Purpose of the study: CPR guidelines recommend limits for rate and depth of chest compressions. Little is known about the interactions between rate and depth. We analyzed the relation between rate and depth of chest compressions during continuous chest compressions (CCC) CPR in out-of-hospital resuscitations.
Methods: Rate and depth signals were extracted from 616 adult cases of manual CPR during out-of-hospital resuscitations attended by a single EMS agency (TVFR, Tigard, Oregon) during 2013 through 2017. Signals were extracted from monitor/defibrillators equipped with CPR monitors. Rescuers received real-time feedback on rate, depth and leaning.
We computed compression depth and velocity from recorded acceleration using forward and reverse digital filtering to preserve phase. Chest compressions (n = 1,172,873) were automatically identified in the velocity signal using a threshold of 25mm/s, and were required to have a peak force of at least 5 kg-f. Peak depth and duration were measured for each compression. Rate was calculated as the inverse of duration.
The dependence of depth on rate was calculated with a generalized linear mixed effect model, isolating differences between cases  and position in the rescue as random effects.
Results: Cases included 1726 (1046 - 2609) (median, IQR) compressions. The model shows that depth depends on rate: 
Depth (mm) = 64.4 (±0.36) – 0.12 (±0.001) * Rate (cpm) , p < 0.001
Observed values are shown in the figure. Above a rate of 90 cpm, compression depths are well modeled as declining linearly with rate. Above the upper recommended bound on rate of 120 cpm, median depth falls below recommended minimum of 50 mm (2"), and it continues to decline at higher rates.
Conclusions: In out-of-hospital manual CPR, compression depth declines with compression rate. Median depth falls below guideline recommendation when rate exceeds current guideline recommendations during CCC CPR.

3 - Compression depth declines below CPR guidelines when rate exceeds guidelines.