Analysis and input data for simulations As mentioned, four questions were posed:

First, in health, we first assessed the effects of a wide range of lung and tissue heterogeneities on oxygen tensions and utilization at all steps of the O2 pathway. This extensive exploration was carried out for conditions of maximal exercise breathing room air at sea level. To this end, input data defining O2 transport conductances (i.e., ventilation, cardiac output, lung and muscle diffusional conductances) from normal subjects exercising maximally at sea level in Operation Everest II (Sutton et al., 1988) were used just as for the previous models (Wagner, 1993, 1996). Lung heterogeneity was analyzed from complete homogeneity (log SD Q̇ = 0), to very high inhomogeneity (log SD Q̇ = 2) as might be seen in the critically ill. We also explored the effects of skeletal muscle heterogeneity on overall O2 uptake (VO2 max) using a similar wide range of log SD V̇_68; , from 0 to 2.0..

However, in all the subsequent analyses, for each level of lung heterogeneity (from log SD Q̇ = 0 to log SD Q̇ = 2), the impact of muscle tissue heterogeneity was assessed from a completely homogenous exercising muscle (log SD V̇_68; = 0), to a likely high degree of muscle metabolism/perfusion inhomogeneity (log SD V̇_68;= 0.5), taking into account that recent experimental studies suggests a log SD V̇_68; of only 0.1 in normal subjects exercising maximally at sea level (Vogiatzis et al, J. Applied Physiol, under review)).

The second question examined the effects of heterogeneity in healthy lungs and muscle on O2 transport and utilization at altitude. For the lung we used log SD Q̇ = 0.5 as a value commonly seen during exercise (Wagner et al., 1987b).This value is near the upper end of the normal range, which is 0.3-0.6 (Wagner et al., 1987a).In muscle, we used preliminary unpublished estimates of log SD V̇68; = 0.1. For non-exercising body tissues we used typical resting total values of V̇ (300 ml/min), V̇: (240 ml/min) and blood flow (5 L/min) for

normal subjects. The input data defining the O2 transport conductances again came from normal subjects exercising maximally at sea level and altitude in Operation Everest II (Sutton et al., 1988) as used above and also in our prior work 2013. However, to study the consequences at more altitudes than were examined in Operation Everest II (which were sea level, 4600m, 6100m, 7600m and 8848m), O2 transport conductance parameters were linearly

Predictive Medicine for Chronic Patients in an Integrated Care Scenario 57

interpolated at 305m (1000 ft.) elevation increments from the data obtained at each of the 5 altitudes studied in Operation Everest II (Sutton et al., 1988).

Data from experimental human exercise studies do not exist for the two variables defining the hyperbolic mitochondrial respiration curve: V̇68; and P. Therefore, we executed the simulations mentioned above using a value for V̇68; (4.6 L/min) that is 20% higher than the measured V̇_max at sea level in Operation Everest II (Sutton et al., 1988) of 3.8 L/min. We chose this value as a reasonable estimate for V̇_68; because it is known that measured V̇_68; is less than mitochondrial capacity to use O2 (i.e., V̇_ ) in healthy fit subjects since exercise capacity is known to be increased when breathing 100% O2 (Welch, 1982; Knight et al., 1992). For P, we used a value of 0.3 mm Hg, similar to what has been found experimentally in vitro (Wilson et al., 1977; Gnaiger et al., 1998; Scandurra & Gnaiger, 2010). Little is known about V̇ /Q̇ heterogeneity in muscle except for measurements made by Richardson using magnetic resonance spectroscopy (Richardson et al., 2001) and recent unpublished data using NIRS that yield dispersion values of about 0.1 as explained earlier.

For the third and fourth question we assessed how substantial variations of the three least well-established determinants of O2 flux and partial pressures in the transport/utilization pathway (V̇ and P50 of the mitochondrial respiration curve and log SD V̇ ) would affect both V̇_ and mitochondrial P_estimates, in health (third question) and in COPD (fourth question). Input data defining O2 transport conductances and lung heterogeneity (i.e. log SD Q̇ = 0.5) from normal subjects exercising maximally at sea level in Operation Everest II (Sutton et al., 1988) were used in health. In disease, measured O2 conductances and lung heterogeneity data came from two previously studied COPD patients (Blanco et al., 2010) exercising maximally (Table II), one with mild (FEV1 = 66 % predicted post- bronchodilator) and one with severe (FEV1 = 23 % predicted post-bronchodilator) COPD. However, even if reasonable, the values of V̇ and P50 assumed to answer the previous question are uncertain, let alone whether there is significant V̇ /Q̇ heterogeneity. Because of this, we carried out simulations over a wide range of possible values of these variables. In the case of V̇68;, it is known that acutely increasing inspired O2 concentration increases exercise capacity, both in health and in COPD (Welch, 1982; Knight et al., 1992; Richardson et al., 2004). How much higher is not known, and so to determine how important knowing V̇_ is to the outcomes of the model we compared outcomes using the previously-used V̇ value (20% higher than actual V̇_68;) to results obtained when V̇ was set to 10 % and 30% above measured V̇_68;. For mitochondrial P50, we used values lower (0.14 mm Hg) and higher (0.46 mm Hg) than 0.3 mm Hg, the value found experimentally in vitro (Wilson

Predictive Medicine for Chronic Patients in an Integrated Care Scenario 58

et al., 1977; Gnaiger et al., 1998; Scandurra & Gnaiger, 2010). Finally, to assess how sensitive the outcomes are to the degree of heterogeneity, we also carried out calculations with log SD V̇_ values of 0.1 (healthy subject estimates), 0.2 and 0.3. With respect to non- exercising body tissues, we used typical resting total values of V̇ (300 ml/min), V̇: (240

ml/min) and blood flow (5 L/min) for normal subjects.

For the two previously studied COPD patients(Blanco et al., 2010) exercising maximally we used measured resting values of whole body V̇_ (V̇_rest) and V̇_: (Table II), along with a blood flow estimate (Q̇_{BCBEGJGKRUWUBX}) from the following formula, which expresses the concept that blood flow is proportional to metabolic rate: Q̇BCBEGJGKRUWUBX= Q̇68;∗ V̇_rest V̇ _max.

3. Results

3.1. Effects of potential lung and muscle heterogeneities on O2 transport and utilization in