Clinical indices (layer 3)¶

pipeline ¶

Clinical indices of a tidal recording or of a PEEP trial (layer 3).

Definitions and evidence: notebooks/07_clinical_indices.ipynb (section 5):

EELI and TIV of a breath: one sample at the frames of the layer 2 breaths, on the signal inside the lung mask; EELI at the start of the breath, TIV = peak - start (TREND: Frerichs et al., Thorax 2017, DOI: 10.1136/thoraxjnl-2016-208357);
per breath: TIV, EELI and share by region, GI, centre of ventilation, respiratory rate, compliance in EIT units (TIV / driving pressure) and in mL/cmH2O (tidal volume / driving pressure); with a tidal volume, the TIV and compliance of each region in mL (share x tidal volume);
tidal recording: median and quartiles over the valid breaths;
PEEP trial: per step, medians of the analysed breaths, compliance (also as % of the best step), Costa collapse and overdistension, changes vs the previous and the first step (EELI in tidal volumes and in mL, compliance); for the trial, the crossing PEEP, the best PEEP and the recruitment-to-inflation ratio, global and by region.

The tables hold the keys (breath_id, step, peep, region) and what this layer computes; what layers 2 and 2b measured stays in recording.breaths, trial.breaths and trial.steps, reached from the same object.

tidal_features ¶

tidal_features(recording: EITRecording, phase: Segment | None = None) -> TidalFeatures

Clinical indices of each breath of a recording at one setting, and their summary.

Parameters:

Name	Type	Description	Default
`recording`	`EITRecording`	Output of `preprocess()`.	required
`phase`	`Segment \| None`	The tidal part of the recording: a segment with `category="phase"` and `label="tidal"`; the summary uses only its breaths. If None, the whole recording.	`None`

Returns:

Type	Description
`TidalFeatures`	The breath, region and summary tables. The summary uses the valid breaths of
`TidalFeatures`	the phase (no quality flag, not excluded).

Raises:

Type	Description
`ValueError`	if the phase is not usable or no breath is inside it.

peep_trial_features ¶

peep_trial_features(trial: PeepTrial, config: AnalysisConfig | None = None) -> PeepTrialFeatures

Clinical indices of each breath and of each PEEP step of a PEEP trial.

The indices of a step come from its analysed breaths (segment_peep_trial()): medians of the breath indices; compliance in EIT units = median TIV / driving pressure of the step, in mL/cmH2O = tidal volume / driving pressure of the step (both kept: the EIT compliance also sees what changes in the slice); Costa collapse and overdistension from the median tidal image of each step; the recruitment-to-inflation ratio between the steps nearest to the PEEP levels of the config, globally and by region.

Parameters:

Name	Type	Description	Default
`trial`	`PeepTrial`	Output of `segment_peep_trial()`.	required
`config`	`AnalysisConfig \| None`	Parameters; defaults of `AnalysisConfig` if None.	`None`

Returns:

Type	Description
`PeepTrialFeatures`	The breath, region, step, step-region and summary tables.

breath_indices ¶

Indices of the distribution of ventilation in one breath, from its tidal image.

The tidal image of a breath is each pixel at the end-inspiratory peak minus the same pixel at the start of the breath (end-expiratory valley), inside the lung mask: the "inspiratory" TIV of TREND (Frerichs et al., Thorax 2017, DOI: 10.1136/thoraxjnl-2016-208357), one sample at the frames of the layer 2 breaths (notebooks/07_clinical_indices.ipynb, sections 1-2).

tidal_images ¶

tidal_images(pixels: ndarray, starts: ndarray, peaks: ndarray, lung_mask: ndarray) -> np.ndarray

Tidal image of each breath: pixel at the peak minus pixel at the start.

Parameters:

Name	Type	Description	Default
`pixels`	`ndarray`	(N, rows, cols) images after the cardiac step.	required
`starts`	`ndarray`	Frame of the start of each breath.	required
`peaks`	`ndarray`	Frame of the peak of each breath.	required
`lung_mask`	`ndarray`	(rows, cols) bool, the ventilated lung.	required

Returns:

Type	Description
`ndarray`	(n_breaths, rows, cols) float, NaN outside the lung mask.

global_inhomogeneity ¶

global_inhomogeneity(image: ndarray) -> float

Global inhomogeneity index of one tidal image (lung pixels, NaN elsewhere).

GI = sum(|DI_xy - median(DI_lung)|) / sum(DI_lung), over the lung pixels (Zhao et al., Intensive Care Med 2009;35:1900-1906, DOI: 10.1007/s00134-009-1589-y). 0 for a homogeneous ventilation; higher when the ventilation is uneven.

Returns:

Type	Description
`float`	GI; NaN if the lung has no tidal variation.

centre_of_ventilation ¶

centre_of_ventilation(image: ndarray) -> tuple[float, float]

Centre of ventilation of one tidal image, ventro-dorsal and right-left.

TIV-weighted mean row (column), divided by the last row (column) of the image (Frerichs et al., Am J Respir Crit Care Med 2006;174:772-779, DOI: 10.1164/rccm.200512-1942OC), on the image grid, not on the regions of the lung, so that a shift of ventilation is not hidden (notebooks 05 and 07). The image is seen from the feet: ventro-dorsal 0 = ventral, 1 = dorsal; right-left 0 = patient right, 1 = patient left. 0.5 is the middle of the image.

Returns:

Type	Description
`tuple[float, float]`	(ventro-dorsal, right-left); NaN if the lung has no tidal variation.

costa ¶

Collapse and overdistension in a PEEP trial, from the compliance of each pixel.

