An observational study, which enrolled 84 patients in an ICU between February and March 2005, showed that between 35% and 45% of patients were treated with inotropes [6Biswal S, Mishra P, Malhotra S, Puri GD, Pandhi P. Drug utilization pattern in the intensive care unit of a tertiary care hospital J Clin Pharmacol 2006; 46(8 ): 945-51.]. Adrenaline is used in patients who are in cardiac arrest or who require inotropic or vasopressor support. Adrenaline may additionally be used in cases of anaphylaxis associated with hemodynamic instability or respiratory distress [1American heart association guidelines for cardiopulmonary resuscitation and emergencycardiovascular care, part 7.4: Monitoring and medications Circulation 2005; 112: IV78-83., 7Ellis AK, Day JH. Diagnosis and management of anaphylaxis Can Med Assoc J 2003; 169(4): 307-11.]. Furthermore, it improves myocardial and cerebral hemodynamics during cardiopulmonary resuscitation (CPR).

In this study [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.], Adrenaline was administered to 14 young normotensive subjects (age 21-40 years, mean 30± 2 years; 8 male, 6 female) and 18 older normotensive subjects (age 50-73 years, mean 60± 2 years; 6 male, 12 female). All subjects had weight within 20% of the ideal body weight. They all had normal history, physical examination and biochemistry. The subjects were instructed to refrain from caffeine and alcohol 24 hours prior to each study morning and they did not take any other medication for the duration of the study. The study was approved by the Human Ethics Committee of the University of Ottawa and written informed consent was obtained.

Arterial blood pressure (ABP) was measured using a blood pressure cuff applied to the arm that was not used for the infusion. Blood pressure was recorded using a Roche Arteriosonde (Roche Medical Electronics Inc., Cranbury, NJ, USA). ECG electrodes were applied to measure heart rate (HR) by a Tektronic 414 monitor (Tektronic Inc., Beaverton, OR, USA). On the study morning, following a rest period of at least 60 minutes, adrenaline was started at 20 ng/kg/min and increased to 40, 80, 120 and 160 ng/kg/min or until the heart rate had increased by 20-25 beats/min or the diastolic blood pressure decreased by 15 mmHg. Each dose was infused for 8 mins. Heart rate and blood pressure were measured every 2 mins for 10 minute periods prior to the start of an infusion and twice during the last 2-3 mins at each infusion rate. Mean and standard deviation are used for analysis.

Table 1 summarizes the data obtained from this study for the different adrenaline doses and populations (young/older and male/female). The following measurements are used for the parameter identification process:

Table 1

Adrenaline Doses and Participants Separated into Young and Older and Young Male, Young Female and Older Male and Female, Respectively

Table 2

Time Course and Drug Titration for Study 3

Table 3

Study 1, Identification: Median Error and IQR in % for Measured and Simulated Pressures and Volumes Over All 16 Identified Segments

Table 4

Study 1, Prediction 1: Median Error and IQR in % for Measured and Predicted Pressures and Volumes Over All 13 Predicted Episodes when the Baseline Parameter Vector is Used as Initial Solution

Table 5

Study 1, Prediction 2: Median Error and IQR in % for Measured and Predicted Pressures and Volumes Over All 13 Predicted Episodes when the Previous Parameter Vector is Used as Initial Solution

Table 6

Study 2, Identification: Median Error and IQR in % for Measured and Simulated Pressures and Volumes Over All 8 Identified Segments

Table 7

Study 2, Prediction: Median Error and IQR in % for Measured and Predicted Pressures and Volumes Over All 6 Predicted Segments when the Previous Solution Vector is Used as Initial Parameter Vector

Table 8

Study 3, Identification: Median Error and IQR in % for Measured and Simulated Pressures and Volumes Over All 5 Identified Segments

Table 9

Study 3, Prediction: Absolute Difference in % for Measured and Predicted Pressures and CI for Predicted Segment h12 when the Parameter Trends for h1 to h6 are Used

• heart rate (HR)
• systolic and diastolic arterial pressures (SAP, DAP)
• left ventricular end-systolic and end-diastolic volume indexes (LVESVI, LVEDVI)
• left ventricular stroke volume (LVSV, as calculated from LVEDVI and LVESVI)

Overall, this study provides 24 unique data sets that may be used.

