Ethical statement

Animal housing and all experimental procedures were approved by the local Committee for Experimental Animal Research (Cantonal Veterinary Office Zurich, Switzerland) under the license number ZH119/2019, and were conforming to the European Directive 2010/63/EU of the European Parliament and the Council on the Protection of Animals used for Scientific Purposes, as well as to the Guide for the Care and Use of Laboratory Animals [20].

Anesthesia and animal instrumentalization

Anesthesia was induced by i.v. injection of ketamine hydrochloride [Ketasol®-100 ad us.vet.; Dr. E. Graeub AG, Berne, Switzerland; 3 mg/kg body weight (BW)] in combination with midazolam (Dormicum®, Roche Pharma (Schweiz) AG, Reinach, Switzerland; 0.2 mg/kg BW) and propofol (Propofol®– Lipuro 1%, B. Braun Medical AG; Sempach, Switzerland 2–4 mg/kg/h; 2–5 mg/kg BW). After intubation, anesthesia was maintained by positive pressure ventilation (fresh gas flow 1–1.5 L/min, 12–15 breaths/min, tidal volume 10–15 mL/kg, FiO2 0.5) of 2–3% isoflurane in oxygen/air mixture and a continuous infusion pump applying propofol. Throughout the procedure the animals additionally received a continuous intravenous infusion of sufentanil (Sufenta® Forte, Janssen-Cilag AG, Zug, Switzerland; 0.05 mg/kg/h).

In all sheep (Table 1), percutaneous ultrasound guided placement of a carotid arterial line (4 Fr) and a multilumen jugular vein catheter (AeroGuard Blue, Arrow®, Teleflex Medical Europe Ltd., Ireland) was performed (Fig. 1). For measurement of ICP, a 9 Fr catheter (Ref. 55-3000, Neuromedex GmbH, Hamburg, Germany) was placed through a right frontal burr hole trephination approximately 2 cm from the sagittal suture. This catheter was placed in the right lateral ventricle, confirmed via inspection of CSF egression along the catheter, and anchored with Ethicon Bonewax (Johnson & Johnson Medical Ltd., Livingston, UK) to avoid CSF leakage. A 4.5 Fr Neuromedex catheter (Ref. 61-1400) was placed in the intrathecal sac to measure ITP via a laminotomy at level L6-7. The same access was used for the spinal needle (Perifix 310 mini set, 5 Fr, B.Braun Melsungen AG, Melsungen, Germany) placement to perform the infusion experiments. In both cases, the catheter and needle were anchored with Ethicon Bonewax (Johnson and Johnson Medical Ltd.) to avoid CSF leakage. Hydrostatic equivalence was maintained between the intraventricular and intrathecal transducers by zeroing them to atmospheric pressure at level of the lateral ventricles and the arterial and venous sensors at the right atrial level. All transducers were fixated to the skin with either surgical clamps or sutures. After instrumentalization the sheep was placed in sternal position throughout the experiment, mimicking horizontal position in humans at which the ITP and ICP are assumed to not be influenced by hydrostatic variations.

Table 1 Demographic data of all sheep used in this study
Fig. 1
figure1

Pressure measurement locations considered in this study. 1, Intracranial pressure (ICP); 2, Intrathecal pressure (ITP); 3, Carotid Arterial Blood arterial blood pressure (ABP); 4, Central Venous venous pressure (CVP)

Experimental protocol

The goal-driven experimental protocol was designed to adequately illuminate how ICP, ITP, ABP, and CVP propagate with each other across a range of pre-defined and well-controlled scenarios. Part of this protocol was a detailed infusion study, which contained intrathecal bolus and CPI. To ensure accurate control, an automated infusion apparatus was used [21]. The apparatus allowed for volume and pressure control of the bolus and CPI, respectively. The peristaltic pump of the pressure controller induced additional oscillations while regulating pressure lower than the roller frequency, which were subsequently filtered using a Butterworth forward–backward band stop filter of order 4 with a stopband of 0.2–0.5 Hz. To perform the infusions, the apparatus was connected to the needle placed in the lumbar thecal sac and was verified to be at the same relative height as the ITP transducer to avoid hydrostatic variations.

Bolus infusions of 2 mL Ringer’s solution were injected directly into the lumbar intrathecal space. Relaxation time was set to 7 min or until baseline values were resumed. CPI contained six unique elevated pressure steps of 3.75 mmHg starting from a sheep-specific pressure that depended on the initial baseline pressure.

Data acquisition and analyses

All data were acquired using the commercially available software, Ponemah v5.1 (Data Science International, St. Paul, USA) with the ACQ-7700 acquisition unit using the Universal XE and ABCD 4 to amplify the signal. All data were acquired at a sampling frequency of 1 kHz, discriminated to 100 Hz and analyzed using custom scripts written in Python 3.7.10 (Open Source, Python Software Foundation, Willmington, Delaware, United States). Baseline mean pressures and pulse amplitudes were measured as 5-min arithmetic means before the first infusion; these values were then used as the defined baseline values for calculation. Values are reported as mean ± SD. The frequency spectrum of the raw data was analyzed using discrete fast Fourier transform (FFT).

