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Advances in obstetric and neonatal intensive care have led to dramatic increases in survival for the most premature and low-birth-weight infants. However, these infants are vulnerable to developing intraventricular hemorrhage and severe neurodevelopmental disabilities. In particular, experts believe disturbances of cerebral blood flow (CBF) regulation are associated with brain injury. Cerebral autoregulation is an essential physiologic process that maintains constant blood flow to the brain despite alterations in blood pressure. Thus, the determination of impaired CBF regulation during the first hours and days of life may prevent brain damage and is a valuable diagnostic to optimize clinical decisions in these vulnerable infants. We propose to develop a bedside diagnostic system, the Real-Time Autoregulation Diagnostic (RAD) system, that will incorporate several single clinical measures into statistical models. These models will in turn provide immediate information about a child's current autoregulation status. This system will aid clinicians in making quality intensive care decisions that will protect the neonatal brain.

Introduction background
Introduction: Background

  • Autoregulation is the body’s ability to keep cerebral blood flow (CBF) at a viable level even though blood pressure (BP) is changing.

  • Autoregulation cannot be directly observed.

  • Figure 1 is a graph of an intact autoregulation scenario. The flat part of the curve between BP values of 30 and 40 is termed the “autoregulatory plateau.” An autoregulatory plateau that becomes increasingly uphill is associated with a worsened autoregulatory condition because a rise in BP results in a rise in CBF, perhaps to levels that cause brain damage in very-low-birth-weight (VLBW) infants.

Introduction the problem
Introduction: The Problem

  • It is important to note that cerebral autoregulation must be determined with a statistical model estimated from an infant’s concurrently observed CBF and BP responses over time. Cerebral autoregulation is a process that exists, but it is almost impossible to address by merely looking at concurrent readings of CBF and BP. PaCO2 is a strong effect modifier to the autoregulation status. This being the case, accurate monitoring of autoregulation diagnostic information is the result of fitting a model to concurrently collected CBF, BP, and PaCO2 data.

  • The goal is to develop an autoregulation statistic, which currently does not exist, that can be estimated “on the fly” from a continuous biological monitoring system on premature newborn children.

Introduction the problem cont
Introduction: The Problem (cont.)

  • Unknown relationships exist between the CBF responses and their predictors, yet high quality predictions are needed in order to develop an autoregulation statistic.

  • A subject must be monitored for a period of time such that a set of estimated CBF values can be predicted in a supposed setting in which the blood pressure increases over a clinically feasible set of values. Then, from this predicted relationship we hope to determine what level of autoregulation exists for a patient at a particular time in order to make sound clinical decisions.

Methods partial least squares pls
Methods: Partial Least Squares (PLS)

PLS has been labeled as a soft modeling approach that has been used in industrial and economic settings. Generally, settings for PLS application have a set of ingredients (predictor variables) and a set of performance measurements (responses). Correlation is often present both within the predictor variables and response variables as well as among the predictor and response variables.

Methods pls notes
Methods: PLS Notes

Excerpt from Tobias, “An Introduction to Partial Least Squares Regression.” Sas Institute.

“Research in science and engineering often involves using controllable and/or easy-to-measure variables (factors) to explain, regulate, or predict the behavior of other variables (responses)…In such so-called soft science applications, the researcher is faced with many variables and ill-understood relationships, and the object is merely to construct a good predictive model. For example, spectrographs are often used to estimate the amount of different compounds in a chemical sample. In this case, the factors are the measurements that comprise the spectrum; they can number in the hundreds but are likely to be highly collinear. The responses are component amounts that the researcher wants to predict in future samples.”

Methods pls notes cont
Methods: PLS Notes (cont.)

Excerpt from Tobias, “An Introduction to Partial Least Squares Regression.” Sas Institute.

“Partial least squares (PLS) is a method for constructing predictive models when the factors are many and highly collinear. Note that the emphasis is on predicting the responses and not necessarily on trying to understand the underlying relationship between the variables. For example, PLS is not usually appropriate for screening out factors that have a negligible effect on the response. However, when prediction is the goal and there is no practical need to limit the number of measured factors, PLS can be a useful tool.”

Methods pls application details
Methods: PLS Application Details

  • In our setting, it is conjectured that the last 10 second set of CBF responses is related to the levels of BP and PaCO2 in that same 10 second window. This implies that our response variables are the CBF values in the last 10 second time window, CBFt-10,..., CBFt-0 with predictors, BP and PaCO2 in the last 10 second time window, BPt-10,..., BPt-0 and PaCO2t-10,..., PaCO2t-0.

  • The PLS procedure reduces the response and predictor variables into a smaller number of orthogonal variables through an eigenvector analysis similar to a principal components algorithm. This allows predictions of CBF for a hypothetical 10 second window in which BP increases from 30 to 40 mm Hg by 1 mm Hg each second while PaCO2 stays fixed at a particular level of interest. We can then plot these predicted responses for a hypothetical time window and determine if CBF remains constant with increasing BP.

Methods pls application details cont
Methods: PLS Application Details (cont.)

  • A plot of the predicted CBF responses with increasing BP for 5 different PaCO2 profiles (PaCO2 = 35, 37.5, 40, 42.5, and 45 mm Hg) gives clinicians information about how levels of PaCO2 may be affecting the CBF-BP slope.

  • Currently, SAS PROC PLS does not provide standard error estimates for predictions. We are currently experimenting with bootstrapping methods in order to quantify the statistical accuracy of our PLS predictions.

Results intact autoregulation
Results: Intact Autoregulation



A “flat slope,” suggesting CBF is constant with increasing BP

PaCO2 Levels

(mm Hg)

Results impaired autoregulation
Results: Impaired Autoregulation

An “uphill slope,” suggesting CBF is increasing with rising BP



PaCO2 Levels

(mm Hg)

Summary conclusions

  • PLS is an effective statistical approach for modeling the CBF-BP relationship for a hypothetical BP increase over time. It provides quality predictions without having to specifically model unknown complex correlation structures.

  • The PLS predictions can be calculated and displayed quickly, giving clinicians information on autoregulation status that is not currently available.


Tobias, R. (1995), “An Introduction to Partial Least Squares Regression,” Nineteenth Annual SAS Users Group International Conference, Cary, NC: SAS Institute, 1250-1257.

Kaiser JR, Gauss CH, Williams DK. Surfactant administration acutely affects systemic and cerebral hemodynamics and gas exchange in very low birth weight infants. Journal of Pediatrics 2004, 144(6):809-814.

Kaiser JR, Gauss CH, Williams DK. The Effects of Hypercapnia on Cerebral Autoregulation in Ventilated Very Low Birth Weight Infants. Pediatric Research In Press.