Cerebral arterial time constant calculated from the middle and posterior cerebral arteries in healthy subjects

  • Agnieszka UrygaEmail author
  • Magdalena Kasprowicz
  • Małgorzata Burzyńska
  • Leanne Calviello
  • Katarzyna Kaczmarska
  • Marek Czosnyka
Original Research


The cerebral arterial blood volume changes (∆CaBV) during a single cardiac cycle can be estimated using transcranial Doppler ultrasonography (TCD) by assuming pulsatile blood inflow, constant, and pulsatile flow forward from large cerebral arteries to resistive arterioles [continuous flow forward (CFF) and pulsatile flow forward (PFF)]. In this way, two alternative methods of cerebral arterial compliance (Ca) estimation are possible. Recently, we proposed a TCD-derived index, named the time constant of the cerebral arterial bed (τ), which is a product of Ca and cerebrovascular resistance and is independent of the diameter of the insonated vessel. In this study, we aim to examine whether the τ estimated by either the CFF or the PFF model differs when calculated from the middle cerebral artery (MCA) and the posterior cerebral artery (PCA). The arterial blood pressure and TCD cerebral blood flow velocity (CBFVa) in the MCA and in the PCA were non-invasively measured in 32 young, healthy volunteers (median age: 24, minimum age: 18, maximum age: 31). The τ was calculated using both the PFF and CFF models from the MCA and the PCA and compared using a non-parametric Wilcoxon signed-rank test. Results are presented as medians (25th–75th percentiles). The cerebrovascular time constant estimated in both arteries using the PFF model was shorter than when using the CFF model (ms): [64.83 (41.22–104.93) vs. 178.60 (160.40–216.70), p < 0.001 in the MCA, and 44.04 (17.15–81.17) vs. 183.50 (153.65–204.10), p < 0.001 in the PCA, respectively]. The τ obtained using the PFF model was significantly longer from the MCA than from the PCA, p = 0.004. No difference was found in the τ when calculated using the CFF model. Longer τ from the MCA might be related to the higher Ca of the MCA than that of the PCA. Our results demonstrate MCA-PCA differences in the τ, but only when the PFF model was applied.


Cerebral arterial blood volume changes Cerebral arterial time constant Cerebral arterial compliance Transcranial Doppler ultrasonography 



This research was supported by the National Science Centre (Poland) under Grant No. UMO-2013/10/E/ST7/00117.

Compliance with ethical standards

Conflict of interest

ICM+ Software is licensed by Cambridge Enterprise, Cambridge, UK, Prof. Czosnyka has a financial interest in a fraction of the licensing fee for ICM+ software. The other authors declare that they have no conflict of interest.

Informed consent

The protocol complied with the Declaration of Helsinki of the World Medical Association, and all participants gave written informed consent before participating in the study. All patients had a study identification number and the data was anonymized before analysis.

Research involving human and animal rights

This study was approved by the bioethical committee of the Wroclaw Medical University (permission no. KB—170/2014).


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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.Department of Biomedical Engineering, Faculty of Fundamental Problems of TechnologyWroclaw University of Science and TechnologyWrocławPoland
  2. 2.Department of Anesthesiology and Intensive CareWroclaw Medical UniversityWrocławPoland
  3. 3.Brain Physics Laboratory, Division of Neurosurgery, Department of Clinical NeurosciencesUniversity of CambridgeCambridgeUK
  4. 4.Department of NeurosurgeryMossakowski Medical Research Centre Polish Academy of SciencesWarsawPoland
  5. 5.Institute of Electronic Systems, Faculty of Electronics and Information TechnologyWarsaw University of TechnologyWarsawPoland

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