31. Cardiac Output Measurement and Correction

31.1. 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 Ktrans 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 T10 value as blood). The inflow artifact may cause up to 100% errors in Ktrans along the length of the vessel when a fixed T10 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.

31.2. 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:.

(31.1)\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. (31.1), 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 Sb(t) shifted by an additive baseline S0;

  • 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 S0 with the corrected baseline signal S0c, for which the AUC of the first peak satisfies the Stewart-Hamilton principle (Eq. (31.1)).

  • The corrected signal is obtained by shifting the bolus curve to the corrected baseline: Sc(t) = S0c + Sb(t). (Alternatively, only the baseline signal can be adjusted OR the flip angle can be corrected.)

  • After Sc(t) is converted to concentration, it yields the corrected blood curve Cc(t).

31.3. 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 S0, 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-based correction algorithm diagram

Fig. 31.1 CO-based correction algorithm diagram.

Next, the baseline is iteratively shifted in increments within the range: Sk(t) = Sb(t) + {\Delta} x k, where k = [-N, N] and {\Delta} = S0/2N by default.

At each iteration, the signal Sk(t) is converted to concentration Ck(t). The first pass peak (defined as the part of Ck(t) between BAT and RCT) is fitted with gamma variate function and the AUCk under the first pass is determined.

This AUCk and the injected contrast dose (in millimoles) are used to estimate cardiac output COk based on Stewart-Hamilton principle (Eq. (31.1)).

After all iterations are completed, the curve Ck(t) that minimizes the difference between the estimated COk and the actual CO value provided by the user. This concentration is returned as the corrected concentration Cc(t).

31.3.1. 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

(31.2)\text{CO} = \text{CI} \times \text{BSA},

where CI (L/min/m2) is the cardiac index and BSA (m2) 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):

(31.3)\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.

31.4. 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.

    CO Correction dialog after loading signal data

    Fig. 31.2 CO Correction dialog with signal data just loaded. The green line indicates RCT.

  • If the loaded curve is signal versus time (Fig. 31.2), 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 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.

  1. 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:
    (i) Shift whole curve vertically,
    (ii) Shift pre-contrast points vertically,
    (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 (Fig. 31.3).

  • 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.

    CO-based correction dialog showing corrected concentration

    Fig. 31.3 CO-based correction dialog showing corrected concentration (yellow) and original concentration (blue). Estimated CO=11.75 L/min. Actual CO = 4.79 L/min.