 Research
 Open Access
Blood pressure waveform contour analysis for assessing peripheral resistance changes in sepsis
 Shaun Davidson^{1}Email authorView ORCID ID profile,
 Chris Pretty^{1},
 Joel Balmer^{1},
 Thomas Desaive^{2} and
 J. Geoffrey Chase^{1}
https://doi.org/10.1186/s1293801806034
© The Author(s) 2018
 Received: 13 August 2018
 Accepted: 9 November 2018
 Published: 20 November 2018
Abstract
Background
This paper proposes a methodology for helping bridge the gap between the complex waveform information frequently available in an intensive care unit and the simple, lumped values favoured for rapid clinical diagnosis and management. This methodology employs a simple waveform contour analysis approach to compare aortic, femoral and central venous pressure waveforms on a beatbybeat basis and extract lumped metrics pertaining to the pressure drop and pressurepulse amplitude attenuation as blood passes through the various sections of systemic circulation.
Results
Validation encompasses a comparison between novel metrics and wellknown, analogous clinical metrics such as mean arterial and venous pressures, across an animal model of induced sepsis. The novel metric O_{fe → vc}, the direct pressure offset between the femoral artery and vena cava, and the clinical metric, ΔMP, the difference between mean arterial and venous pressure, performed well. However, O_{fe → vc} reduced the optimal average time to sepsis detection after endotoxin infusion from 46.2 min for ΔMP to 11.6 min, for a slight increase in false positive rate from 1.8 to 6.2%. Thus, the novel O_{fe → vc} provided the best combination of specificity and sensitivity, assuming an equal weighting to both, of the metrics assessed.
Conclusions
Overall, the potential of these novel metrics in the detection of diagnostic shifts in physiological behaviour, here driven by sepsis, is demonstrated.
Keywords
 Septic shock
 Cardiovascular monitoring
 Arterial pressure waveform
 Pressure catheter
 Linear leastsquares
Background
One of the leading worldwide causes of intensive care unit (ICU) admission and mortality is cardiovascular disease and dysfunction (CVD), which costs an estimated $863 billion USD per annum (2010), and is the cause of roughly 31% of global deaths (2013) [1]. Thus, research into mitigating these large human and economic costs is a significant and ongoing field, ranging from work on less invasively estimating useful, but difficult to measure, clinical metrics [2–5], or a lumped model of the cardiovascular system [6, 7], in an ICU environment, to work on investigating, selecting or estimating metrics of preclinical risk of cardiovascular [8, 9] and arterial disease [10, 11].
A notable contributor to the aforementioned human and economic costs is sepsis, a distributive shock condition that drives myocardial depression [12], is associated with 20–50% mortality in affected patients, and is, itself, responsible for some 10.4% of ICU admissions in the US [13]. Inadequate or incorrect diagnosis of conditions such as sepsis leads to increased length of stay, cost and mortality, further inflating the above figures [14, 15]. Management of CVD in the ICU is typically informed by measurements from catheters situated near the heart. Despite, or potentially partially due to, the information rich nature of their output waveforms, the use of these catheters is not necessarily associated with improved clinical outcomes [16, 17].
Specifically, the human mind can simultaneously track only three to four variables effectively [18]. The volume of information presented to clinicians in an ICU environment is often far greater than this number. Thus, simplification, abstraction, and synthesis to present the most relevant pieces of clinical information in an easy to interpret form, in realtime, has potential to provide significant benefits to patient diagnosis and titration of treatment.
The circulatory system can be broken down into pulmonary and systemic circulations. Due to the smaller diameter of arteries and veins in the pulmonary circulation, catheters are typically placed in the systemic circulation [19], popularly in the aorta, femoral artery or vena cava [20–22]. The catheter measured pressure waveform passing through the systemic circulation is modulated by the systemic circuit. Thus, the evolution of the blood pressure waveform contains information on the condition of the systemic circulation, and patient condition. There is potential to extract some of this information directly from these catheter pressure waveforms, without first having to model the entire circulatory system. This approach could offer significant insight for relatively minimal effort.
Several existing methods compare input and output waveforms without specific modelling of the associated systems. Transfer functions are among the most common, frequently generated using either fast Fourier transforms [23] or empirical mode decomposition [24]. While these two methods are adept at extracting information directly from waveforms, neither method is able to directly leverage the extensive a priori knowledge available on the circulatory system, making it more difficult to isolate specific physiological regions and influences in the waveforms, and thus making results more difficult to interpret as the result of specific physiological phenomena [25]. Further, both methods provide full spectra as an output for every set of heartbeats analysed, an output that is not necessarily any easier for a clinician to rapidly parse than the initial waveforms. Potentially due to these issues, most existing studies utilising transfer functions in cardiovascular medicine focus on longer term trends and the circulatory system’s autoregulation mechanisms [26, 27], rather than intrabeat cardiovascular mechanics as in this study.
In contrast to the spectra output by transfer functions, clinical practice favours very simple, lumped approximations of the entire waveform, such as mean arterial pressure (MAP) and mean venous pressure (MVP) [19]. However, these simple metrics can fail to isolate different influences, such as breathing, or, in the case of venous pressure, downstream heart behaviour, that can make changes in these metrics more difficult to interpret as the result of specific physiological phenomena. Hence, the novel metrics produced must be readily and easily interpreted by clinical staff, while providing greater insight and ensuring physiological and clinical relevance.
This paper proposes a method for helping bridge this gap between the complexity of information available and the simple, lumped values favoured clinically. It focuses on comparing amplitude and mean values between analogous sections of the aortic, femoral and vena cava pressure waveforms. Similar to a transfer function, it is a direct comparison of an input to an output, but operates in the time domain and provides simple, lumped outputs instead of a full frequency spectrum. Method outputs are compared to wellknown clinical metrics over an experimental data set of induced sepsis, a condition both clinically relevant, as previously mentioned, and diverse and difficult to diagnose [28, 29]. This method has the potential to provide outputs for easy, rapid interpretation in a clinical environment, while retaining more information from the underlying pressure waveforms than the wellknown lumped parameters currently used in critical care.
