Targeted Neonatal Echocardiography in Patients With Hemodynamic Instability

Medical advances have enabled enhanced diagnostic and therapeutic precision tailored to individual needs, referred to as “precision medicine.”¹  The value of bedside imaging to characterize the rapidly changing hemodynamic status during the postnatal transition period or in common pathophysiologic states, such as septic shock and acute pulmonary hypertension (PH), has led to adoption in practice by neonatologists globally. This has prompted change in the utility of echocardiography from a cross-sectional consultative modality to a longitudinal point of care modality.^2–5  Careful integration of hemodynamic information from sequential assessments provides enhanced diagnostic clarity and enables thoughtful appraisal of treatment effect or lack thereof. Decreasing costs, increasing portability of ultrasound equipment, access to image management software, and structured training programs have contributed to this emerging field.⁶ 

Targeted neonatal echocardiography (TNE) refers to the use of standardized imaging to provide comprehensive appraisal of heart function, shunt physiology, and pulmonary or systemic hemodynamics. These specialized skills require structured training, creating a path to levels of competency. Clinical practice guidelines and recommendations for training have been proposed by the Australasian Society of Ultrasound in Medicine⁷  and the American Society of Echocardiography,^8–11 which include basic and advanced training curriculums. This has prompted the need to develop local training programs to account for the diversity and uniqueness of training centers globally.¹⁰  Furthermore, training has focused on competencies relevant to clinical assessments performed by neonatologists, rather than set numbers of studies or fixed training times.¹²  Although educational programs continue to evolve, they are still lacking in many regions, which may contribute to variance in practice.

Standardization of training methods and quality assurance processes that can effectively incorporate ultrasound into clinical practice are imperative. The support of pediatric cardiology services is crucial for providing advice, back up, and guidance when the limitations of the neonatologists are reached.¹³  Additionally, collaboration with radiology in some institutions may help facilitate uploading and image storage. In many centers, positive academic collaboration between specialties has evolved over time and led to innovation and scientific discovery. Creating a bridge from comprehensive training to successful clinical practice relies upon the integration of structure, processes, and outcomes within quality assurance frameworks. The value of bedside cardiac imaging in guiding patient care and enhancing outcomes will be recognized through development of a robust foundation for integration of care. Please refer to the Executive committee introductory paper for discussion on Class of Recommendations and Level of Evidence (LOE), organization of the writing committees, and document review and approval.

1. Training in Targeted Neonatal Echocardiography should be structured and in alignment with published guidelines and standards (Class I, LOE C-EO)

2. Targeted Neonatal Echocardiography programs should be established in collaboration with pediatric cardiology and include a mechanism for quality assurance (Class I, LOE C-EO)

Clinicians traditionally have relied on blood pressure (BP), heart rate, capillary refill, urinary output, and plasma lactate, however, they are imprecise from a diagnosis perspective.^14,15  Hemodynamic assessment requires an understanding of normal cardiac anatomy and physiology, including determinants of blood flow, driving pressure, and vascular resistance.¹⁶  The dynamic nature of hemodynamics, affected by factors such as respiratory mechanics and fluid balance, may be challenging to interpret.^14,17,18  For example, the pathophysiologic nature of hypotension in a neonate may include a hemodynamically significant ductus, decreased heart function with acidosis, and/or a need for volume resuscitation. Hypotension, commonly defined by a mean BP less than the gestational age (GA), has not reliably correlated to cardiac output nor blood flow distribution, regardless of GA.¹⁷  Therefore, it is not surprising that treatment of hypotension, based on a nonjudicious and imprecise approach, has not led to improvement in patient outcomes.¹⁹  In a cohort of patients born at less than 30 weeks gestation, the mean BP goal (>GA) in the first 24 hours had high specificity (88%) but low sensitivity (30%) for identifying patients with low systemic blood flow, as assessed through superior vena cava (SVC) flow.²⁰  Additionally, BP measurement doesn’t correlate with left ventricular (LV) output, regardless of GA, highlighting the need for comprehensive hemodynamic assessment using TNE.²¹ 