Costa et al., Intensive Care Med 2009;35:1132-1137, DOI: 10.1007/s00134-009-1447-y; formulas as reported by Shono and Kotani, J Intensive Care 2019;7:4, DOI: 10.1186/s40560-019-0358-4 (notebooks/07_clinical_indices.ipynb, section 4):

compliance of a pixel at a step = TIV of the pixel / driving pressure of the step;
each pixel has its best compliance, at its best PEEP;
at a step with a PEEP below the best PEEP of the pixel, its loss of compliance as % of its best is collapse; above, overdistension;
collapse (overdistension) of a step = mean of the pixel %, weighted by the best compliance of each pixel, over the pixels of the lung mask;
the crossing of the two curves is the PEEP with the best balance between them.

Compliance stays in EIT units: the method needs no tidal volume. An error common to all the pixels of a step (its driving pressure, the share of the tidal volume seen by the slice) shifts them together and appears as collapse or overdistension.

collapse_and_overdistension ¶

collapse_and_overdistension(pixel_compliance: ndarray, peep: ndarray, lung_mask: ndarray) -> pd.DataFrame

Collapse and overdistension (%) of each step (Costa 2009, formulas of Shono and Kotani 2019, see the module docstring).

collapse(step) = sum(loss_pixel(step) x best_pixel) / sum(best_pixel) over the pixels whose best PEEP is above the PEEP of the step, with loss_pixel = (best_pixel - compliance_pixel(step)) / best_pixel x 100; overdistension the same over the pixels whose best PEEP is below it. The loss of a pixel is at most 100 %.

Parameters:

Name	Type	Description	Default
`pixel_compliance`	`ndarray`	(n_steps, rows, cols) compliance of each pixel at each step (TIV / driving pressure); NaN where unknown, e.g. a step without a driving pressure.	required
`peep`	`ndarray`	PEEP of each step.	required
`lung_mask`	`ndarray`	(rows, cols) bool, the pixels used.	required

Returns:

Type	Description
`DataFrame`	One row per step: `collapse` and `overdistension` (%); NaN for a step
`DataFrame`	without compliance, and for every step if fewer than 2 steps have one or no
`DataFrame`	pixel has a positive best compliance.

crossing_peep ¶

crossing_peep(peep: ndarray, collapse: ndarray, overdistension: ndarray) -> float

PEEP where the collapse and overdistension curves cross (Costa 2009).

Going up in PEEP, collapse - overdistension must change sign, from positive to negative: linear interpolation between the two steps, or the PEEP of a step where the two are equal between them. Curves that only touch (the difference goes back to positive, or stays at 0 up to the highest PEEP) do not cross. If they cross more than once, the lowest crossing.

Returns:

Type	Description
`float`	The crossing PEEP; NaN if the curves do not cross.

recruitment ¶

Recruitment-to-inflation ratio (R/I) of a PEEP trial, from EIT.

R/I (Chen et al., Am J Respir Crit Care Med 2020;201:178-187, DOI: 10.1164/rccm.201902-0334OC): when PEEP falls from a high to a low level, the lung loses more volume than its compliance at the low PEEP predicts; the excess is the volume that was recruited at the high PEEP:

predicted volume  = C_low x dPEEP
recruited volume  = dEELV - C_low x dPEEP
R/I               = (recruited volume / dPEEP) / C_low

With EIT the change of end-expiratory lung volume is the change of EELI converted with the tidal volume / TIV of the low PEEP step (Wang et al., Med Sci Monit 2020;26:e922609, DOI: 10.12659/MSM.922609), and C_low = tidal volume / driving pressure of the low step. The tidal volume cancels in R/I, which therefore needs only EIT and the driving pressure:

R/I = dEELI / (C_EIT,low x dPEEP) - 1,   with C_EIT,low = TIV_low / driving_low

and it applies to a region with its own EELI and EIT compliance. The original method reads one expiration after the drop of PEEP; here each level is the equilibrium EELI of a step, as in Wang 2020.

ri_steps ¶

ri_steps(peep: ndarray, high: float, low: float, min_drop: float) -> tuple[int, int] | None

The two steps used for R/I: the nearest to the high and to the low PEEP.

The high step is the step nearest to high; the low step is the step nearest to low among those at least min_drop below the high step (the first one if two are equally near).

Parameters:

Name	Type	Description	Default
`peep`	`ndarray`	PEEP of each step.	required
`high`	`float`	Target high PEEP (e.g. 15).	required
`low`	`float`	Target low PEEP (e.g. 5).	required
`min_drop`	`float`	Smallest drop of PEEP between the two steps.	required

Returns:

Type	Description
`tuple[int, int] \| None`	Index of the high and of the low step, or None if no pair drops enough.

recruitment_to_inflation ¶

recruitment_to_inflation(eeli_high: float, eeli_low: float, tiv_low: float, driving_low: float, peep_drop: float, tidal_volume_low: float) -> tuple[float, float]

R/I and recruited volume between a high and a low PEEP step (see the module).

Parameters:

Name	Type	Description	Default
`eeli_high`	`float`	EELI of the high step (EIT units, global or of a region).	required
`eeli_low`	`float`	EELI of the low step, of the same region (EIT units).	required
`tiv_low`	`float`	TIV of the low step, of the same region (EIT units).	required
`driving_low`	`float`	Driving pressure of the low step (cmH2O).	required
`peep_drop`	`float`	PEEP of the high step minus PEEP of the low step (cmH2O).	required
`tidal_volume_low`	`float`	Tidal volume of the low step, times the share of the region for a region (mL); NaN if unknown.	required

Returns:

Type	Description
`float`	R/I, and the recruited volume in mL (NaN without a tidal volume); NaN if a value
`float`	is missing or the low compliance or the drop of PEEP is not positive.