Methods
Experimental data
All experimental procedures and protocols were reviewed and approved by the Institutional Animal Care and Use Ethics Committee of the University of Liège, Belgium (Reference Number 141726). Their guidelines conform completely with the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 8523, revised 1996), as well as EU DIRECTIVE 2010/63/EU on the protection of animals used for scientific purposes.

An induced model of septic shock using an endotoxin infusion (lipopolysaccharide from E. coli, 0.5 mg/kg) over 30 min, causing inflammatory responses, capillary leakage and decreased afterload, leading to hypovolemia, global tissue hypoxia, and cardiac failure [31]. As such, this model of septic shock would be expected to cause dramatic changes in the behaviour of the systemic circulation.

Several PEEP driven recruitment manoeuvres (both pre and postendotoxin infusion), which drive a change in preload conditions and are typically associated with a decrease in mean blood pressure and cardiac output [32].

One to four infusions of 500 mL saline solution over 30 min periods (both pre and postendotoxin infusion), simulating fluid resuscitation therapy, a key component of hemodynamic resuscitation in severe sepsis, which results in a change in circulatory volume [33–37].
Once sepsis was sufficiently progressed that the subject was near death, and the arterial and venous waveforms became drastically different and largely incoherent, information was discarded. Due to the extremely advanced stage of circulatory failure at which this occurred, this information is likely of no use for diagnostic ICU monitoring. Note that not all pigs completed the entire protocol due to varying reactions to the endotoxin infusion. As such, the length of the monitoring period varies. However, each dataset consists of at least 5000 heartbeats.
Novel metric methodology
The method involves two distinct input–output comparisons. The first is between aortic pressure (P_{ao}, input) and femoral pressure (P_{fe}, output), encompassing the arterial system. The second is between femoral pressure (P_{fe}, input) and vena cava pressure (P_{vc}, output), encompassing both the arterial and venous systems, and the transfer between them. There are several reasons for the selections of these comparisons, both in a general ICU, and a sepsis context. First, all three locations are typical, well utilised sites for catheters in the ICU [20–22]. Second, comparing P_{ao} and P_{fe} allows isolation and evaluation of arterial dynamics, including arterial tone, which is known to change in sepsis [38]. Similarly, comparing P_{fe} and P_{vc} allows isolation and evaluation of the behaviour of the capillary beds, which are also known to be significantly influenced by sepsis [31]. Thus, these two comparisons isolate different components of the circulatory system that should be differently effected by sepsis, and will thus differently modulate the blood pressure waveforms passing through them as patient condition changes. Therefore, metrics derived from these comparisons, with other influences accounted for, should respond to and capture these sepsis driven dynamics.
From aortic pressure (P _{ao}) to femoral pressure (P _{fe})
Both P_{ao} and P_{fe} are situated in the arterial half of systemic circulation, and have very similar waveforms [19]. The primary distinction between the waveforms is the dicrotic notch in P_{ao}, which is a sharp dip in pressure due to the aortic valve shutting at the end of systole. Due to the elastic nature of the arterial system, this sharp dip has been largely smoothed out by the time the pressure wave reaches the femoral artery, and thus is typically not present in P_{fe}. This difference must be accounted for when comparing the two waveforms. The process used to compare P_{ao} and P_{fe} is thus:
 1.
Select P_{ao} and P_{fe} for a set of four heartbeats from beat i to beat i + 3. A set of four heartbeats corresponds to approximately one breathing cycle as set by a mechanical ventilator (15 bpm), and thus minimises fluctuations in the results due to applied pulmonary pressure [19].
 2.Compare peak and trough timing of P_{ao} and P_{fe} to determine phase lag:where, for example, t_{max(Pfe,i)} represents the peak timing of the ith beat of P_{fe}. δ_{ao → fe} is thus a positive value, in ms, representing the average amount of time by which P_{fe} lags P_{ao}, based on the differences in min and max timing of these two waveforms.$$\delta_{ao \to fe} = {\text{mean}}\left( {\left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {t_{{{ \hbox{max} }(P_{fe} ,i)}} } &  & {t_{{{ \hbox{max} }(P_{ao} ,i)}} } \\ \vdots & & \vdots \\ {t_{{{ \hbox{max} }(P_{fe} ,i + 3)}} } &  & {t_{{{ \hbox{max} }(P_{ao} ,i + 3)}} } \\ \end{array} } \\ {\begin{array}{*{20}c} {t_{{{ \hbox{min} }(P_{fe} ,i)}} } &  & {t_{{{ \hbox{min} }(P_{ao} ,i)}} } \\ \vdots & & \vdots \\ {t_{{{ \hbox{min} }(P_{fe} ,i + 3)}} } &  & {t_{{{ \hbox{min} }(P_{ao} ,i + 3)}} } \\ \end{array} } \\ \end{array} } \right]} \right)$$(1)
 3.
Shift P_{ao} right (forward in time) by δ_{ao → fe} such that the peaks and troughs of P_{ao} are aligned with those of P_{fe}. Henceforth, \(\widehat{P}_{ao}\) refers to P_{ao} that has undergone this phase shift alignment.
