Within the blood, oxygen bonds to hemoglobin as a function of PaO2 per the relationship defined by the oxygen dissociation curve. Because blood, like most fluids, is noncompressible, the compartments of the cardiovascular system can be treated as mixing chambers. We can model the transport of oxygen within the cardiovascular system as a solute with concentrations, SaO2 and SvO2, carried by the blood.
The output concentration of a material from a mixing chamber is a function of the solute carrier flow, chamber volume, and input concentration.34 Three types of chambers are modeled: a simple mixing chamber used for most compartments; connecting chambers used for capillaries; and consumption chamber used for tissue.
A series of these compartments can be linked together to create a larger model of the cardiovascular system as illustrated in Figure 6. This model is based on the work of Rideout’s 10-compartment model31 and the assumptions that blood flow is nonpulsatile and unidirectional, all mixing chambers are perfect, and red blood cells travel at the same rate as the blood.
In summary, it should be noted that the oxygen transport system is complex, with many inputs and outputs, and a model could eventually be developed that is just as complex. However, from an engineering standpoint, simplifying the model provided us not with perfection but with sufficient guidance.
A complete, idealized adult model was first developed on a personal computer as a means of verifying the performance against other published results.31 This model was then modified to represent a neonate’s physiology by adjusting physiologic variables such as the respiratory compartment RC, tidal volume, cardiovascular compartment volumes, blood flow, transport time, and cardiac output. The variables were based on values available in the literature and allometric equations scaled for a neonate weighing 1500 g. The neonate model software was then run on a PC workstation and its output compared with published data. The model was then used to experiment with fuzzy logic control and motion artifact rejection without the need for initial animal or human studies.35 Computer modeling of neonatal oxygen transport is realizable and can be a useful tool for creating control algorithms.
Integrating the Model Into the Algorithm
It is possible to integrate the neonate model into the control algorithm. However, this migration requires that it operate in a real-time environment. As a means of meeting the product’s computing performance criteria: reduced complexity, system resources, and processing time, the model is distilled into a nonlinear transfer function; a simplified version is shown in Figure 7. This transfer function determines the relative FiO2 change required to reach a specific SpO2 target. For example, if the target is 92% and the current SpO2 value is 94%, the control algorithm, using the thick line, would reduce the current FiO2 value by 5%.
Self-tuning can be added to the model-based algorithm by creating a supervisor that tracks inputs such as the models performance (eg, percent time close to target), number of manual adjustments, number or rapid desaturations, etc. Every second the supervisor binned the percentage of time that the neonate stayed at 1 of 3 ranges, normoxemia, hyperoxemia, and hypoxemia. At 2-minute intervals, the supervisor would adjust the model to improve performance using the following algorithm:
- Get 3 values: normoxemia, hyperoxemia, and hypoxemia
- IF mostly normoxemia THEN
ELSE IF mostly hyperoxemia THEN large steepening of curve
ELSE IF mostly hypoxemic THEN large flattening of curve
- IF hyperoxemia > hypoxemia THEN slight steepening of curve
- ELSE slight flattening of curve
For example, if the neonate has been consistently hyperoxemic, the controller would steepen the latter 2 segments of the transfer function by moving points 3 and 4 to 3’ and 4’ as shown in Figure 7. This would cause the controller to increase its FiO2 change when above target; instead of a 5% change at 94% SpO2 the controller would now affect an 8% change.
Because this control method, referred to as the adaptive model (AM) algorithm, adapts itself toward maintaining maximal normoxemia, it requires no tuning or setup by hospital staff. Like the state machine (SM) algorithm, it also accounts for the nonlinearity of the system. Disturbances to the system such as shunting and bradycardia, however, could not be recognized by the instrument without further inputs such as heart rate, SvO2, etc.
A second-generation automatic SpO2 controller, developed at British Columbia’s Children’s Hospital, was used in this study. It contained 3 user-selectable control algorithms: SM, proportional-integral-differential (PID), and AM. The device used the SpO2 signal from a commercial pulse oximeter as an input signal and controlled the patient’s FiO2 level by actuating a motorized mechanical air/oxygen gas blender. A manual override feature was provided in the gas blender. The SM algorithm was ported from a first-generation controller, and implementation details have been published previously.14,15 The results of the first-generation controller study were used to tune the algorithm in this study as a means of improving its performance. Implementation details on the PID algorithm can be found in previous publications.36,37 SpO2 and FiO2 (per the blender setting) were sampled once per second and stored to memory for further analysis.
Performance was defined as 3 criteria in the following order of importance: percent duration of SpO2 spent in normoxemia, hypoxemia, and hyperoxemia; number of 60-second periods <85% SpO2 and >95% SpO2; and number of manual adjustments. Normoxemia for the closed-loop control algorithms was defined as ±2.5% of their target SpO2. Manual mode normoxemia was defined within the range of 90% to 95% SpO2, the range that clinical staff attempted to maintain when performing oxygen therapy per standard hospital guidelines. Target SpO2 error is the difference between the controller’s SpO2 target and the actual SpO2; it was used as an additional performance criterion for comparing the closed-loop control algorithms with each other. It was not reasonable to use this criterion for manual mode comparison because no attempt was made by clinical staff to maintain SpO2 at a specific target SpO2. Two-tailed paired t tests were used to analyze the performance criteria with P <0.05 indicating significance.
