Jiming Zhang^{1}, Carlo Uribe^{2}, Benjamin Cheong^{1,2}, Paolo Angelini^{2}, and Raja Muthupillai^{1}

LV mass computed from commonly used bi-plane and tri-plane ellipsoidal models can deviate significantly when compared to LV mass estimated from a stack of short axis balanced SSFP cine MR images. The results from the study show that by using different geometric assumptions for the shape of the endocardium (Cut-cone+cone) and epicardium (Cut-cone+parabola), it is possible to estimate LV mass with just two projections that is comparable to that obtained from a full stack of short axis slices.

LV mass
calculated from the difference between epicardial and endocardial LV volumes is an independent predictor of risk in
cardiovascular disease. Echocardiography
and x-ray angiographic methods estimate LV volume from few select projections by making geometric assumptions
about the shape of LV. In contrast cardiac MRI (CMR) LV mass is calculated by delineating endo- and epicardial
contours on a stack of cine slices in the short-axis (SAx) orientation
without making any geometric assumptions.
Studies have shown that these CMR measurements are both accurate and
precise^{1,2}. However, acquiring
the SAx stack is time consuming and challenging for patients with
compromised respiratory function.
Previously we considered three new geometric models (in addition to the
conventional biplane and triplane models) to capture the shape of LV (Figure 1)
and demonstrated that LV volumes estimated from a sub-set of projections were comparable
to the values obtained from a fully sampled dataset^{3}. However these models were not evaluated for
the estimation of LV mass.

In this work, we show that by modeling the endocardium and epicardium of the LV with distinct shapes, it is possible to obtain a reliable estimate of LV mass from as few as three projections and comparable to conventional geometric bi-plane and tri-plane models of the LV.

*
Patient population*: Data acquired from 980 middle
and high school kids (recruited as a part of an IRB approved sudden cardiac
death screening study) with no known history of heart disease (578 male, age:
12.6±1.1yrs, range: 10-15years) were used in this analysis.

*MRI
acquisition*: VCG gated cine balanced steady state free
precession images of the LV (spatial resolution 2x2x8mm^{3};
temporal resolution < 50 ms) were acquired within SAx
covering the whole LV, left ventricular outflow tract (LVOT) and horizontal
four chamber (4CH) orientations using a 32 Channel RF coil for signal
reception.

*
Data
analysis*: Endocardial and epicardial borders were
circumscribed on the stack of SAx slices acquired at end-diastole (ED).
Furthermore, the cross sectional endo- and epicardial areas of the SAx slice which
included the dominant papillary muscle (Ap) was also recorded. The
length of the left ventricle (measured from mitral annulus valve plane to the
endocardium of the apex) from 4CH and LVOT
orientations, as well as the diameter of
the left ventricle for both epi- and endo- myocardium at the level of the
mitral annulus in the 4CH and LVOT views was also recorded.

*LV
models*: In addition to the widely used biplane and
triplane models of the LV, we propose three additional models (parabola,
cutcone+prabola and cutcone+cone) to account for the shape of the LV. From this basis set, a total of fifteen models were constructed by considering
independent models for the endo- and epicardium (Figure 2).

*
Data analysis*: LV mass estimated from the stack of SAx slices
was considered as the reference measurement.
Five models used the same geometric model for both epicardium and
endocardium volume to calculate the LV mass and the remaining ten models used a
different geometric model for epicardium and endocardium. Bland-Altman analysis
of the percentage-error in the calculation of LV mass compared to the reference
measurement of all fifteen models is shown in Figure 2. (Expressed as bias ± 1 standard deviation ).

The average LV mass for this subject cohort calculated from fully sampled SAx data set is 60.7±17.9g. The main findings of this study are: Based on the result from Figure 2 and Bland-Altman plot of all data point for LV mass estimated from Triplane model and one best performed mixing model (Figure 3),

1. Among the mixed models (different model for end- and epicardium), the Cutcone+Parabola model for epi- and Cutcone+cone model for endocardial volumes yielded the least error for estimating LV mass (3%).

2. Bland-Altman analysis show that conventional triplane model underestimates LV mass by 6.2%, and the mixed model (endo: Cutcone+Cone, Epi: Cutcone+Parabola) overestimates LV mass by 3.2%.

3. Conventional geometric models: Biplane and Triplane model of the LV overestimate LV mass by 45% and underestimates LV mass by 6% respectively.

4. When the shape of the LV was assumed to be same for both endo-and epicardium, the LV mass calculated from the three proposed models resulted in substantial underestimation of LV mass (Figure 2).

1. In this cohort of young children, our results show that the estimation of LV mass using conventional geometric models such as biplane and triplane can result in significant errors.

2. Among the fifteen models considered, a mixed shape model (Cutcone+parabola for epicardium and Cut cone + cone model for endocardium) yields LV mass estimates with just two projections that are comparable to that obtained with a full stack of short axis slices.

1. Thiele, H et al. JCMR,4(3), 327-339,2002.

2. Malm, S et al. JACC, 44(5),1030-5,2004.

3. Zhang, J et al, ISMRM, 25 (2017): # 30.

Figure 1. Geometric models considered in the current study. A_{p}, and r_{2}:
area and radius from short-axis slice at papillary muscle level; L: longer
length from apex to base in 4CH and LVOT views; r_{1}: bigger half
width at mitral valve annulus in 4CH and LVOT views; h_{1}: length from
base to papillary muscle level; h_{2} = L – h_{1}; A_{1}
and A_{2}: area from 4CH and LOVT respectively.

Figure 2. Percentage error in LV mass estimated from Bland-Altman analysis (values
are given as Bias ± 1SD).

Figure 3. Bland-Altman plot of the percent error in LV mass calculated from
Triplane model (left), and a mixed model (right, cutcone+parabola model for
epicardium and cutcone+cone model for endocardium) versus LV mass calculated
from SAx stack. Solid and dashed black lines indicate bias and 1 standard
deviation from bias respectively. (Tp: Triplane; Epi: epicardium; Endo:
endocardium).