 4.Use linear least squares on analogous regions of the aligned \(\widehat{P}_{ao}\) and P_{fe} to find relative amplitude and associated offset between waveforms:where relative amplitude is A_{ao → fe} and identification offset is Δ_{ao → fe}. The waveform regions used in identification are highlighted in Fig. 1, and minimise the influence of the dicrotic notch on the linear least squares process.$$\left[ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {\widehat{P}_{ao} \left( {t_{{{ \hbox{min} }\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{ao} \left( {t_{{{ \hbox{max} }\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} \\ \end{array} } \right)} & {\begin{array}{*{20}c} 1 \\ \vdots \\ 1 \\ \end{array} } \\ \vdots & \vdots \\ {\left( {\begin{array}{*{20}c} {\widehat{P}_{ao} \left( {t_{{{ \hbox{min} }\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{ao} \left( {t_{{{ \hbox{max} }\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} \\ \end{array} } \right)} & {\begin{array}{*{20}c} 1 \\ \vdots \\ 1 \\ \end{array} } \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} {A_{ao \to fe} } \\ {\Delta_{ao \to fe} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {P_{fe} \left( {t_{{{ \hbox{min} }\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} \\ \vdots \\ {P_{fe} \left( {t_{{{ \hbox{max} }\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} \\ \end{array} } \right)} \\ \vdots \\ {\left( {\begin{array}{*{20}c} {P_{fe} \left( {t_{{{ \hbox{min} }\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} \\ \vdots \\ {P_{fe} \left( {t_{{{ \hbox{max} }\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} \\ \end{array} } \right)} \\ \end{array} } \right]$$(2)
 5.As A_{ao → fe} scales the entire P_{ao} waveform, thus modifying its mean value, Δ_{ao → fe} is heavily dependent on A_{ao → fe}, and thus a poor indication of the actual pressure offset between the two waveforms. Thus, Eq. 3 is used to provide O_{ao → fe}, a direct calculation of the mean difference between measured P_{ao} and the reconstructed P_{fe}, and is defined:$$O_{ao \to fe} = {\text{mean}}\left( {\left[ {\begin{array}{*{20}c} {\widehat{P}_{ao} \left( {t_{{{\text{start}}\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} & 1 \\ \vdots & \vdots \\ {\widehat{P}_{ao} \left( {t_{{{\text{end}}\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} & 1 \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} {A_{ao \to fe} } \\ {\Delta_{ao \to fe} } \\ \end{array} } \right]  \left[ {\begin{array}{*{20}c} {\widehat{P}_{ao} \left( {t_{{{\text{start}}\left( {\widehat{P}_{ao} ,i} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{ao} \left( {t_{{{\text{end}}\left( {\widehat{P}_{ao} ,i + 3} \right)}} } \right)} \\ \end{array} } \right]} \right)$$(3)
The resulting metrics characterising the relationship between the two pressure waveforms are the relative amplitude, A_{ao → fe}, and the direct pressure offset, O_{ao → fe}.
From femoral pressure (P _{fe}) to central venous pressure (P _{vc})
Between the femoral artery and the vena cava sit the capillary beds of the systemic circulation, where vessel diameter, flow rate and pressure drop significantly [19]. The pulsatile blood pressure wave in P_{fe} ceases to exist in the capillaries, and P_{vc} is, instead, a result of upstream flow out of the capillaries and downstream right heart behaviour. In an input–output sense, P_{fe} drives flow in the capillaries which, in turn, is the upstream driver of P_{vc}. While the direct pressure–pressure comparison from “Experimental data” section is a significant simplification of the relationship between P_{fe} and P_{vc}, the capillary beds between the two waveforms are amongst the areas of the body most effected by sepsis, thus this easily achievable comparison is likely to be sensitive to sepsis. To interpret P_{vc} as the result of upstream behaviour, as much of the downstream right heart influence on the waveform must be filtered out as possible.
Equation 4 yields the value of j providing the best agreement in directional peak to peak variation between P_{vc} and P_{fe}. This process functions by aligning the interbeat P_{fe} and P_{vc} waveforms based on their response to lower frequency influences. Even though j is not constrained in Eq. 4, it is consistently found to be equal to 3 or 4, which supports the validity of this approach, and yields a consistent and reasonable result.
 1.
Select four heartbeats for both P_{fe} and P_{vc}, from the beginning of beat i to the end of beat i + 3 for P_{fe} and from the beginning of beat i + j to the end of beat i + j + 3 for P_{vc}, where j is the subject specific number of heartbeats’ time it takes for a pressure wave to pass through the systemic circulation.
 2.Compare peak and trough timing of P_{fe} and P_{vc} to determine phase lag. Note this lag is additional to the lag already implemented by the term j:t_{max(Pvc)} refers specifically to the ‘V’ peak of the waveform, and t_{min(Pvc)} to the ‘Y’ trough. δ_{fe → vc} is once again a positive value as defined, in ms, this time representing the amount of time by which P_{vc} lags P_{fe}.$$\delta_{fe \to vc} = {\text{mean}}\left( {\left[ {\begin{array}{*{20}c} {\begin{array}{*{20}c} {t_{{{ \hbox{max} }(P_{vc} ,i + j)}} } &  & {t_{{{ \hbox{max} }(P_{fe} ,i)}} } \\ \vdots & & \vdots \\ {t_{{{ \hbox{max} }(P_{vc} ,i + j + 3)}} } &  & {t_{{{ \hbox{max} }(P_{fe} ,i + 3)}} } \\ \end{array} } \\ {\begin{array}{*{20}c} {t_{{{ \hbox{min} }(P_{vc} ,i + j)}} } &  & {t_{{{ \hbox{min} }(P_{fe} ,i)}} } \\ \vdots & & \vdots \\ {t_{{{ \hbox{min} }(P_{vc} ,i + j + 3)}} } &  & {t_{{{ \hbox{min} }(P_{fe} ,i + 3)}} } \\ \end{array} } \\ \end{array} } \right]} \right)$$(5)
 3.
