on 29-May-2025 (Thu)

“unrolled” graphical representation of a recurrent neural network (C) where we use sequence data (x 1 ,x 2 ,x 3 ) to make sequence predictions (y 1 ,y 2 ,y 3 ) while preserving information through the hidden states h 1 ,h 2 ,h 3

data-driven agent-based modeling (DDABM)

The second assumption is that agents are homogeneous. This may seem a strong assumption, but in fact it is without loss of generality. To see this, suppose that h(x) is our model of agent behaviour, where x is state, or all information that conditions the agent’s decision. Heterogeneity can be embedded in h by considering individual characteristics in state x, such as personality traits and socio-economic status, or, as in our application domain, housing characteristics.

Classification evaluation methods

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Accuracy

tf.keras.metrics.Accuracy()

sklearn.metrics.accuracy_score()

Not the best for imbalanced classes

The intensity of S2 has less diagnostic importance. (This contrasts with S1, in which intensity is more important than splitting.)

The correct explanation for normal splitting—increased “hangout” in the pulmonary circulation—was discovered in the 1970s.30,31

Splitting refers to the separation of the aortic component (A2) and the pulmonic component (P2) during expiration (left column) and inspiration (right column). There are two normal patterns (single and physiologic) and three abnormal patterns (wide physiologic, wide fixed, and paradoxic)

During inspiration the interval separating A2 and P2 increases by about 20 to 30 milliseconds (ms) (Fig. 40.1).18,29,31

Although the phonocardiogram almost always records both components of S2, the human ear perceives them as a single sound during expiration in more than 90% of normal persons.32

In normal persons during inspiration, the human ear either perceives two components (physiologic splitting, heard in 65% to 75% of normal adults; see Fig. 40.1)† or still perceives a single component (single S2, heard in 25% to 35% of normal adults)

The older the person, the more likely S2 will be single instead of physiologic.32,35

Harvey suggests mimicking the normal expiratory sound by striking a single knuckle against a tabletop and mimicking inspiratory physiologic splitting by striking two knuckles almost simultaneously.33 Constant suggests mimicking inspiratory splitting by rolling the tongue as in a Spanish dr or tr, or saying pa-da as quickly and sharply as possible.34

It is sometimes heard at a slightly lower location, especially in patients with chronic pulmonary disease, and at a slightly higher location in those who are obese.35

A2 coincides with the incisura (i.e., notch) on the aorta tracing, P2 coincides with the incisura on the pulmonary artery tracing, and both sounds occur a short interval after completion of mechanical systole (the interval between the end of mechanical systole and valve closure is called hangout)

On the left side of the heart, hangout is very short (10 ms, i.e., the aortic valve closes almost immediately after completion of mechanical systole). However, on the right side of the heart, hangout is longer (60 ms) because the compliant pulmonary circulation offers so little resistance to continued forward flow

Changes in hangout also explain in part why splitting normally increases during inspiration and why most patients with pulmonary hypertension have a single S2 (see the text)

Fig. 40.1 reveals that all three abnormal second heart sounds—wide physiologic, fixed, and paradoxic—have audible splitting during expiration (dotted lines in Fig. 40.1). Therefore the best screening tool for the abnormal S2 is audible expiratory splitting that persists when the patient sits up.36-39

Wide physiologic splitting may result from P2 appearing too late or A2 too early (Table 40.1).18,37 The most common cause is RBBB

In pulmonic stenosis the A2-P2 interval correlates well with severity of stenosis (gauged by the RV systolic pressure; r = 0.87, p <.001),40 although in many patients the clinician must listen at the third interspace to hear splitting because the mur- mur is too loud at the second interspace

In most patients with pulmonary hypertension the normal hangout interval dis- appears and S2 is single. S2 becomes wide in these patients only if there is associated severe RV dysfunction and prolonged RV systole.30,31,41

Most patients with pulmo- nary hypertension and a wide S2 have either long-standing severe pulmonary hyper- tension30,31,41 or massive pulmonary embolism (the wide S2 of pulmonary embolism is temporary, usually lasting hours to days).42!