Echocardiography has increasingly been used to characterize deranged hemodynamics. In adults, bedside echocardiography has modified management, with abnormalities found in 33% of scans of patients in an ICU setting.²²  Another adult ICU study demonstrated that in 85% of cases, bedside echocardiography provided valuable information, with 37% of patients benefitting from a subsequent change in management, whether fluid administration, inotrope use, or vasopressor support.^22,23  The 2015 American Society of Echocardiography guidelines for longitudinal use of echocardiography to guide hemodynamic care in adults highlighted the utility of serial assessment.²⁴  In a review of an established neonatal hemodynamics consult service in Canada, 48% of bedside echocardiography evaluations resulted in a change in management.²⁵  An important consideration in neonates is the potential coexistence of congenital heart disease (CHD) as an etiology for cardiac compromise. The 2011 guidelines for use of TNE (by neonatologists) recommend that the first echocardiogram include comprehensive imaging, which will enable reliable detection of CHD.⁸  If performed by a neonatologist with advanced hemodynamic training, the initial study should be reviewed within 6 hours by a pediatric cardiologist. Neonates without CHD may then be serially followed by TNE, adjusting management as needed with changing hemodynamics. The expert neonatal hemodynamic consultation model can be summarized into 3 major phases: (1) clinical review, (2) standardized TNE evaluation, and (3) integration and medical recommendation (Fig 1). Comprehensive assessment and integration of clinical and echocardiography findings supports a precision-based approach to management.

A recent publication from a large perinatal center revealed that the primary indications for hemodynamic consultation (as defined above) included patent ductus arteriosus (PDA) assessment (61%), pulmonary hemodynamics (27%), and systemic hypotension (9%).²⁵  In a 4-year period, the hemodynamic consult team performed 553 TNE consultations on 268 infants, of which 48% directly impacted care by either implementing new therapies or avoidance of unnecessary interventions.²⁵  A recent expert commentary highlights the need for competency-based training, quality assurance, and collaboration between neonatology and cardiology.¹²  Without high-quality image acquisition and interpretation, data collected may be inaccurate and potentially misdirect care. Quality assurance processes for echocardiography laboratories and ultrasound programs have improved correlation among measurements.^26,27  Development of disease (indication) specific protocols for PDA evaluation, hypotension, and pulmonary hypertension provides a framework for establishing competencies and are essential for quality assurance.¹²  Although program structure for TNE may vary between institutions, the overarching goal is to enhance the care of neonates by providing enhanced diagnostic precision and tailored management.

1. The application of TNE should be performed by trained operators who have completed structured training, and echocardiography information should be integrated within the clinical context to formulate a diagnostic impression (Class IIa, Level C-EO)

2. All TNE studies should be stored on a secure archive and reported according to a standardized framework (Class IIa, Level C-EO)

Comprehensive assessment in infants with a structurally normal heart must include multiple measurements. When utilizing TNE, it is imperative to integrate surrogate indices of cardiovascular physiology, thus formulating diagnostic impressions and guiding therapies.

Systemic blood flow and cardiac output can be assessed utilizing Doppler measures obtained in the left and right ventricular (RV) outflow tracts, SVC, descending aorta, and systemic peripheral vessels (Table 1). LV output (LVO) is a good estimator of systemic blood flow in the absence of a PDA, whereas RV output (RVO) provides an estimate of pulmonary blood flow (PBF), assuming there is no pulmonary to aortic shunt or significant pulmonary regurgitation.²⁸  Normal neonatal values for VTI and cardiac index have been published,^29,30  but these measurements can have significant error with inappropriate interrogation angle or inaccurate LV outflow tract diameter measurements. In addition, the presence of turbulent PDA flow close to the main pulmonary artery makes the tracing of the velocity time integral (VTI) envelope unreliable. Because of the presence of shunts in neonates, LVO and RVO may not reflect whole-body systemic perfusion.³¹  In an attempt to mitigate such confounders, SVC flow was proposed as a marker of systemic blood flow from the upper body, including the brain,³²  that is not influenced by the presence of shunts. The presence of diastolic flow reversal in the descending aorta is a marker of significant diastolic steal in a hemodynamically significant PDA and may suggest postductal systemic underperfusion.^33,34  Similarly, pulse wave Doppler may be used to provide a surrogate assessment of the adequacy of blood flow to abdominal organs and the brain. Absent or reversed diastolic flow in the peripheral vessels is abnormal, although angle of insonation and vascular resistance of the organs may impact the reliability of the interpretation of these findings.