Shift P_{fe} right by δ_{fe → vc} such that the peaks and troughs of P_{fe} are aligned with those of P_{vc}. Henceforth, \(\widehat{P}_{fe}\) refers to P_{fe} that has undergone this phase shift, and is thus aligned with P_{vc}.
 4.Use linear least squares on analogous regions of \(\widehat{P}_{fe}\) and P_{vc} to find:where relative amplitude is A_{fe → vc}, and identification offset is Δ_{fe → vc}. The waveform regions used in identification are highlighted in Fig. 2, and minimise the influence the upstream behaviour of the right atria and ventricle on the linear least squares process.$$\left[ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {\widehat{P}_{fe} \left( {t_{{max\left( {P_{vc} ,i + j} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{fe} \left( {t_{{min\left( {P_{vc} ,i + j} \right)}} } \right)} \\ \end{array} } \right)} & {\begin{array}{*{20}c} 1 \\ \vdots \\ 1 \\ \end{array} } \\ \vdots & \vdots \\ {\left( {\begin{array}{*{20}c} {\widehat{P}_{fe} \left( {t_{{max\left( {P_{vc} ,i + j + 3} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{fe} \left( {t_{{min\left( {P_{vc} ,i + j + 3} \right)}} } \right)} \\ \end{array} } \right)} & {\begin{array}{*{20}c} 1 \\ \vdots \\ 1 \\ \end{array} } \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} {A_{fe \to vc} } \\ {\Delta_{fe \to vc} } \\ \end{array} } \right] = \left[ {\begin{array}{*{20}c} {\left( {\begin{array}{*{20}c} {P_{vc} \left( {t_{{max\left( {P_{vc} ,i + j} \right)}} } \right)} \\ \vdots \\ {P_{vc} \left( {t_{{min\left( {P_{vc} ,i + j} \right)}} } \right)} \\ \end{array} } \right)} \\ \vdots \\ {\left( {\begin{array}{*{20}c} {P_{vc} \left( {t_{{max\left( {P_{vc} ,i + j + 3} \right)}} } \right)} \\ \vdots \\ {P_{vc} \left( {t_{{min\left( {P_{vc} ,i + j + 3} \right)}} } \right)} \\ \end{array} } \right)} \\ \end{array} } \right]$$(6)
 6.Once again, due to A_{fe → vc} scaling the entire P_{fe} waveform, and thus modifying its mean, Δ_{fe → vc} provides a poor indication of the actual pressure offset between P_{fe} and the reconstructed P_{vc}. Thus, Eq. 7 is used to provide O_{fe → vc}, a direct calculation of the mean difference between P_{fe} and the reconstructed P_{vc}.$$O_{fe \to vc} = {\text{mean}}\left( {\left[ {\begin{array}{*{20}c} {\widehat{P}_{fe} \left( {t_{{{\text{start}}\left( {\widehat{P}_{fe} ,i} \right)}} } \right)} & 1 \\ \vdots & \vdots \\ {\widehat{P}_{fe} \left( {t_{{{\text{end}}\left( {\widehat{P}_{fe} ,i + 3} \right)}} } \right)} & 1 \\ \end{array} } \right] \times \left[ {\begin{array}{*{20}c} {A_{fe \to vc} } \\ {\Delta_{fe \to vc} } \\ \end{array} } \right]  \left[ {\begin{array}{*{20}c} {\widehat{P}_{fe} \left( {t_{{{\text{start}}\left( {\widehat{P}_{fe} ,i} \right)}} } \right)} \\ \vdots \\ {\widehat{P}_{fe} \left( {t_{{{\text{end}}\left( {\widehat{P}_{fe} ,i + 3} \right)}} } \right)} \\ \end{array} } \right]} \right)$$(7)
The parameters of interest are the relative amplitude, A_{fe → vc}, and the direct pressure offset, O_{fe → vc}.
Analyses
 1.
Take the median value for a given metric of a 30 min baseline sample (‘Baseline’ in Fig. 3) at the beginning of the recording
 2.
Take the median values for a given metric of rolling 10 min samples, excluding the baseline region, and with the beginning of each sample shifting by 1 min each time (‘S1’, ‘S2’, ‘S56’, ‘S57’ in Fig. 3).
 3.
Omit the samples involving the 10 min directly after endotoxin infusion, as this region is transitional cannot be easily characterised as ‘sepsis’ or ‘healthy’.
 4.
Categorise samples prior to endotoxin infusion as ‘healthy’ (‘S1’, ‘S2’ in Fig. 3), and thus a true negative/false positive, and post endotoxin infusion as ‘sepsis’ (‘S56’, ‘S57’ in Fig. 3), and thus a true positive/false negative.
 5.
Use a range of different baselinesample median thresholds, τ, to develop the ROC curve.
 1.
A direct comparison of the ROC curves themselves, and the closeness of each curve to ‘perfect’ identifiability with a sensitivity and specificity of 1.0. This comparison illustrates the potential ability of each metric to differentiate between sepsis and healthy behaviour, across a variety of thresholds.