In this study [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.], 251 patients were screened over 18 months for low cardiac output (CO) upon ICU admission after coronary artery bypass grafting (CABG) surgery. Approval of the local Ethics Committee and preoperative written consent was obtained. Patients having a cardiac index (CI) of less than 2.2 l / min / m² upon ICU admission (despite adequate arterial and filling pressures) were randomly assigned to 14-hour treatment with adrenaline (n=7) or milrinone (n=11) to achieve a CI of greater then 3 l / min / m².

Drugs were given by continuous infusion without a bolus. Treatment in the ICU and the care provided to the patients was at the discretion of the clinical staff in charge. With the exception of the hemodynamic goals given above and the prohibition of using diuretics or hydroxyethylstarch preparations during the treatment duration, no specific therapeutic instructions were given.

All patients had a radial arterial line, a central venous catheter and a pulmonary artery catheter for continuous measurement of mixed venous oxygen saturation (SvO₂) and CI (Vigilance, Edwards Lifesciences LLC, Irvine, CA, USA). Hemodynamics were recorded every two hours for a 14 hour treatment period after ICU admission. The hemodynamic variables recorded include: mean arterial pressure (MAP), central venous pressure (CVP), mean pulmonary artery pressure (MPAP), HR and CI. The following subset of available measurement data are used for the parameter identification process:

• heart rate (HR)
• mean arterial and mean pulmonary artery pressures (MAP, MPAP)
• cardiac index (CI)
• central venous pressure (CVP)

Overall, this data from [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.] provided 8 data sets for use.

This study [17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.] included 30 patients with hyperdynamic septic shock and was approved by the local Ethics Committee and written informed consent was obtained from the patient’s closest relative. To be included in the study after volume resuscitation and treatment with dopamine up to a dose of 20μg/kg/min, the patients had to have the following baseline condition:

• MAP ≤60mmHg
• signs of altered perfusion (oliguria, <30ml/hr) or increased lactate level (>2.5mml/l)
• CI > 3.5l / min / m²

Heart rate was monitored continuously and the routine clinical monitoring included a thermodilution pulmonary artery catheter, with continuous monitoring of mixed venous oxygen saturation (SvO₂) and a radial and femoral artery catheter. Measurements of MAP, CVP, MPAP were taken and CO was measured by thermodilution. Each patient received either epinephrine or norepinephrine + dobutamine. Epinephrine infusions were started at 0.3 μg/kg/min. The infusion rate was titrated on MAP at 5-min intervals to obtain a MAP > 80mmHg, with a stable or increased CI.

Table 2 summarizes the adrenaline titration given. The following measurements are used for the parameter identification process:

• heart rate (HR)
• mean arterial and mean pulmonary artery pressures (MAP, MPAP)
• cardiac index (CI)
• central venous pressure (CVP)

Overall, 5 data sets were available for use in this study.

As discussed before, the effects of adrenaline can be summarized as an increase in HR and contractility, vasoconstriction in most systemic arteries and veins and an increase in the central blood volume. These effects in turn lead to an increase in SV and systemic arterial pressure (SAP). Diastolic arterial pressure (DAP) is decreasing, and thus a relatively constant mean arterial pressure (MAP) results, but with a largely increased pulse pressure (PP). Consequently, from these physiologically expected effects the model parameters (see Fig. 1) that should be most influenced by adrenaline, are:

• left and right ventricular end-systolic elastances (E_eslvf, E_esrvf); also representing the contractility
• arterial and pulmonary elastances E_ao and E_pa; as affected by the change in pulse pressure
• systemic arterial resistance R_sys; as affected by vasoconstriction
• systemic elastance E_sys (1/compliance); affected by increases in V_sys

As the most pronounced changes are expected in E_eslvf, E_esrvf, E_ao and E_pa, these parameters are termed the adrenaline-specific parameters. Changes in these parameter values are therefore used for predicting the future response towards a change in dose of adrenaline or over time. However, for studies 2 and 3 [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.,17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.], changes in R_sys and E_sys were also included in the prediction rules. This difference can be explained by the overall much longer time periods for these 2 studies, where the hemodynamic status of the patients is more likely to have changed, for example due to vasoconstriction and/or a change in blood volume over that time period.

This study provided the best data for the identification process, with very detailed data reported over a variety of subjects and conditions. As this study was a planned interventional clinical trial study, it took place in a very controlled environment and adrenaline was administered into each participant following a strict protocol. It is thus safe to assume it was administered in exactly the same way, with the same dose, and over the same time, for each participant.

