A Novel GMM-Based Estimated Splitting Coefficient of Second Heart Sound for Diagnosing Aortic Septal Defect

A fixed split in the second heart sound (HS) (
${S}_{{2}}$
) indicates an aortic septal defect (ASD). This work aims at the shortcomings of using the time interval (
${T}_{{A_{{2}}}\rightarrow {P_{{2}}}}$
) between the sounds produced by the aortic valve closure (
${A}_{{2}}$
), as well as the pulmonary valve closure (
${P}_{{2}}$
) to evaluate the fixed split
${S}_{{2}}$
, which is
${T}_{{A_{{2}}}\rightarrow {P_{{2}}}}$
easily influenced by the heartbeat and difficult to distinguish from other types of splits
${S}_{{2}} $
without considering the entire respiratory phase and the third HS (
${S}_{{3}}$
). Thus, this study proposes a novel methodology for detecting an ASD using estimated split coefficients of
${S}_{{2}}$
(
${S_{{2}}}_{\text {split}}$
) combined with the number (
${N}_{S_{{2}}}$
) of
${S}_{{2}}$
covered by the moving window with 9 s. The important contributions are highlighted as follows: 1) a novel, simple, and efficient methodology based on the Gaussian mixture model (GMM) is proposed for estimating the sounds of
${A}_{{2}}$
and
${P}_{{2}}$
; 2) an overlapping rate (OLR)-based estimated
${S_{{2}}}_{\text {split}}$
is proposed to overcome the split degree influenced by the heartbeat when using the parameter
${T}_{{A_{{2}}}\rightarrow {P_{{2}}}}$
; 3) to achieve high precision of the wide splitting of ASDs, the statistics of
${N}_{S_{{2}}}-{S_{{2}}}_{\text {split}}$
and
${N}_{S_{{2}}}-{T}_{{A_{{2}}}\rightarrow {P_{{2}}}}$
are proposed for analysis; and 4) to avoid drawing a unilateral conclusion, the correct ratio (CR) is proposed to predict an ASD. The criteria, derived based on the combination of
$\mu _{_{N_{S_{{2}}}, {S_{{2}}}_{\text {split}}}}+\sigma _{_{N_{S_{{2}}}, {S_{{2}}}_{\text {split}}}}\geq 0.45$
,
$\mu _{_{N_{S_{{2}}}, {S_{{2}}}_{\text {split}}}}\geq 0.6$
,
$\sigma _{_{N_{S_{{2}}}, {S_{{2}}}_{\text {split}}}}\leq 0.01$
,
$0.05\leq \mu _{_{N_{S_{{2}}}, {T}_{{A_{{2}}}\rightarrow {P_{{2}}}}}}\leq 0.1$
, and
$\text {CR}\geq 0.9$
, are determined to detect ASD. The performance evaluation, as opposed to the state-of-the-art algorithms, demonstrates that the overall accuracy,
${F}1$
score. and Cohen’s kappa coefficient achieved by the proposed algorithm all exceed up to 3% compared with the second highest performance metrics.