In patients with audible expiratory splitting (and regular rhythm), the absence of fixed splitting significantly decreases the probability of atrial septal defect (LR = 0.1; see EBM Box 40.1), whereas the presence of fixed splitting increases the probability of atrial septal defect only modestly (LR = 2.6; see EBM Box 40.1)

Patients with false-positive results (i.e., fixed splitting without atrial septal defect) commonly have the combination of RV failure and audible expiratory splitting from bundle branch block or some other cause.18

In elderly adults with aortic flow murmurs, the finding of paradoxic splitting does not distinguish significant aortic stenosis from less severe disease

S2-OPENING SNAP In contrast to the split S2, the S2-opening snap interval is slightly wider, the opening snap is loudest at the apex, and the opening snap ushers in the diastolic rumble of mitral stenosis at the apex. Patients with S2-opening snap sometimes have a triple sound (split S2 + opening snap) during inspiration at the upper sternal border

S2-PERICARDIAL KNOCK In contrast to the split S2, the S2-knock interval is slightly wider, the pericardial knock is loudest at or near apex, and the knock is always accompanied by elevated neck veins

S2-THIRD HEART SOUND In contrast to the split S2, the S2-S3 interval is 2 to 3 times wider, and S3 is a low- frequency sound heard best with the bell.

LATE SYSTOLIC CLICK-S2 Clicks are loudest at or near apex and are often multiple. Their timing changes with maneuvers (see Chapter 46).

For example, in mitral stenosis patients, the loud P2 defined either as an S2 that is louder at the left side of the upper sternum compared with the right side21 or as a split S2 with a louder second component20 did not discriminate patients with pulmonary hyperten- sion from those without it (see EBM Box 40.1).

Even when A2 and P2 were precisely identified by phonocardiography (e.g., A2 corresponds to aortic inci- sura on simultaneous aortic pressure tracing), the relative intensities of the two components did not correlate well with pulmonary pressure.44

Others suggested audible splitting at the apex indicates pulmonary hypertension (because P2 should not be heard at the apex, and any splitting at that location indicated that P2 was abnormally loud),32 but even this finding correlated better with the etiology of heart disease—it is common in atrial septal defect and pri- mary pulmonary hypertension—than it did with measurements of pulmonary pressure.41,44

In patients with aortic flow murmurs, an absent or diminished S2 increases the probability of significant aortic stenosis (LR = 3.8; see Chapter 44).

In addition, the palpable S2 in patients with mitral stenosis accurately detects pulmonary arterial pressures greater than or equal to 50 mm Hg (positive LR = 3.6, negative LR = 0.05; see EBM Box 40.1). In this study the palpable P2 was defined as an abrupt tapping sensation coincident with S2 at the second left intercostal space

Nonetheless, one study of patients with cirrhosis did demonstrate that the loud P2 increased probability of pulmonary hypertension (i.e., portopulmonary hyper- tension, LR =17.6; see EBM Box 40.1; see Chapter 8)

S2 occurs after the peak of the carotid pulse and coincides with its downslope.

The two components of S2 are best heard with the diaphragm of the stethoscope and over the left second interspace, close to the sternal border.

A2 is widely transmitted to the right second interspace, along the left and right sternal border, and to the cardiac apex. P2 is normally best heard and recorded over the upper left sternal border and is poorly transmitted.

S2 is best heard when patients are semirecumbent (30 to 40 degrees upright) with quiet inspiration.

The major determinants of A2 intensity (and therefore the major determinants of S2) include (table 3):

● Aortic pressure, a major determinant of the velocity of valve closure

● Relative proximity of the aorta to the chest wall

● Size of the aortic root

● Mobility and structural integrity of the aortic valve

The intensity of P2 is determined by:

● Pulmonary arterial pressure, particularly the diastolic pressure

● Size of the pulmonary artery

● Mobility and structural integrity of the pulmonary valve

The intensity of P2 is determined by comparing its intensity with A2. An increased P2 intensity is suggested when it is louder over the left second interspace or when there is transmission to the cardiac apex.

Increased intensity of P2 often occurs in:

• Pulmonary arterial hypertension of any etiology (most common, even with pulmonary regurgitation) [22].

• Idiopathic pulmonary artery dilation.

• Atrial septal defect (ASD); P2 is increased considerably and frequently greater than A2 over the left second interspace.

A2 is soft in patients with mitral regurgitation (MR), and P2 may appear to be increased. In these circumstances, one cannot rely on the relative intensity of P2 for the diagnosis of pulmonary hypertension (PH)

Decreased intensity of A2 occurs in:

• Conditions that decrease the mobility and integrity of the aortic valve

• Severe aortic regurgitation (AR) or stenosis

• Hypotension

Increased intensity of A2 often occurs in:

• Systemic hypertension.

• Coarctation of the aorta.