Hence, this part of the study presented concentrates on demonstrating the ability of the CVS model to simulate the different effects of adrenaline, identifying general relationships between adrenaline dose and model parameters, and testing the model’s shorter term predictive ability in response to changes in dose.

All 16 individual data sets obtained from the study (6 data sets per dose for Y and O group plus one additional set for the YM, YF and OM, OF groups at baseline, see also Table 1) were identified using the methods described in [10Starfinger C, Hann CE, Chase JG, Desaive T, Ghuysen A, Shaw GM. Modelbased cardiac diagnosis of pulmonary embolism Comput Methods Programs Biomed 2007; 87(1): 46-60.-12Starfinger C, Chase JG, Hann CE, et al. Prediction of hemodynamic changes towards peep titrations at different volemic levels using a minimal cardiovascular model Comput Methods Programs Biomed 2008; 91(2): 128-34.]. The changes in the adrenaline-specific parameters (E_eslvf , E_esrvf , E_ao and E_pa) in the Y group were observed and a linear fit was obtained for the 5 dose changes from baseline to 160 ng/kg/min. This trend is used for prediction.

Predictions are performed for the (independent) O group and then the (independent) YM, YF, OM andOF data sets. The first prediction in each data set uses the baseline parameters identified for each of these groups (O, OM, OF, YM, YF), as it is necessary to have a baseline solution vector of model parameters to begin. The adrenaline-specific parameters (E_eslvf , E_esrvf , E_ao and E_pa) are then modified to account for a change in dose from the baseline, using the linear prediction rule obtained from the linear fit in the Y group. With these modified adrenaline-specific parameters, the model is run and the predicted hemodynamic output signals for SAP, DAP, MAP, LVEDVI, LVESVI and SV are compared to the clinical data from [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.]. Median absolute percentage errors and the inter-quartile range (IQR) are calculated.

A second type of prediction is also performed. In this case, the previous model parameter value vector identified from the previous change in dose is used, rather than those from the baseline parameter vector. This effectively shortens the interval or dose over which the adrenaline-specific parameter changes are employed. The adrenaline-specific parameters (E_eslvf , E_esrvf , E_ao and E_pa) are then modified based on the linear prediction rule as before and the model is then forward simulated again to obtain a prediction of the hemodynamic outcome to the change in dose. Finally, the resulting predicted output signals for SAP, DAP, MAP, LVEDVI, LVESVI and SV are compared to the clinical data. Median absolute percentage errors and the inter-quartile range (IQR) are calculated.

In this study, the pulmonary artery pressure is not given and has to be estimated. The pulmonary artery pressure is estimated as a constant pressure over all dosages and participant groups with a systolic value of 25 mmHg and a diastolic value of 12 mmHg. Note, that this estimation is physiologically incorrect, as the pulmonary artery pressure is expected to change with different doses of adrenaline. However, by keeping this pressure fixed for all identifications, it can be guaranteed that only a constant error is added to the identification process. This error can be much better managed if it is similar for all identified segments. Naturally, information about the pulmonary circulation is lost and the value of E_pa will also not necessarily represent a true value in this case.

These 2 studies are used as further tests. In particular, they test the potential to correctly identify patient-specific parameters in the absence of diastolic and systolic pressure measurements, given only the mean arterial pressures MAP and MPAP. In addition, these 2 studies do not provide end-systolic or end-diastolic volumes, relying instead on the cardiac index. Finally, the data in these studies covers much longer time periods extending the prediction range.

As noted, these 2 studies measure a very minimal amount of data. Hence, several assumptions have to be made to use the data in this study:

• SV is calculated based on HR and CI with an assumed BSA = 2m² in all cases
• ESV is assumed as SV+10ml
• EDV is calculated as ESV+SV
• left and right ventricular volumes are assumed to be the same
• systolic and diastolic pressures are estimated based on Fig. (3) as obtained from [5Klabunde RE. Cardiovascular physiology concepts. Lippincott Williams and Wilkins 2004.]

In these 2 studies, there is only a limited amount of data available. In comparison to study 1, this data is very inhomogeneous and was not obtained in a controlled study. Instead, it was taken observationally over time periods of 14 and 24 hours, respectively. Therefore, these data sets were not intended to truly predict the patient’s response towards a change in dose in adrenaline, or over the course of time.

The goal in these data sets is to show the accuracy of the identification process by testing if an overall rule can be found that shows a consistent way of identifying the main adrenaline-specific parameters. If such a simple, linear rule can be found, using all or most of the data points available, then this rule would show that the parameters evolved in a consistent manner. This rule could then be used to predict the patient’s response for a specific point in time. If successful, it would demonstrate the approach of using drug-specific rules and parameter changes to enhance identification and prediction.