An evaluation was defined as the application of manual and automatic control on a preterm baby on a specific day. Each evaluation (day) would have ≥1 hour of manual oxygen therapy and ≥1 hour of closed-loop therapy (SM, AM, or PID) data recorded. An attempt would also be made to apply the other algorithms, each for an hour.
Applying the Model to Patients
Sixteen clinical evaluations were performed on 7 low-birth-weight ventilated preterm babies. We purposely chose subjects that were relatively unstable and would challenge the controller. Demographic characteristics of the enrolled babies are shown in Table 1. An investigator was present during automatic control to provide technical support, monitor the controller’s performance, and record clinical events (suctioning, patient motion, etc). Investigators did not apply therapy to the patient.
Each clinical evaluation occurred during the 8:00 AM to 10:00 PM period of a single day. Some evaluations were done on the same baby but took place on the following days as shown in Table 2. Manual FiO2 adjustment was allowed and recorded during the automatic algorithms. Also, during the trial’s closed-loop control periods, the automatic controller was not turned off during clinical interventions such as suctioning, diaper change, physiotherapy, etc. The 3 automatic algorithms SM, PID, and AM along with manual oxygen therapy were applied to the neonates as described in Table 2. Note that during some clinical evaluations, several variations of an algorithm were run for at least a 1-hour period. The PID algorithm generally required some tuning to ascertain an optimal set of gain parameters. In an effort to avoid the effects of long-term changes in physiology, the algorithms were run consecutively. Tables 3 through 5 list the performance criteria data, comparing manual therapy to each closed-loop therapy. Additionally, Tables 6 and 7 compare the AM algorithm to the SM and PID algorithms, respectively.
When compared with manual therapy, all 3 control algorithms significantly increased the patient’s duration in normoxemia by reducing time in hyperoxemia. They did not reduce time in hypoxemia when compared with manual mode. In our 1993 study, in which we compared the SM algorithm to manual therapy, the algorithm used in that study produced a slight but significant increase in the hypoxemic duration.15 The improvements made to the SM algorithm and applied in this study successfully reduced the time at hypoxemia to a duration equivalent to that of manual mode. The AM algorithm performed well and had the greatest mean duration at normoxemia, 60%, when compared with manual therapy. As shown in Table 7, it also performed better than the PID algorithm in this criterion. With respect to duration at normoxemia, however, the SM algorithm performed better than the AM.
The PID algorithm demonstrated a significant improvement in reducing the number of 60-second events >95% and <85%. The SM algorithm also significantly reduced the number of 60-second events >95% SpO2. Compared with manual therapy, the AM algorithm did show improvement in the number of these events; however, it was not significant. This result was not expected because it was postulated that the nonlinear nature of the model would adjust the FiO2 by smaller increments when below target and larger increments when above target, reducing potential oscillation in labile babies. The AM algorithm may have had more of these events >95% because its median target SpO2 was 94% vs the 93% median target for the PID and SM algorithms. In other words, the AM algorithm had a target that was closer to the 95% threshold of this criterion.
All 3 control algorithms significantly reduced the number of manual adjustments. The AM algorithm demonstrated the most significant improvement when compared with manual therapy. Comparing the AM algorithm to the other closed-loop algorithm (Tables 6 and 7), there was no significant difference in performance.
Regarding usability, we found that the PID algorithm worked well when its gain factors were properly tuned. This, however, required experience with the controller, understanding its response. The SM algorithm performed well and required minor setup. We found that the AM algorithm was the most convenient algorithm because it required no setup or previous experience with the controller, demonstrating that a model of the neonate can be used to create a transfer function that, in turn, can become a viable part of a closed-loop control algorithm.
Driven by the requirements to engineer a product that balanced safety, efficacy, and performance, we sought to automate the difficult task of neonatal oxygen therapy by reducing the manual therapy’s set of inputs and outputs. To verify control algorithms, our computer model of the neonatal oxygen transport system further simplified the neonate’s complex physiology. We idealized the neonatal computer model and integrated it into a closed-loop oxygen therapy device. Its performances against the manual process and 2 other control algorithms were assessed in the clinical setting on ventilated low-birth-weight infants. The results showed the model-based controller, like the other 2 closed-loop control algorithms, had significantly better performance than manual therapy. When compared with the other algorithms, the AM algorithm’s performance was equivalent but not significantly better. Because the AM’s performance is similar to the other algorithms and it required no initial setup or in-process tuning, it potentially may provide a slightly better O2 therapy device.
In Joseph Conrad’s novel, The Secret Agent, his character Michaelis states, “… All idealism makes life poorer. To beautify it is to take away its character of complexity – it is to destroy it.” Conrad’s words are certainly appropriate with regard to the pursuit of knowledge, truth, and understanding. However, within the challenge of engineering a product, we found utility in simplicity.
Name: Edmund Morozoff, MASc.
Contribution: This author helped design the study, conduct the study, analyze the data, write the manuscript, and develop the model and device.
Name: John A. Smyth, LRCPSI, FRCPC.
Contribution: This author helped design the study, conduct the study, analyze the data, and write the manuscript.
Name: Mehrdad Saif, PhD.
Contribution: This author helped design the study, analyze the data, and write the manuscript.
This manuscript was handled by: Maxime Cannesson, MD, PhD.
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