• Ascending aortic aneurysm; a "tambour" quality of A2 is commonly heard (table 3).

• When the aortic root is relatively anterior and closer to the anterior chest wall, as in tetralogy of Fallot and transposition of the great arteries.

Decreased intensity of P2 occurs in:

• Conditions that decrease the mobility and integrity of the pulmonary valve.

• Pulmonary stenosis and regurgitation.

• Significant RV outflow obstruction associated with a soft and delayed P2. The low pulmonary artery pressures also play a role in attenuating P2.

Electromechanical delay of the RV (table 3 and figure 2):

- Right bundle branch block (RBBB) (movie 3), artificial pacing from the LV, and Wolff-Parkinson-White (WPW) syndrome with LV preexcitation.

- Premature beats and an idioventricular rhythm of LV origin (QRS complex of RBBB morphology) are also associated with wide splitting.

Hemodynamic causes:

- Increased resistance to RV ejection and prolongation of RV ejection time are other important causes of wide expiratory splitting of S2 as seen in pulmonary valve, infundibular, supravalvular, or pulmonary branch stenosis, and pulmonary arterial hypertension.

In patients with pulmonary valve and infundibular stenosis, wide splitting of S2 is associated with reduced intensity of P2, while P2 is accentuated in PH and pulmonary branch stenosis.

In pulmonary valve stenosis, the degree of expiratory splitting of S2 (the A2-P2 interval) is directly related to the severity of stenosis and RV systolic hypertension [24]. Further splitting of S2 during inspiration usually occurs in these conditions, but wide splitting of S1 is not observed.

- Isolated reduction of the LV ejection time may also cause wide splitting of S2, due to the early occurrence of A2. Examples of this hemodynamic abnormality include severe MR when forward stroke volume decreases with increases in regurgitant volume [25]. In constrictive pericarditis, differential filling of the ventricles occurs during inspiration, resulting in a lower LV stroke volume [26].

Fixed splitting of S2 has been defined as ≤20 ms of variation in the A2-P2 interval between the inspiratory and expiratory phases of respiration [27]. However, such limitation in variation of splitting may be difficult to discern clinically, so wide and variable splitting may be difficult to distinguish from wide and fixed splitting.

One common cause of wide and fixed splitting of S2 is a large interatrial communication (ASD, common atrium) and left-to-right or bidirectional shunt; abnormally wide splitting of S2 occurs, and respiratory variations of the A2-P2 intervals are minimal or absent (movie 4).

The other cause of fixed splitting of S2 is RV failure, when the RV is unable to vary its stroke volume during inspiration, and inspiratory prolongation of its ejection time and delay of P2 does not occur. Therefore, any condition that induces severe RV failure, such as RV outflow obstruction, PH, and primary RV dysfunction, can be associated with fixed splitting (table 3).

Electromechanical delay Left bundle branch block, artificial RV pacing, preexcitation of the RV (WPW syndrome), and premature beats of RV origin are examples of conduction disturbances associated with delayed activation of the LV, and consequently delayed completion of LV ejection causes a delayed A2 and reversed splitting of S2.

A markedly prolonged LV ejection time may delay A2 sufficiently to cause reversed splitting of S2. With fixed LV outflow tract obstruction, as in patients with aortic valve stenosis, LV ejection time is lengthened, and reversed splitting of S2 usually indicates hemodynamically significant outflow obstruction (movie 5). However, P2 may be inaudible due to the long ejection systolic murmur of aortic stenosis, making it difficult to recognize the reversed splitting.

A prolonged LV ejection time and reversed splitting of S2 can occur with myocardial dysfunction, as in myocardial ischemia, or in patients with long-standing severe AR [30]. However, reversed splitting is rarely observed with severe heart failure (HF) because of the concomitant decrease in stroke volume, which is an important determinant of LV ejection time.

The distinction between hypertrophic cardiomyopathy (HCM) and MR or ventricular septal defect (VSD), conditions in which the character and locations of the systolic murmur may appear similar on auscultation, is facilitated by recognizing the character of S2 splitting. Reversed splitting suggests HCM, while physiologic splitting favors MR or VSD.

Absence of A2 is occasionally observed in severe calcific aortic stenosis with an immobile aortic valve. A2 may be absent in some patients with severe AR due to destruction of the valve leaflets.

However, a truly single S2 is rare. An apparently single S2 usually results from the inability to hear or record P2 due to emphysema, obesity, or pericardial effusion.