For study 2, prediction rules are obtained from the absolute percentage changes in the model parameter values from one point in time to the next, except for the change from baseline to t2. This percentage difference is not included because this change is expected to be much higher, as the effect of adrenaline is expected to be more pronounced compared to the other time points where the adrenaline dose is kept at a more constant level. A total of 6 predictions are performed for study 2 from t4 to t14, using the previous solution as baseline solution in each case. For example, for predicting the response at t4, the parameters from t2 are used plus the re-calculated adrenaline-specific parameters using the overall population rule, as described before. In contrast to study 1, where the adrenaline-specific parameters are E_eslvf , E_esrvf , E_ao and E_pa, for this data set it was necessary to also re-calculate the systemic and pulmonary arterial resistances R_sys and R_pul and the systemic elastance E_sys. These 3 additional parameters changed significantly during the time course of the study and were thus included in the overall population rule.

Similarly to study 2, the prediction rules for study 3 are obtained from the absolute percentage changes in the parameters from one point in time to the next. However, here only the change from h1 to h6 is used. The baseline change was excluded for the same reason as in study 2. For similar reasons the change to h24 was excluded, as this change covers a long time period (12 hours). In addition, while the doses for h1, h6 and h12 are similar, there is a much lower dose at h24. Hence, only 1 prediction is performed for study 3 and this is the prediction for h12, using the data obtained from h1 and h6.

This prediction from study 3 serves as another test of the CVS model and identification process. The goal is to show that all parameters are identified in such a consistent way that h1-h6 adrenaline-parameter specific rules can be found to predict h12. The adrenaline-specific parameters E_eslvf , E_esrvf , E_ao and E_pa and used with study 1 are augmented for study 3 to include R_sys, which changed considerably during the long time course of this study. Fig. (4) shows the prediction rules obtained for studies 2 (solid line) and 3 (dashed line) for E_eslvf and E_esrvf over a time period of 1 to 24 hours, where the similarity over disparate studies indicates a consistent underlying physiological behaviour.

Fig. (5) shows in the upper panel (solid line) the mean systolic arterial pressure (SAP) over all 16 segments as given in [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.]. These 16 segments are the 6 measurements for the young and older groups at baseline, 20, 40, 80, 120 and 160 ng/kg/min adrenaline (segments 1-6 young, 7-12 older), plus 4 measurements, which are obtained by separating the young and older groups for male and female, respectively. The circles are the simulated CVS model outputs obtained when the CVS model is re-run with the identified patient-specific parameters.

Fig. (3) Change in diastolic and systolic blood pressure in comparison to a relatively constant mean arterial pressure with administration of epinephrine (adrenaline) over time, as obtained from [5Klabunde RE. Cardiovascular physiology concepts. Lippincott Williams and Wilkins 2004.].

Fig. (4) Linear prediction rules for Eeslvf (upper panel) and Eesrvf (lower panel) for studies 2 (Heringlake et al., solid line) and 3 (Levy et al., dashed line).

Fig. (5) Study 1: Clinical mean systolic (SAP), diastolic (DAP) and mean (MAP) arterial pressure as obtained from [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.] vs simulated pressures. Solid lines represent the clinical data and circles represent the CVS model simulation output using identified patient-specific parameters.

Fig. (6) Study 1: Clinical mean left ventricular end-diastolic (LVEDVI) and end-systolic (LVESVI) volume index as obtained from [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.] vs simulated volume indexes. Solid lines represent the clinical data and circles represent the CVS model simulation output using identified patient-specific parameters.

Fig. (7) Study 2: Clinical mean arterial (MAP), mean pulmonary artery (MPAP) pressure and cardiac index (CI) as obtained from [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.] vs simulated pressures and CI. Solid lines represent the clinical data and circles represent the CVS model simulation output using identified patient-specific parameters.

Fig. (8) Study 3: Clinical mean arterial (MAP), mean pulmonary artery (MPAP) pressure and cardiac index (CI) as obtained from [17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.] vs simulated pressures and CI. Solid lines represent the clinical data and circles represent the CVS model simulation output using identified patient-specific parameters.

The middle panel shows as a solid line the mean arterial pressure (MAP) as available in [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.] for all 16 segments. The circles depict the CVS model output data when re-run using patient-specific parameters. The lower panel shows the same results for the diastolic arterial pressure (DAP).