 2.A comparison of the closeness to ‘perfect’ identifiability across all five pigs when the same relative threshold per metric was employed. Traditionally, aggregate ROC performance of a metric is evaluated by summing the area under the curve of each component plot, providing an indication of potential metric performance across thresholds and subjects. However, in this study, the desire is to assess each metric’s capability as limited by the clinical necessity to select a single a priori threshold, relative to a baseline median reading, which is applicable and effective across all subjects. Thus, this approach compares the averaged closeness to perfect identifiability achieved by each metric across all subjects for a given threshold, relative to subject specific baseline median values of said metric. The distance from ‘perfect’ identifiability employed in this approach was calculated using:where τ represents the set of possible threshold choices, relative to a subjectspecific baseline reading, for a given metric. Thus, ε is equivalent to the geometric distance from a given point on an ROC curve, for a given metric, to the top lefthand corner of the ROC axes, where sensitivity and specificity are given equal weighting. An example plot of ε for 4 demonstrative metrics is provided in Fig. 4.$$\varepsilon \left( \tau \right) = \left\ {\left[ {\begin{array}{*{20}c} {\left( {1  sensitivity\left( \tau \right)} \right)} \\ {\left( {1  specificity\left( \tau \right)} \right)} \\ \end{array} } \right]} \right\_{2}$$(8)
Of the four demonstrative metrics, metrics 1, 2, and 3 all have identical optimal ε values, and thus identical combined sensitivity and specificity performance at their respective optimum thresholds. However, metric 1, with an extremely low optimal threshold, is likely to generate a larger amount of false positives in a broader data set than the limited data set used for validation. Metrics 2 and 3 are more robust, with higher thresholds likely to prevent false positives due to random fluctuations in a broader data set. Of these two, metric 3 is superior to metric 2 due to the broader range of relatively low ε values, implying a lessened reliance of metric performance on picking the exact optimal threshold, as compared to metric 2. Finally, metric 4 demonstrates poor performance across the full range of thresholds trialled.
 3.
A comparison of how quickly after endotoxin infusion each metric reaches that metrics’ optimum threshold, corresponding to minimum ε, as established in the previous comparison. This comparison serves to illustrate how rapidly each metric can provide warnings about oncoming septic shock, which is of significant clinical importance [29].
Overall, this set of analyses provides a reasonably comprehensive picture of the clinical response of each metric to sepsis, as well as the sensitivity, specificity, and generalisability of this clinical response for use as a diagnostic tool.
Results
Overall, O_{fe → vc} and the analogous ΔMP demonstrate consistently strong results, as do P_{ao} and A_{ao → fe}. Conversely, A_{fe → vc}, O_{ao → fe} and MVP, while displaying promising results for certain pigs, fail to consistently demonstrate strong results and thus are poor metrics for broad identification of sepsis. While the ROC plots serve to demonstrate the potential of a number of these metrics to serve as identifiers of sepsis, they do not provide clear, direct differentiation between the four metrics that appear to have the potential to perform well.
The rapidity with which each metric reaches the minimum optimal threshold from Fig. 6, t, in minutes, and the percentage of false positives reported prior to endotoxin infusion, %FP
Pig  A _{ ao → fe}  O _{ ao → fe}  A _{ fe → vc}  O _{ fe → nvc}  MAP  MVP  ΔMP  

t  %FP  t  %FP  t  %FP  t  %FP  t  %FP  t  %FP  t  %FP  
Pig 1  9  0  168  0  168  0  8  0  1  36.1  8  19.4  33  0 
Pig 2  1  7  1  0  14  0  17  0  1  11.6  22  0  22  0 
Pig 3  3  29.8  52  0  131  0  31  0  38  0  134  0  68  0 
Pig 4  24  0  1  100  148  0  1  3.6  17  0  1  100  94  0 
Pig 5  1  36.4  1  15.2  29  0  1  27.3  1  100  8  0  14  9.1 
Mean  7.6  14.6  44.6  23  98  0  11.6  6.2  11.6  29.5  34.6  23.9  46.2  1.8 
Discussion
Clinical potential of novel metrics
Overall, the metrics novel metrics O_{fe → vc} and A_{ao → fe}, as well as the clinical metrics MAP and ΔMP provide strong results in Figs. 5 and 6, demonstrating an ability to reach a relatively high sensitivity and specificity at a fixed, intersubject sepsis detection threshold. The remaining three metrics appear to perform relatively poorly. Interestingly, MVP, despite being an output from the systemic circulation and capillary beds, which are primarily effected by sepsis, is a poor diagnostic. However, MVP appears to contribute positively to the metric ΔMP, which has similar performance and a considerably more conservative, but robust, threshold than the associated MAP.
As mentioned in “Analyses” section, the breadth of optimal regions in Fig. 6 is also of importance, as it indicates metric insensitivity to selection of a specific, appropriate threshold. O_{fe → vc}, ΔMP, and A_{ao → fe} have reasonably broad optimal zones (6–11%, 29–33%, and 1–5%, respectively), suggesting some resilience to suboptimal threshold selection. Note that the plot in Fig. 6 does not differentiate between whether the deviation from perfect identifiability of a metric is due to a loss of sensitivity or specificity, providing instead a combined metric with a 1:1 weighting between the two values. A separation of metric sensitivity and specificity is instead provided in Table 1.
From Table 1, arterial metrics MAP and A_{ao → fe}, with their low 1% of baseline median thresholds, are highly sensitive, with mean times to sepsis detection of 11.6 and 7.6 min, respectively. However, this sensitivity comes at some cost in terms of specificity, with MAP and A_{ao → fe} having a false positive rate of 29.5% and 14.6%, respectively, prior to endotoxin infusion. Note that A_{ao → fe} appears clearly superior to MAP in Table 1, where false negatives after the initial declaration of sepsis are omitted, but not in Fig. 6, where these false negatives are included. The sensitivity of these arterial metrics to sepsis likely corresponds to a sepsis driven loss in arterial tone [38], resulting in significant pulse energy being lost in the arterial system.
Arterialvenous metrics are more conservative, trading some sensitivity for increased specificity. O_{fe → vc}, with its threshold of 6%, has an average time to detection of 11.6 min and a mean false positive rate of 6.2%, and ΔMP with its threshold of 29% an average time to detection of 46.2 min and mean false positive rate of 1.8%. While the various metrics exist on a continuum without a clear ‘best’ metric across all categories, the results in Table 1 and Fig. 6 do make a very convincing case for the effectiveness of O_{fe → vc} as the superior metric, closely followed by ΔMP.