Assessment of LV performance includes indices of preload, diastolic and systolic function, and contractility (Table 2). Pulse wave Doppler assessment of pulmonary vein flow may provide information as well as left heart volume loading, whereas mitral valve inflow and isovolumic relaxation time (IVRT) are markers of LV preload and compliance. Ejection fraction (EF) may be calculated using the Simpson’s biplane method or bullet method (5/6 area-length). M-mode measurements assume that the LV is circular in cross-section, which is not always true, particularly in the setting of abnormal RV loading conditions and are, therefore, not recommended. In addition, it is only a measure of global ventricular performance.²⁸  Advanced measures of LV systolic performance based on tissue Doppler imaging or strain analysis are currently under investigation in several research studies but have not been validated for routine clinical practice.

Several neonatal diseases may lead to acute alterations in pulmonary hemodynamics, which are characterized by elevated pulmonary vascular resistance (PVR) and increased RV afterload.³⁵  The subsequent consequences of intrinsic vulnerability of the immature myocardium include RV systolic dysfunction, hypertrophy, and/or dilation. In the presence of persistent or significantly elevated PVR, PBF may be compromised; intra and extracardiac shunts may further impact heart function and the efficacy of oxygenation. Pulmonary hypoperfusion will negatively impact LV filling, whereas RV dysfunction may lead to impaired LV systolic performance secondary to interventricular interaction.^35,36  The combination of poor LV preload and LV contractile dysfunction may result in poor cardiac output and systemic hypoperfusion.²⁸ 

A holistic approach involves the integration of assessment of the severity of PH, RV, and LV performance, and shunt dynamics, which enables a refined therapeutic approach. For instance, treatment options for patients with acute PH may include vasodilators to target increased PVR, inotropic support to optimize RV, and/or LV systolic function, and prostaglandins to re-establish ductal patency when systemic blood flow is compromised. Manipulation of the ratio between PVR and systemic vascular resistance with systemic vasoconstrictors, which do not induce pulmonary vasoconstriction (eg, vasopressin, low-dose norepinephrine), may aid in transductal shunt reversal to promote PBF.³⁵  Assessment of the severity of PH includes estimation of RV systolic pressure (RVSp) through tricuspid regurgitant (TR) jet, directionality of PDA shunt, assessment of the interventricular septum (IVS), and pulmonary artery Doppler (Table 3). In the presence of a PDA, direction of shunt is the most reliable marker used to quantify pulmonary pressures in relation to the systemic circulation. RVSp is a surrogate estimate of pulmonary artery systolic pressure but may be underestimated in patients with abnormal RV systolic performance or when the TR jet is incomplete. IVS motion is governed by the transmural pressure differential between the RV and LV. In patients with acute or chronic PH, end-systolic septal position may be flat (moderate PH) or paradoxical, bowing into the LV (severe PH). The presence of high end-systolic LV pressure (systemic hypertension) may mask this finding; therefore, measurement of systemic BP is important in the PH evaluation. Eccentricity index provides an objective assessment of the IVS motion in systole and diastole.³⁷  End-diastolic septal flattening is usually representative of RV volume loading, eg, intracardiac shunts. Furthermore, alterations in PVR can be assessed objectively with PVR index: the ratio between pulmonary artery acceleration time (PAAT) and RV ejection time. In the presence of augmented resistance, there is rapid acceleration of the flow in the beginning of the ejection period, which may coincide with notching of the waveform downslope.²⁸  This can be observed by subjective assessment of the shape of the flow envelope. The usual shape resembles an isosceles triangle, whereas in the presence of increased resistance the envelope resembles a right angle triangle with or without notching²⁸  (Fig 2).

Qualitative assessment of RV performance has poor interobserver reliability,³⁸  highlighting the need for quantitative markers. Tricuspid annular plane systolic excursion (TAPSE) and fractional area change (FAC) may be used to estimate RV systolic function with published neonatal reference values,^39,40  whereas assessment of inferior vena cava (IVC) and RV end diastolic diameter can be surrogates of RV preload³⁴  (Table 4, Fig 3). TAPSE measures the downward vertical distance that the tricuspid annulus moves during systole as a marker of longitudinal motion of the RV, whereas RV FAC provides an estimate of ejection fraction.⁴¹  Lastly, RV:LV area is an objective measurement of RV dilation.