Mean reactions

To gain initial insights into how the pressures of interest reacted to the volumetric pressure changes induced by the infusions, mean reactions were calculated after the data was pre-processed. Outliers were rejected by using a z-score rejection method with a σcrit of 3. Then, to remove effects of the cardiac and respiratory waveforms, the data was lowpass filtered using a 4th order forward/backward Butterworth filter with a cutoff frequency of 0.1 Hz (10 s periods). This excluded physiologic effects while retaining the bulk effects seen by infusions. Mean changes were calculated for the bolus and CPI. Temporal offsets were calculated using cross-correlation.

The pressure changes over the six discrete bolus infusions are calculated as peak post-infusion pressure minus peak pre-infusion pressure of the lowpass filtered data (Fig. 2). The constant pressure infusions are split into six discrete pressure steps. The mean pressure steps, calculated as the averages over the entire length of the pressure step once the pressure has stabilized, was calculated.

Fig. 2
figure2

Visualization of how mean changes in pressure were calculated for bolus infusions (top) and constant pressure infusions (bottom). Individual pressure steps used for the constant pressure infusions can be seen in bottom. Horizontal lines depict the upper and lower limits used for calculations. Please note that the timeframe represents elapsed time. Shown on data from Sheep F. ICP intracranial pressure; ITP intrathecal pressure; ABP arterial blood pressure; CVP central venous pressure

Pulse amplitude reactions

Pressure signals were evaluated over lumbar intrathecal bolus and constant pressure infusions. All amplitudes were calculated as the difference between the systolic and diastolic pressures (Fig. 3). Pulse amplitudes during bolus infusions were calculated as arithmetic averages 10 s pre and post infusion. Amplitudes during constant pressure infusions were calculated as arithmetic averages over the length of the entire pressure step.

Fig. 3
figure3

Visualization of how reactions were calculated during bolus infusions (Top) and constant pressure infusions (Bottom). Individual pressure steps used for the constant pressure infusions Horizontal lines illustrate example upper and lower limits of pressure waveforms. All amplitudes are peak-to-peak. Please note that the timeframe represents elapsed time. ICPamp, intracranial pressure pulse amplitude; ITPamp, intrathecal pressure pulse amplitude; ABPamp, arterial blood pressure pulse amplitude; CVPamp, central venous pressure pulse amplitude

CSF outflow resistance

CSF outflow resistance (Rout) was calculated using the methods outlined in Eklund et al. [10] using ICP data during bolus (Eqs. 1, 2) and constant pressure infusion (Eq. 3) methods. For the bolus method (CSF outflow resistance (Rout) was calculated using the methods outlined in Eklund et al. [10] using ICP data during bolus (Eqs. 1, 2) and CPI (Eq. 3) methods. For the bolus method (Fig. 4A), the pressure–volume index (PVI) is first calculated with:

$$PVI = { }frac{Delta V}{{log left( {frac{{P_{p} – P_{0} }}{{P_{r} – P_{0} }}} right)}}{ ,}$$

(1)

where (Delta {text{V}}) is the amount of infused volume, ({text{P}}_{{text{p}}}) is the peak pressure post-infusion, ({text{P}}_{{text{r}}}) is the resting pressure just before the infusion, and P0 is the reference pressure (assumed to be zero). Then, Rout can be determined from the spontaneous relaxation curve post-infusion (Eq. 2),

$$R_{out} = frac{{tP_{r} }}{{PVI*log left[ {frac{{left( {frac{{P_{t} }}{{P_{p} }}} right)left( {P_{p} – P_{r} } right)}}{{P_{t} – P_{r} }}} right]}} ,$$

(2)

where ({text{t}}) is the time post-infusion and ({text{P}}_{{text{t}}}) is the relaxation pressure at time ({text{t}}). Relaxation pressures were taken at 1-, 2-, 3-, and 4-min post bolus infusion to calculate Rout as an average across these four timepoints.

Fig. 4
figure4

A Bolus infusion method for calculating Rout. B CPI method for calculating Rout. Pressure curves taken from sheep F. Please note that the timeframe represents elapsed time. Pr, resting pressure pre-infusion; Pp, peak pressure post infusion; Pt, relaxation pressure at time t post infusion; Pb, pre-infusion baseline pressure; Pa, average pressure during infusions

For the CPI method (Fig. 4B), infusion pressures were averaged across the entire pressure step once pressures attained steady state. Each infusion pressure step is taken as the pre-infusion baseline pressure (Pb) and average pressure during (Pa) infusion and divided by the infusion rate required to maintain the pressure at the next step (Eq. 3).

$$R_{out} = frac{{P_{a} – P_{b} }}{{Q_{inf} }}$$

(3)

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