Sepsis is a fast acting condition [19], thus rapid diagnosis and treatment are highly important, and an increase in detection time from 11.6 min (O_{fe → vc}) to 46.2 min (ΔMP) is significant relative to the time scale on which sepsis acts [29]. The relatively low, but distinct, threshold of 6–11% compared to the ΔMP threshold of 29–33% could suggest that the pressure–pressure comparison and filtering method used to derive O_{fe → vc} succeeds in removing the effects of right heart behaviour of MVP, providing a clearer picture of the underlying blood flow that has passed through the systemic circulation, and thus a clearer diagnostic picture. Reduction of the ΔMP threshold away from the optimal point to a similar false positive rate to O_{fe → vc} yields a 16.0 min detection time and 6.4% false positive rate at a 13% threshold, but also increases the false negative rate from 3.0 to 43.9%, as compared to the 9.0% false negative rate of O_{fe → vc}. Thus, at this operation point, O_{fe → vc} provides a shorter detection time, as well as lower false positive and false negative rates, at negligible additional cost to ΔMP. The overall sensitivity and relative robustness of these arterialvenous metrics in detecting sepsis matches expectations, as the area between the aorta or femoral artery and vena cava includes the capillary beds and microcirculation most affected by septic shock [29, 31], and supports the application of the pressure–pressure comparison approach to these waveforms.
It is worth noting that what loss in specificity is observed in the arterialvenous metrics is often driven by the mechanical ventilation RMs in the experimental protocol. Similarly, the relatively higher rate of false positives in O_{fe → vc} as compared to ΔMP are due to the fact that both the input (P_{ao}) and output (P_{vc}) for ΔMP lie in the thoracic cavity, and are thus both subject to an increase during a RM, thus partially cancelling each other out. In contrast, only the output (P_{vc}) of O_{fe → vc} lies within the thoracic chamber, thus the RM increases output without directly influencing input, resulting in a more significant decrease in O_{fe → vc}. It is important to note that, first, this decrease is physiological. Thus, the metrics are correctly representing underlying behaviour. Additionally, both metrics are largely able to avoid false positives due to this behaviour. Clinically, this specific issue might be managed by simply not reporting during RMs, in which case %FP for O_{fe → vc,} ΔMP, MAP and A_{ao → fe} fall to 1.0%, 0.0%, 21.8% and 7.2% respectively. However, the presence of false positives due to RMs illustrate in a broader sense a limited ability to distinguish between a decrease in pressure offset due to a relative increase in upstream pressure and a relative decrease in systemic resistance.
Limitations
Overall, there are several limitations to this study that bear mention. First, and most importantly, one of the key difficulties in the diagnosis of sepsis is distinguishing sepsis from other disease states [28]. While the experimental data here is detailed, and includes a variety of clinically standard interventions alongside induced sepsis, it does not include nonsepsis disease states to provide a broader range of potential ‘false positive’ situations. This omission is an important consideration. Thus, the specificity results presented here more represent the ability of the method to distinguish between baseline and septic behaviour as opposed to sepsis and alternative disease states.
However, sepsis is typically diagnosed in the manner of a syndrome rather than a disease, with a reliance on the manifestation of a family of infectiondriven symptoms, which typically respond to a family of treatments [29, 31]. This paper validates the ability of the presented methodology to accurately and rapidly identify one of these important signifiers of sepsis, associated with a sepsis driven fall in arterial tone as well as systemic resistance. Thus, while the methodology presented may not be posed to identify sepsis in isolation, it is capable of accurately and rapidly identifying metrics that can meaningfully contribute to the diagnosis of sepsis, along with other diseases [19, 29].
Further limitations include the study being limited to pigs, rather than humans, though this issue, as always, provides an excellent opportunity to explore an induced, controlled disease state with heavy instrumentation and provide a rigorous foundation for further studies translated to humans. The use of a baseline state is also a potential limitation, as patients on admission to an ICU are often not in a healthy, baseline circulatory state. However, once again, sepsis is representative of a series of symptoms and a further degradation of an unhealthy, but nonseptic, circulatory system should be similarly diagnostic of sepsis as a degradation of a healthy circulatory system. Further, the baseline readings of the pigs varied considerably as the pigs had been anaesthetised, instrumented, and subject to a sternotomy, with varying response to these procedures, further accentuated by their highly varied response to the subsequent endotoxin infusion. Thus, there is some variability and thus some test of robustness in the methods reliance on a ‘healthy’ state baseline reading.
Conclusions
The arterial metrics A_{ao → fe} (the relative pressure pulse amplitude between the aorta and femoral artery) and MAP were found to be highly sensitive to sepsis, providing rapid detection of the onset of symptoms, but at some cost in specificity. The arterialvenous metrics ΔMP and O_{fe → vc} (the direct pressure offset between the femoral artery and vena cava) were found to provide more robust, at a slight cost to sensitivity, detection of the onset of sepsis, with mean times to detection from endotoxin infusion of 46.2 min and 11.6 min respectively. Overall, the novel O_{fe → vc} provided the best combination of specificity and sensitivity, assuming an equal weighting to both, of the metrics assessed, followed by ΔMP. The novel metrics described in this paper do not require significantly more instrumentation to calculate than existing wellknown and reported clinical metrics, and only minimal computational effort. Thus, these metrics have the potential to provide further, clinically relevant and easily interpretable information to clinicians at the patient bedside, for little to no additional clinical effort. Thus, the results in this paper provide a case for further evaluation of the clinical usefulness of these metrics, and their potential diagnostic benefits.