Tissue Doppler imaging (TDI) allows measurement of peak systolic (s’), early diastolic (e’), late diastolic (a’), and peak isovolumetric contraction velocities.⁴¹  It provides additional information regarding systolic and diastolic performance of both ventricles (Tables 2 and 4, Fig 4). Strain analysis estimates absolute tissue deformation and is expressed as a percentage of change according to its shape at baseline, whereas strain rate is the speed at which deformation occurs as a measure of contractility⁴²  (Fig 5). These new modalities are currently under research, with limited normative data and information regarding reproducibility or relevance to disease states^43,44 ; however, they are likely to assist in further understanding and characterizing neonatal diseases impacting cardiovascular performance.

Blood flow through shunts is governed by Poiseuille’s law such that viscosity, pressure gradient across the structure, and length and diameter of the structure are the determinants of shunt volume. Table 5 summarizes the specific TNE measurements for shunts. It is important to assess not only the physical size of the shunt but also markers of shunt volume and its impact on systemic and pulmonary circulations. Markers of systemic underperfusion may include abnormal diastolic flow in the descending aorta as well as in peripheral vessels (celiac, superior mesenteric and middle cerebral arteries) (Table 1). Pulmonary overcirculation may be indirectly assessed using markers of LV volume loading such as pulmonary vein diastolic flow (D wave > 0.5 m per sec), mitral inflow, and IVRT (Table 2), whereas left atrial (LA) dilation can be assessed using LA:Ao ratio. Furthermore, intra, or extracardiac shunts that produce an unbalanced circulation (abnormal ratio between pulmonary and systemic blood flow or Qp:Qs) may be recognized through the identification of differences in ventricular outputs. An increase in left-to-right shunt volume in a PDA will increase the LVO:RVO ratio, suggesting an increase in Qp:Qs. Conversely, significant intracardiac shunts (ie, atrial septal defect [ASD] and ventricular septal defect [VSD]) will produce higher RVO versus LVO and volume loading of the right heart. Atrial septal defects should be suspected in patients with increased end-diastolic eccentricity index, where the IVS assumes a flat shape in end-diastole. A multiparametric approach is essential to overcome reliability issues of single measurements (eg, diameter), understanding shunt impact and the need for therapy.

A comprehensive TNE protocol provides added information to clinical signs of cardiovascular pathologies. Beyond its use in the assessment of PDA and PH, it can add significant insights in neonatal shock and hypotension, hypoxic-ischemic encephalopathy, sepsis, arterio-venous malformations, etc. In addition, longitudinal assessment provides important information about disease progression and response to therapies. In patients in whom CHD is suspected, consultation with the pediatric cardiology team is warranted, as further imaging evaluation and subsequent management may differ in patients with CHD.

1. In absence of shunts, LVO and RVO may be used to provide estimates of systemic and pulmonary flows, respectively, though a protocol for image optimization and assessment is crucial with potential for error (Class IIa, LOE B-NR)

2. Estimation of pulmonary pressures in relation to systemic circulation should be primarily assessed based on direction of PDA shunt (Class IIa, LOE B-NR)

3. A multiparametric approach to assessment of hemodynamic assessment of PDA provides an enhanced appraisal of shunt vol and impact (Class IIa, LOE B-NR)

4. RVSp can be used as a surrogate estimate of pulmonary artery systolic pressure but may be underestimated in patients with abnormal RV systolic performance or when the TR jet is incomplete (Class IIa, LOE B-NR)

5. Measures of RV function such as TAPSE and FAC have published neonatal reference values and may be used to assess neonates with structurally normal hearts (Class IIa, LOE B-NR)

Although the prevalence of CHD is only about 1% of live births worldwide,⁴⁵  the spectrum varies significantly, ranging from simple structural abnormalities like an ASD, VSD, or PDA, to complex lesions, such as a double outlet right ventricle or hypoplastic left heart syndrome. As stated previously, in any neonate with a concern for significant CHD, the first echocardiogram should be interpreted by a pediatric cardiologist within 6 hours and can be performed by a neonatologist with formal training in neonatal hemodynamics.^3,8,12  Once a diagnosis of CHD has been made, a TNE should include several important components as outlined in this section.

