Second Largest Eigenvalue of the Transition Probability Matrix for the Markov Chain Constructed from the Arterial Blood Pressure Waveform is Not Correlated to Shock Index in Hemorrhagic Human Subjects


  • Brett Collar Purdue University
  • Marvi Bikak Indiana University School of Medicine
  • Paul Brown Paradigm4
  • Zachary Pitluk Paradigm4
  • Mohammad Adibuzzaman Regenstrief Center for Healthcare Engineering


Correctly identifying when a hemorrhagic patient needs immediate medical attention to prevent acute hypotensive episode (AHE) is vital in the short- and long-term care, but is often complicated due to the physiological responses in the sympathetic and parasympathetic nervous systems that mask symptoms until a significant amount of blood loss has occurred. These physiological responses affect the arterial blood pressure waveform, changing both dynamics and waveform morphology. Through the use of Markov chain analysis of the arterial blood pressure waveform, we first analyzed patient blood pressure waveforms from a challenge dataset published by Computing in Cardiology 2009 and the MIMIC III database. Markov chain analysis was applied to 20 second intervals over the entirety of a patient’s known acute hypotensive episode. Each interval or segment is one second apart from the previous segment with a nineteen second overlap. The mixing rate (2nd largest eigenvalue of the transition probability matrix) was determined for all segments. A subset of patients showed a Pearson correlation coefficient with shock index (SI), i.e., with the ratio of heart rate and systolic blood pressure, similar to a previous swine study. These patients (mean correlation coefficient -0.423 ± 0.32, median -0.352) were found to have been administered pressors (vasoconstrictors), compared to patients who were not administered pressors (mean correlation coefficient 0.392 ± 0.29, median 0.447). Patients were also analyzed based on diagnoses of gastrointestinal bleeding by the ICD-9 code, and mixing rate results were compared between patients in this subgroup and found to have no significance as a metric of predicting acute hypotensive episodes.






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