Declarations
Authors’ contributions
SD contributed to the conception and design of the study, acquisition, analysis and interpretation of the data, and drafted the manuscript. CP contributed to the design of the study, acquisition and interpretation of the data, and revision of the manuscript. JB contributed to the design of the study, interpretation of the data, and revision of the manuscript. TD contributed to the design of the study, acquisition and interpretation of the data, and revision of the manuscript. JGC contributed to the conception and design of the study, interpretation of the data, and revision of the manuscript. All authors read and approved the final manuscript.
Acknowledgements
Not applicable.
Competing interests
The authors declare that they have no competing interests.
Availability of data and materials
The datasets used and/or analysed during the current study are available from the corresponding author on reasonable request.
Consent for publication
Not applicable.
Ethics approval and consent to participate
All experimental procedures and protocols were reviewed and approved by the Institutional Animal Care and Use Ethics Committee of the University of Liège, Belgium (Reference Number 141726). Their guidelines conform completely with the Guide for the Care and Use of Laboratory Animals published by the US National Institutes of Health (NIH Publication No. 8523, revised 1996), as well as EU DIRECTIVE 2010/63/EU on the protection of animals used for scientific purposes.
Funding
This work was supported by the Engineering Technologybased Innovation in Medicine (eTIME) consortium grant [eTIME318943]; the EU FP7 International Research Staff Exchange Scheme (IRSES) grant [#PIRSESGA2012318943]; and the University of Canterbury `Canterbury Scholarship’ grant.
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. The Creative Commons Public Domain Dedication waiver (http://creativecommons.org/publicdomain/zero/1.0/) applies to the data made available in this article, unless otherwise stated.
Authors’ Affiliations
References
 Mozaffarian D, Benjamin EJ, Go AS, Arnett DK, Blaha MJ, Cushman M, Das SR, de Ferranti S, Després JP, Fullerton HJ. Heart disease and stroke statistics—2016 update a report from the American Heart Association. Circulation. 2015. https://doi.org/10.1161/CIR.0000000000000366.View ArticleGoogle Scholar
 Kamoi S, Pretty C, Balmer J, Davidson S, Pironet A, Desaive T, Shaw GM, Chase JG. Improved pressure contour analysis for estimating cardiac stroke volume using pulse wave velocity measurement. Biomed Eng Online. 2017;16(1):51.View ArticleGoogle Scholar
 Davidson S, Pretty C, Pironet A, Desaive T, Janssen N, Lambermont B, Morimont P, Chase JG. Minimally invasive estimation of ventricular dead space volume through use of FrankStarling curves. PLoS ONE. 2017;12(4):e0176302.View ArticleGoogle Scholar
 Davidson SM, Kannangara DO, Pretty CG, Kamoi S, Pironet A, Desaive T, Chase JG. Modelling of the nonlinear endsystolic pressure–volume relation and volumeatzeropressure in porcine experiments. In: Engineering in medicine and biology society (EMBC), 2015 37th annual international conference of the IEEE. IEEE; 2015:6544–7.Google Scholar
 Davidson S, Pretty C, Pironet A, Kamoi S, Balmer J, Desaive T, Chase JG. Minimally invasive, patient specific, beatbybeat estimation of left ventricular time varying elastance. Biomed Eng Online. 2017;16(1):42.View ArticleGoogle Scholar
 Hann CE, Chase JG, Shaw GM. Integralbased identification of patient specific parameters for a minimal cardiac model. Comput Methods Programs Biomed. 2006;81(2):181–92.View ArticleGoogle Scholar
 Starfinger C, Chase J, Hann C, Shaw G, Lambermont B, Ghuysen A, Kolh P, Dauby P, Desaive T. Modelbased identification and diagnosis of a porcine model of induced endotoxic shock with hemofiltration. Math Biosci. 2008;216(2):132–9.MathSciNetView ArticleGoogle Scholar
 Lin WH, Zhang H, Zhang YT. Investigation on cardiovascular risk prediction using physiological parameters. Comput Math Methods Med. 2013;2013:21.Google Scholar
 Zhang YT, Zheng YL, Lin WH, Zhang HY, Zhou XL. Challenges and opportunities in cardiovascular health informatics. IEEE Trans Biomed Eng. 2013;60(3):633–42.View ArticleGoogle Scholar
 Gao Z, Li Y, Sun Y, Yang J, Xiong H, Zhang H, Liu X, Wu W, Liang D, Li S. Motion tracking of the carotid artery wall from ultrasound image sequences: a nonlinear statespace approach. IEEE Trans Med Imaging. 2018;37:273–83.View ArticleGoogle Scholar
 Gao Z, Xiong H, Liu X, Zhang H, Ghista D, Wu W, Li S. Robust estimation of carotid artery wall motion using the elasticitybased statespace approach. Med Image Anal. 2017;37:1–21.View ArticleGoogle Scholar
 Hunter J, Doddi M. Sepsis and the heart. Br J Anaesth. 2010;104(1):3–11.View ArticleGoogle Scholar
 Martin GS, Mannino DM, Eaton S, Moss M. The epidemiology of sepsis in the United States from 1979 through 2000. N Engl J Med. 2003;348(16):1546–54.View ArticleGoogle Scholar
 Angus DC, LindeZwirble WT, Lidicker J, Clermont G, Carcillo J, Pinsky MR. Epidemiology of severe sepsis in the United States: analysis of incidence, outcome, and associated costs of care. Crit Care Med. 2001;29(7):1303–10.View ArticleGoogle Scholar