Fig. (6) shows in the upper panel the left ventricular end-diastolic index (LVEDVI) as given in [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.], whereas the lower panel shows the left ventricular end-systolic index (LVESVI). A total of 16 identifications were performed, with 6 identifications each in the young and older group plus another 4 identifications separated for male and female, as described previously. The circles represent the CVS model output signals.

Table 3 gives an overview of how well the CVS model output data matches the data given in [15White M, Leenen FHH. Effects of age on cardiovascular responses to adrenaline in man Br J Clin Pharmacol 1997; 43: 407-14.]. The absolute median percentage error is given as well as the inter-quartile range (IQR). These two values are calculated over all 16 identified segments.

Table 4 gives the median absolute percentage errors and IQR for prediction 1 in study 1. This prediction uses a population-specific rule obtained only from the young population to describe the changes in the main adrenaline-specific model parameters caused by an increase in the adrenaline dose from baseline and 20 ng/min/kg to 160 ng/min/kg. Note that the baseline solution vector was used as initial solution for each time step and only the adrenaline-specific parameters were updated according to the population-specific rule.

Table 5 gives the median absolute percentage errors and IQR for prediction 2 in study 1. This second prediction uses the same population-specific rules as were used in prediction 1. However, in contrast to prediction 1, the previous solution is used as initial solution, rather than the baseline solution. Thus, for example, for predicting and calculating the parameters for a dose of 120 ng/min/kg, the identified parameters for a dose of 80 ng/min/kg are used.

Fig. (7) shows in the upper panel (solid line) the mean arterial pressure (MAP) over 14 hours as given in [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.]. The circles represent the CVS model outputs obtained when the CVS model is re-run with the identified patient-specific parameters. The middle panel shows as a solid line the mean pulmonary artery pressure (MPAP) as obtained from [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.] over the 14 hour study period. The circles depict the CVS model output data when re-run using the identified parameters. The lower panel shows the same results for the cardiac index (CI).

Table 6 gives an overview of how well the CVS model output data matches the data given in [16Heringlake M, Wernerus M, Grunefeld J, et al. The metabolic and renal effects of adrenaline and milrinone in patients with myocardial dysfunction after coronary artery bypass grafting Crit Care 2007; 11(2): R51.] in terms of median and inter-quartile range (IQR). These values are provided over all 8 identified segments for the total 14-hour study period.

Table 7 gives the median absolute percentage errors and IQR for predicting the hemodynamic responses in MAP, MPAP and CI based on the time in the study. Note, that the rules for the adrenaline-specific parameters were obtained from the middle time segments at 2 to 12 hours. The hemodynamic responses are predicted for 6 different time segments at 4, 6, 8, 10, 12 and 14 hours. The previous parameter solution vector was used as the initial solution for each predicted segment.

Fig. (8) shows in the upper panel (solid line) the mean arterial pressure (MAP) over 24 hours as given in [17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.]. The circles represent the simulated CVS model outputs obtained when the CVS model is re-run with the identified patient-specific parameters. The middle panel shows as a solid line the mean pulmonary artery pressure (MPAP) as obtained from [17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.] over the 24 hour study period. The circles represent the CVS model output data when re-run using the identified parameters. The lower panel shows the same results for the cardiac index (CI). It should be noted that the last prediction for MPAP in Fig. (7) is significantly less accurate than all other predictions. This effect could be random but the variation in MPAP is not sufficient enough to properly assess this result, since it is still only 2 mmHg in error, which is clinically small. Further results over a longer time period that have bigger fluctuations in MPAP would be required to fully understand whether or not this effect is a potential modeling error that needs to be addressed.

Table 8 gives an overview of how well the CVS model output data matches the data in [17Levy B, Bollaert PE, Charpentier C, et al. Comparison of norepinephrine and dobutamine to epinephrine for hemody-namics, lactate metabolism, and gastric tonometric variables in septic shock: a prospective, randomized study Intensive Care Med 1997; 23(3): 282-7.]. The median absolute percentage error is shown, as well as the inter-quartile range (IQR). These two values are calculated over all 5 identified segments for the total study period of 24 hours.

Table 9 gives the median absolute percentage errors and IQR for predicting the hemodynamic responses in MAP, MPAP and CI based on the time in the study. The rules for the adrenaline-specific parameters were obtained from the time segments h1 and h6 to predict a single response at h12. The parameter solution vector at h6 was used as initial solution for the prediction of h12.