TNE evaluation in patients with CHD should always include characterization of systemic hemodynamics. LV function is a good surrogate of cardiac output. As previously discussed, conventional LV functional indices include shortening fraction (SF) and EF. LV short-axis views using M-mode and 2-dimensional echocardiography (2DE) allow for measurement of the LV end-diastolic dimension (LVEDD) and end-systolic dimension (LVESD) (Fig 6). LVEDD can be compared with standardized normal values using Z-scores to determine if the ventricle is small, dilated, or appropriate in size.⁴⁶  Similarly, LV septal and posterior wall thickness Z-scores can also be used to assess for hypertrophy.⁴⁶ 

It is important to recognize that all measures of LV function depend on preload, afterload, and heart rate and may not accurately reflect true LV contractility. For example, decreased preload associated with veno-arterial extracorporeal membrane oxygenation⁴⁷  or a ventricular assist device precludes the use of SF and EF to assess ventricular performance. Increased afterload from systemic hypertension, severe aortic stenosis, and aortic coarctation can adversely affect SF and EF such that removal of the increased afterload can improve SF and EF. Additionally, SF and EF may not represent true LV performance in the setting of significant mitral regurgitation since the regurgitant fraction does not contribute to cardiac output. Patient factors such as sedation, paralysis, and ventilator support may influence ventricular pressure estimations. Lastly, supraventricular, or ventricular tachycardia can limit LV filling time and preclude accurate LV functional assessment.

Evaluating the RV in a structurally abnormal heart requires an understanding of the specific CHD physiology and ability to discern whether the RV abnormalities are appropriate compensatory changes or pathologic changes. As there are no lesion-specific normative data in neonates, recognizing this distinction requires considerable expertise. Echocardiography assessment of RV size and function are similar to patients with structurally normal hearts as discussed previously, albeit with considerable additional caveats.

RV size can be evaluated quantitatively by measuring the end-diastolic diameters at the basal and mid-cavitary levels, end-diastolic length, and planimetered areas at end-diastole and end-systole in the apical 4-chamber view (Fig 7A and 7B).⁴⁸  These measurements are generally useful in simple lesions, but they have limited value in complex lesions like Ebstein anomaly, tricuspid atresia, and pulmonary atresia with intact ventricular septum. RV size can also be quantified with the RV:LV ratio (Fig 7C), such that elevated values can signify RV enlargement (as in total anomalous pulmonary venous return), LV hypoplasia (as in hypoplastic left heart syndrome) or left-sided obstructive lesions (as in aortic coarctation). Absolute measurements and corresponding Z-scores of cardiovascular structures can help distinguish between RV enlargement and LV hypoplasia.

Normative neonatal values in structurally normal hearts are available for RV FAC and TAPSE, but their utility is limited in the setting of significant CHD.^41,48  Nonetheless, FAC correlates with EF as measured by MRI in patients with various CHDs (hypoplastic left heart syndrome and tetralogy of Fallot).^49,50  Unfortunately, even outside of the neonatal period, there is limited utility of TAPSE in patients with significant CHD, particularly after cardiac surgery.^51–53  Although evaluation of RV strain mechanics has been shown to be feasible and reproducible in neonates with structurally normal hearts, this has not been evaluated in neonates with significant CHD.^54,55  Therefore, qualitative visual assessment of RV size and function and FAC calculated from planimetered RV diastolic and systolic areas remain the most commonly used techniques in clinical practice and can usually be reliably performed and serially compared.⁸ 

Neonates with unrepaired or palliated CHD are at high risk of developing pulmonary vascular disease secondary to pulmonary overcirculation or left-sided obstructive lesions.⁵⁶  Echocardiography methods used to assess pulmonary hemodynamics are no different than in structurally normal hearts and include a combination of 2DE (septal flattening), color mapping (shunt flow direction), and spectral Doppler interrogation (velocities of tricuspid and pulmonary regurgitation) (Fig 8).

There are a few important caveats to remember for patients with significant CHD. By definition, patients with either ductal dependent pulmonary circulation (such as pulmonary atresia) or systemic circulation (such as critical aortic coarctation) have systemic pulmonary artery pressure. In addition, measures of RV systolic pressure (septal position as well as tricuspid regurgitation and VSD flow velocities) cannot be used to estimate pulmonary artery pressure in patients with RV outflow tract obstruction (such as tetralogy of Fallot). However, pulmonary artery pressures can still be estimated in the setting of significant obstruction if there is pulmonary regurgitation or a PDA (Fig 9). Unfortunately, both PAAT and RV ejection time have limited use in this situation.⁵⁷  Furthermore, the simplified Bernoulli equation does not take length into account, and estimation of pressure gradients in patients with a long tortuous PDA (as is often seen with pulmonary atresia), a large PDA or patients with shunts (such as a Blalock Taussig shunt or a ductal stent) may not be accurate. As this information is critical to a patient’s clinical presentation and future surgical planning, more invasive methods of assessment are often required.