 Pineda LA, Hathwar VS, Grant BJ. Clinical suspicion of fatal pulmonary embolism. Chest J. 2001;120(3):791–5.View ArticleGoogle Scholar
 Frazier SK, Skinner GJ. Pulmonary artery catheters: state of the controversy. J Cardiovasc Nurs. 2008;23(2):113–21.View ArticleGoogle Scholar
 Chatterjee K. The swanganz catheters: past, present, and future a viewpoint. Circulation. 2009;119(1):147–52.View ArticleGoogle Scholar
 Halford GS, Baker R, McCredden JE, Bain JD. How many variables can humans process? Psychol Sci. 2005;16(1):70–6.View ArticleGoogle Scholar
 Hall JE. Guyton and Hall textbook of medical physiology. Philadelphia: Elsevier Health Sciences; 2010.Google Scholar
 Gershengorn HB, Wunsch H, Scales DC, Zarychanski R, Rubenfeld G, Garland A. Association between arterial catheter use and hospital mortality in intensive care units. JAMA Intern Med. 2014;174(11):1746–54.View ArticleGoogle Scholar
 Gershengorn HB, Garland A, Kramer A, Scales DC, Rubenfeld G, Wunsch H. Variation of arterial and central venous catheter use in United States intensive care units. J Am Soc Anesthesiol. 2014;120(3):650–64.View ArticleGoogle Scholar
 Harvey S, Harrison DA, Singer M, Ashcroft J, Jones CM, Elbourne D, Brampton W, Williams D, Young D, Rowan K. Assessment of the clinical effectiveness of pulmonary artery catheters in management of patients in intensive care (PACMan): a randomised controlled trial. Lancet. 2005;366(9484):472–7.View ArticleGoogle Scholar
 Welch P. The use of fast Fourier transform for the estimation of power spectra: a method based on time averaging over short, modified periodograms. IEEE Trans Audio Electroacoust. 1967;15(2):70–3.View ArticleGoogle Scholar
 Huang NE, Shen Z, Long SR, Wu MC, Shih HH, Zheng Q, Yen NC, Tung CC, Liu HH. The empirical mode decomposition and the Hilbert spectrum for nonlinear and nonstationary time series analysis. In: Proceedings of the Royal Society of London A: mathematical, physical and engineering sciences. The Royal Society; 1998:903–95.Google Scholar
 Davidson S, Pretty C, Balmer J, Desaive T, Chase J. An investigation into the clinical utility of transfer functions between the aortic and femoral pressure waveforms. In: 10th IFAC symposium on biological and medical systems (BMS 2018). São Paulo, Brazil; 2018.Google Scholar
 Berger RD, Saul JP, Cohen RJ. Transfer function analysis of autonomic regulation. I. Canine atrial rate response. Am J Physiol Heart Circ Physiol. 1989;256(1):H142–52.View ArticleGoogle Scholar
 Saul JP, Berger RD, Albrecht P, Stein S, Chen MH, Cohen R. Transfer function analysis of the circulation: unique insights into cardiovascular regulation. Am J Physiol Heart Circ Physiol. 1991;261(4):H1231–45.View ArticleGoogle Scholar
 Poeze M, Ramsay G, Gerlach H, Rubulotta F, Levy M. An international sepsis survey: a study of doctors’ knowledge and perception about sepsis. Crit Care. 2004;8(6):R409.View ArticleGoogle Scholar
 Dellinger RP, Levy MM, Rhodes A, Annane D, Gerlach H, Opal SM, Sevransky JE, Sprung CL, Douglas IS, Jaeschke R. Surviving Sepsis Campaign: international guidelines for management of severe sepsis and septic shock, 2012. Intensive Care Med. 2013;39(2):165–228.View ArticleGoogle Scholar
 Douglas WR. Of pigs and men and research. Space Life Sci. 1972;3(3):226–34.Google Scholar
 Nguyen HB, Rivers EP, Abrahamian FM, Moran GJ, Abraham E, Trzeciak S, Huang DT, Osborn T, Stevens D, Talan DA. Severe sepsis and septic shock: review of the literature and emergency department management guidelines. Ann Emerg Med. 2006;48(1):54.e51.View ArticleGoogle Scholar
 Jardin F, Farcot JC, Boisante L, Curien N, Margairaz A, Bourdarias JP. Influence of positive endexpiratory pressure on left ventricular performance. N Engl J Med. 1981;304(7):387–92.View ArticleGoogle Scholar
 Boyd JH, Forbes J, Nakada TA, Walley KR, Russell JA. Fluid resuscitation in septic shock: a positive fluid balance and elevated central venous pressure are associated with increased mortality. Crit Care Med. 2011;39(2):259–65.View ArticleGoogle Scholar
 Vincent JL, Gerlach H. Fluid resuscitation in severe sepsis and septic shock: an evidencebased review. Crit Care Med. 2004;32(11):S451–4.View ArticleGoogle Scholar
 Schierhout G, Roberts I. Fluid resuscitation with colloid or crystalloid solutions in critically ill patients: a systematic review of randomised trials. BMJ. 1998;316(7136):961–4.View ArticleGoogle Scholar
 Stewart RM, Park PK, Hunt JP, McIntyre RC Jr, McCarthy J, Zarzabal LA, Michalek JE. Less is more: improved outcomes in surgical patients with conservative fluid administration and central venous catheter monitoring. J Am Coll Surg. 2009;208(5):725–35.View ArticleGoogle Scholar
 Kastrup M, Markewitz A, Spies C, Carl M, Erb J, Grosse J, Schirmer U. Current practice of hemodynamic monitoring and vasopressor and inotropic therapy in postoperative cardiac surgery patients in Germany: results from a postal survey. Acta Anaesthesiol Scand. 2007;51(3):347–58.View ArticleGoogle Scholar
 Bogle R, Vallance P. Regulation of vascular smooth muscle tone in sepsis. Pharmacology of vascular smooth muscle. 1996:369–86.Google Scholar
 Wright DB. Receiver operating characteristics curves. Encyclopedia of statistics in behavioral science. 2005.Google Scholar