 2019 PMID: 30857507 `__).
The CI *during exercise* does vary with age
and it is decreased in patients with heart disease
(`Carlsson 2012 PMID: 22839436 `__).
BSA can be calculated using one of several
`BSA formulas `__
using the subject's weight and height, such as the classic Du Bois formula
(`Du Bois 1916 PMID: 2520314 `__):
.. math::
:label: dubois_bsa
\text{BSA} = 0.007184 \times \text{W}^{0.425} \times \text{H}^{0.725},
where W is the subject's weight in kilograms, and H is the height in centimeters.
.. _aifcorrect_dialog:
CO-Based Correction Dialog
--------------------------
The constrained conversion is accessed by selecting **Dynamic Analysis** >
**CO Measurement and Correction**, which is accessible both with and without
images. This command opens a dialog panel that enables the user to
select parameters for this operation and view the results. The top part
of the panel shows the plot of the signal or concentration data.
The bottom part has the controls for setting up the methods.
The routine consists of two steps:
1. **CO Measurement.** The CO is estimated from the concentration curve
obtained using regular signal-to-concentration conversion,
2. **Concentration Correction.** Corrected concentration is computed using the CO-based
constrained conversion with the *actual* (measured or estimated)
CO value entered by the user.
These steps are described in detail below.
1. **CO Measurement.**
- Click **Load** to load the blood signal or concentration curve.
This curve must be previously saved as a text file with two columns:
(1) time and (2) signal (or concentration).
Any additional columns will be ignored.
- If the loaded curve is concentration versus time
(e.g., previously converted using **Dynamic Analysis** >
**Concentration Conversion**), then no further processing is required.
Make sure that the box next to the **Conversion** button reads
**No Conversion** and proceed to the next step.
.. _fig_co_dialog_si:
.. figure:: ../images/co_dialog_si.png
:alt: CO Correction dialog after loading signal data
:scale: 70%
:align: center
:figclass: align-center
CO Correction dialog with signal data just loaded.
The green line indicates RCT.
- If the loaded curve is signal versus time (:numref:`fig_co_dialog_si`),
configure the signal-to-concentration conversion.
Click **Attributes** to enter the T10 for blood in seconds
(default T10 = 1.4 s). Next, click **Concentration** to open
the :ref:`Concentration Conversion ` dialog.
Use this dialog to set the conversion method, baseline definition,
and parameters (TR, FA, contrast agent relaxivity). Click **OK**.
- The concentration curve will be displayed in the plot area (FIG?)
along with the first pass and gamma variate fit.
The visibility of these curves can be turned on and off using check boxes
below the plot. The curve colors can be changed by clicking the color swatches,
which open color picker palettes.
- Determine the recirculation time (RCT). By default, RCT is determined
automatically upon loading data and also when the user clicks
**Recirculation start** button.
Alternatively, the user may set the RCT manually by clicking the plot area
at the start of the recirculation peak.
- Enter the contrast **Dose** in **millimoles** (NOT milliliters).
- The parameters **Gamma variate precision** (default 50)
and **Cardiac output precision** (default 500) 8i ø
set the precision (stopping criteria) for the iterative
process. Lower precision values will result in faster processing,
but less reliable estimate.
- Click **Estimate CO** to compute the CO corresponding to the uncorrected data.
This command will populate the corresponding text box with the CO (L/min).
This estimated CO value may be outside of the normal physiological range
if the blood signal is distorted by artifacts.
2. **Concentration Correction.**
- To obtain the corrected concentration, enter the subject's CO value
(in L/min), measured or estimated) into the text box labeled **Actual CO**
in the section labeled **Input Function correction**.
- Select the correction **Method** from the dropdown menu: |br|
(i) Shift whole curve vertically, |br|
(ii) Shift pre-contrast points vertically, |br|
(iii) Adjust flip angle.
- Next, click **Correct**. This will begin the iterative process.
After processing is finished, the corrected curve will be displayed
in the plot area (:numref:`fig_co_dialog_conc`).
- To save the uncorrected curve (the curve obtained using regular conversion),
click **Save original**. The uncorrected concentration will be saved as
a text file. To save the corrected curve as a text file, click **Save corrected**.
By default, these files are saved in the Temp folder inside the FireVoxel directory.
|top|
.. _fig_co_dialog_conc:
.. figure:: ../images/co_dialog_conc.png
:alt: CO-based correction dialog showing corrected concentration
:scale: 70%
:align: center
:figclass: align-center
CO-based correction dialog showing corrected concentration (yellow)
and original concentration (blue). Estimated CO=11.75 L/min.
Actual CO = 4.79 L/min.