1. FAC correlates with EF as measured by MRI in patients with various CHDs, such as hypoplastic left heart syndrome and tetralogy of Fallot and may be used for serial assessments of systolic heart function in neonates with CHD (Class IIa, LOE B-NR)

In patients with significant CHD, the presence of concomitant intra (ASD or VSD) and extracardiac shunts (PDA) are common and often required to maintain adequate oxygenation and cardiac output. Therefore, it is crucial to understand the anatomy and physiology of the primary defect, any associated lesions, and the function of the shunt (Table 6). Shunt assessment uses the same echocardiography methods described previously: 2DE to measure anatomic size, color mapping to evaluate shunt direction, and spectral Doppler interrogation to confirm shunt direction and estimate pressure gradients.⁸  This evaluation is important because shunts play a critical role in the patient’s physiology, clinical status, and potential need for immediate intervention.

As previously discussed, establishment and maintenance of a TNE program must include appropriate equipment, standard practices, and protocols related to study performance,^8,58,59  image archiving, and report generation, all in coordination with pediatric cardiology.¹²  All members of a TNE team must be keenly aware of the limitations associated with hemodynamic assessment and quantification in a neonatal echocardiogram, because neonates are different from older children.⁶⁰  Unique characteristics of transitional neonatal physiology, including ductal closure, changing PVR, faster heart rates, smaller cardiovascular structures, and patient movement all contribute to higher measurement variability and potential for errors. Quantification of blood flow can be limited by noncircular structures. Elevated RV and pulmonary arterial systolic pressures can preclude accurate assessment of shunt volumes as well as LV function by M-mode echocardiography.

Exclusion of CHD starts with assessment of the neonate. If there is a concern for CHD based on the fetal evaluation, pulse oximetry screening, patient symptomatology, or physical examination, then the pediatric cardiology service should be consulted. As previously discussed, the initial comprehensive echocardiogram may be performed by a trained TNE team but should be interpreted by a pediatric cardiologist within 6 hours.^3,8  Consistently utilizing a protocol that requires careful 2D sweeps and color mapping in all of the standard pediatric echocardiography views as outlined in published guidelines and corroborating findings in more than 1 view will ensure a comprehensive assessment of cardiac anatomy and physiology and prevent diagnostic errors (Table 7).⁵⁸ 

1. Quality assurance processes, have led to improved correlation among measurements in echocardiography laboratories and, must be established within programs utilizing TNE (Class 1, LOE C-EO)

2. Protocols should be used within a TNE program to ensure standardization and minimize diagnostic errors (Class 1, LOE C-EO)

Longitudinal TNE evaluation enables enhanced diagnostic precision and refined approach to treatment. Neonates, and particularly preterm infants, are at risk for systemic and cerebral hypoperfusion because of several disease processes and physiologic changes during the transitional period. Routine clinical methods (eg, blood pressure, capillary refill) of assessing adequacy of the circulation are, however, limited predictors of cardiovascular well-being and systemic blood flow and provide no diagnostic insight. TNE assessment may enhance diagnostic precision. Access to ultrasound equipment, use of standardized imaging protocols, archiving and reporting mechanisms, collaborations between neonatology and cardiology, and quality assurance mechanisms are essential components of TNE programs.

CHD

congenital heart disease

FAC

fractional area change

IVS

interventricular septum

LVO

left ventricular output

PAAT

pulmonary artery acceleration time

PDA

patent ductus arteriosus

PH

pulmonary hypertension

PVR

pulmonary vascular resistance

RVO

right ventricular output

RVSp

right ventricular systolic pressure

SVC

superior vena cava

TAPSE

tricuspid annular plane systolic excursion

TDI

tissue Doppler imaging

TNE

targeted neonatal echocardiography

TR

tricuspid regurgitation

VTI

velocity time integral