Cardiopulmonary responses to maximal aerobic exercise in patients with cystic fibrosis

Abstract

Cystic fibrosis (CF) is a debilitating chronic condition, which requires complex and expensive disease management. Exercise has now been recognised as a critical factor in improving health and quality of life in patients with CF. Hence, cardiopulmonary exercise testing (CPET) is used to determine aerobic fitness of young patients as part of the clinical management of CF. However, at present there is a lack of conclusive evidence for one limiting system of aerobic fitness for CF patients at individual patient level. Here, we perform detailed data analysis that allows us to identify important systems-level factors that affect aerobic fitness. We use patients' data and principal component analysis to confirm the dependence of CPET performance on variables associated with ventilation and metabolic rates of oxygen consumption. We find that the time at which participants cross the gas exchange threshold (GET) is well correlated with their overall performance. Furthermore, we propose a predictive modelling framework that captures the relationship between ventilatory dynamics, lung capacity and function and performance in CPET within a group of children and adolescents with CF. Specifically, we show that using Gaussian processes (GP) we can predict GET at the individual patient level with reasonable accuracy given the small sample size of the available group of patients. We conclude by presenting an example and future perspectives for improving and extending the proposed framework. The modelling and analysis have the potential to pave the way to designing personalised exercise programmes that are tailored to specific individual needs relative to patient's treatment therapies.

Fig 1. GP is a probability distribution over functions.

The thick solid red line is the true function f and the thick dashed black line is the GP “prior”. (a) Thin grey lines show sample functions of the GP. (b) Blue bullets indicate five data points sampled from f. The GP distribution is updated using these sample data points. The thin grey dashed lines show m(x) ± 2s(x).

Fig 2

(a) The work rate for each participant is increased at a rate dependent on their past test performance. (b) Participant age is correlated with test performance for young participants, but not for older ones.

Fig 3. Ratio of oxygen utilisation and total breathing throughout the test.

Markers indicate the volitional exhaustion times for each participant.

Fig 4

(a) Correlation of FEV₁ with the maximal tidal volume achieved throughout the test. (b) Correlation between FEV₁ and FVC is high. Note that, although FVC and FEV₁ are good predictors of poor test performance, they are unable to distinguish better performing participants.

Fig 5

(a) Total ventilation plotted against oxygen utilisation. We observe that breathing pattern is strongly correlated with test performance. (b) Exponential curves are fitted through the raw data, further highlighting this dependence.

Fig 6. Slope of the fitted curves (logV˙E against V˙O2) from Fig 4(b) plotted against the total energy transfer during the test.

We find a relatively poor characterisation of the variance between performances. (b) By instead plotting the oxygen consumption at a fixed rate of breathing, we better capture differences in performance.

Fig 7

(a) Breathing patterns subdivided into the breathing rate and tidal volume. These data appear uninformative for predicting test performance. (b) With the additional inclusion of the oxygen consumption at a fixed rate of breathing, we find that these variables now almost perfectly capture variation in participant performance.

Fig 8. The first principal component obtained via PCA accounts for over 90% of the variation in test performance.

(b) Similar levels of variance are accounted for by taking only the normal component of the first principal component, θ, in the breathing frequency direction.

Fig 9

(a) Quantifying the relationship between the anaerobic threshold and overall test performance. Thresholds were calculated using an automated procedure based on previous methods [46] (b) ${\dot{\text{V}}\text{O}}_{2\text{max}}$ is the best single predictor of overall test performance.

Fig 10. Predictions (asterisks) vs. exact values (bullets).

Red bars show the 95% confidence intervals, m_i(x_i) ± 1.96 s_i(x_i) around the predicted value, where m_i and s_i are GP prediction mean and standard deviation based on all but the i’th data point.

Fig 11

(a) Tidal volume (V_T), an estimate for the dead volume (V_D) and Breathing frequency BF from the data. (b) Changes in ventilatory parameters during exercise for the 15 CF patients using the proposed form of ${\dot{\text{V}}}_{\text{D}}$ = ${\dot{\text{V}}}_{\text{DB}}$ + a × W(t). In the case of ${\dot{\text{V}}}_{\text{E}}$ the solid dots represent values extracted from the data, for ${\dot{\text{V}}}_{\text{D}}$ and ${\dot{\text{V}}}_{\text{A}}$ these represent values taken from model simulations (see S1 File). In all cases the red stars represent the group mean.

Fig 12. Schematic of the variables and processes in the proposed ODE-based mathematical model.

Adapted from Timischl [51] and Batzel et al. [86].