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State-space representation is a powerful tool for simulating physical systems on digital computers, necessitating the conversion of the transfer function into state-space form. Consider an nth-order linear differential equation with constant coefficients, like those encountered in an RLC circuit. The state variables are selected as the output and its n−1 derivatives. Differentiating these variables and substituting them back into the original equation produces the state equations.
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State Space to Transfer Function01:21

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The conversion of state-space representation to a transfer function is a fundamental process in system analysis. It provides a method for transitioning from a time-domain description to a frequency-domain representation, which is crucial for simplifying the analysis and design of control systems.
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Watershed functional lung space: a pendelluft-aware EIT segmentation method.

Peter Somhorst1, Juliette E Francovich1, Diederik Gommers1

  • 1Department of Intensive Care, Erasmus Medical Center, Rotterdam, The Netherlands.

Physiological Measurement
|January 23, 2026
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Summary
This summary is machine-generated.

A new watershed segmentation method for functional lung space (FLS) selection in electrical impedance tomography (EIT) better captures pendelluft during assisted mechanical ventilation (AMV). This approach improves EIT analysis by including lung regions affected by pendelluft.

Keywords:
electrical impedance tomographyfunctional lung spacesegmentationwatershed

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Area of Science:

  • Respiratory Physiology
  • Medical Imaging
  • Computational Biology

Background:

  • Pendelluft, the inter-regional air movement in the lungs, causes phase shifts in aeration curves.
  • Electrical impedance tomography (EIT) quantifies lung aeration and can detect pendelluft.
  • Current functional lung space (FLS) selection using tidal impedance variation (TIV) thresholds may exclude pendelluft regions due to phase shifts.

Purpose of the Study:

  • To develop and evaluate a novel watershed segmentation method for FLS selection in EIT.
  • To compare the novel Watershed FLS with the conventional TIV-based FLS, particularly during transitions in mechanical ventilation.
  • To assess the impact of the FLS selection method on pendelluft quantification.

Main Methods:

  • A watershed segmentation algorithm was developed for FLS selection based on pixel amplitude and local peaks.
  • The Watershed FLS includes regions where local peaks align with the TIV-based FLS.
  • The algorithm was tested on 11 patients transitioning from controlled mechanical ventilation (CMV) to assisted mechanical ventilation (AMV).

Main Results:

  • No significant difference in FLS size was observed between TIV FLS and Watershed FLS during CMV.
  • Switching to AMV significantly decreased TIV FLS but not Watershed FLS, resulting in a smaller TIV FLS compared to Watershed FLS.
  • Pendelluft magnitude was significantly higher when quantified using Watershed FLS compared to TIV FLS during AMV.

Conclusions:

  • Conventional TIV-based FLS selection may inadvertently exclude lung regions affected by pendelluft.
  • The Watershed FLS method retains pendelluft-associated pixels, offering a more comprehensive analysis.
  • This improved FLS selection has the potential to enhance EIT analysis accuracy in patients with spontaneous breathing efforts.