Peripheral artery disease (PAD) is a progressive atherosclerotic occlusive disease affecting at least 8 million Americans (Allison et al., 2007; Ostchega, Paulose-Ram, Dillon, Gu, & Hughes, 2007). Decreased arterial blood flow to the lower extremities results in skeletal muscle ischemia, experienced as pain associated with walking, or claudication (Falcone et al., 2003). In PAD clinical trials, claudication is most often assessed during standardized treadmill (TM) testing before and after an intervention using pain self-reports. The aim of this secondary analysis from the Exercise Training for Claudication (ETC) Study was to model pain trajectories during a peak walking test after 12 weeks of treatment in participants in four randomly assigned treatment groups-TM, arm ergometry (AE), combination (TM and AE), and usual care (UC)-in comparison with baseline patterns.
At rest, patients with claudication have sufficient blood flow to supply the tissues of the legs with oxygen and nutrients. During the increased metabolic demand caused by lower extremity physical activity such as walking, supply no longer meets demand, leading to skeletal muscle ischemia and pain, called claudication. This cramplike pain occurs in the lower extremities in areas distal to one or more arterial stenoses or blockages. The pain most often affects the calf muscles but also occurs in the buttocks, thigh, or even the foot (Hiatt & Brass, 2006). Typically, claudication pain commences shortly after exercise begins, with more strenuous activity, such as faster pace or uphill walking, leading to quicker onset of pain (Bick, 2003). Claudication pain may become severe within minutes or even seconds of onset, significantly limiting walking, and resolves only when walking stops. Claudication discomfort is relieved quickly (within 1 to 2 minutes) by the cessation of exercise but recurs whenever exercise is resumed (Hiatt & Brass, 2006).
Claudication may stabilize but does not remit spontaneously and may progress (Falcone et al., 2003). Thus, the unpleasant sensory and emotional experience (Loeser & Treede, 2008) of claudication is chronic, intermittent, and acute. Claudication limits mobility and physical functioning and decreases quality of life (McDermott et al., 2001; Regensteiner et al., 2008). It diminishes self-rated physical health to a point similar to those who have chronic heart failure (Smolderen, Pelle, Kupper, Mols, & Denollet, 2009). Pain becomes central to life (Olson & Treat-Jacobson, 2004), affecting social and role functioning (Johnstone, 2004; Treat-Jacobson et al., 2002), generating powerlessness (Gibson & Kenrick, 1998), and compromising sense of self (Treat-Jacobson et al., 2002).
Walking is both the proximate cause of and the first-line treatment for claudication (Hirsch et al., 2006). Since the publication of the first clinical trial results (Larsen & Larsen, 1966), the efficacy of supervised walking exercise training for improving walking capability in individuals with claudication has been well documented. Exercise training, consisting of repeated bouts of TM or track walking until moderate claudication pain is induced, generally results in an increase in the time or distance that patients can walk prior to onset of claudication and the time or distance that patients can walk before pain forces them to stop (Watson, Ellis, & Leng, 2008).
Improvement after exercise training using walking modalities is likely due to a combination of local skeletal muscle factors and systemic cardiovascular factors (Stewart, Hiatt, Regensteiner, & Hirsch, 2002), but it is hypothesized to result primarily from local metabolic adaptations in the skeletal muscle of the lower extremity (Yang et al., 2008). Nevertheless, many people with PAD find that their claudication reduces tolerance of the duration and intensity of walking exercise during training, which limits conditioning effects on the cardiovascular system.
In contrast, upper extremity aerobic exercise training such as AE (hand-biking) does not cause lower limb ischemia and associated pain and may contribute to systemic adaptations. Thus, patients with PAD should be able to achieve a higher exercise training intensity with arm ergometry than with walking exercise training, resulting in greater potential for systemic cardiovascular conditioning (Treat-Jacobson, Bronas, & Leon, 2009; Walker et al., 2000; Zwierska et al., 2005).
Measuring Claudication Pain
Treadmill tests have long been the standard for assessing the impact of claudication interventions (Hiatt, Nawaz, Regensteiner, & Hossack, 1988; Watson et al., 2008). The test is symptom limited, with participants walking until pain severity prevents them from continuing. Time or distance to onset of pain (pain-free walking distance) and total walking time or distance to exercise-limited pain (peak walking distance) both have been used to assess walking function and treatment efficacy. Measurement protocols vary. The simplest approach is to mark times when the test begins, the patient signals onset of pain, and walking stops because pain becomes unbearable. Other protocols involve patient self-reports of pain at regular intervals (e.g., every 30 or 60 seconds) throughout the TM test using a numeric rating scale (NRS).
To be useful, pain measurement scores in intervention trials for claudication need to be responsive in the natural history sense (scores from individual patients during a test should reflect intraindividual change) and in detecting clinically important interindividual differences in intraindividual change between patients assigned to different treatment groups (Dekker, Dallmeijer, & Lankhorst, 2005; Terwee, Dekker, Wiersinga, Prummel, & Bossuyt, 2003).
Numeric rating scales are simple, ubiquitous devices that permit self-report of pain intensity using integer numbers ranging from 0 (no pain) to some highest number that represents worst imaginable pain, with numbers between representing increasing levels of pain (Jensen & Karoly, 2001). Higher numbers represent increased levels of pain, but patients are not expected to be able to identify equal differences in pain, so the scale is graded, or ordinal (cf. Raudenbush & Bryk, 2002, pp. 317-325). When applied in the assessment of claudication during TM tests, the rating scores of an individual traverse the entire scale, increasing monotonically (i.e., scores stay the same or increase) as the test flows through time, from 0 when the TM begins to the highest number (severest pain), at which point testing ceases.
Pain intensity is a latent variable, the severity of which is experienced continuously (Jensen & Karoly, 2001). When patients report observed scores on NRSs, they are indicating when a change on the underlying continuum of pain is noticeable (Zimmer, 2005). The scores represent passage across thresholds that have shown ordinal properties in experimental and clinical evaluations (Price, Bush, Long, & Harkins, 1994); higher number words are used to indicate more pain, but differences between reported numbers do not represent equidistant differences on latent pain scales. For this reason, cumulative probability models are used to model response functions on ordinal scales (Hedecker & Gibbons, 2006; Raudenbush & Bryk, 2002; Skrondal & Rabe-Hesketh, 2004).
Issues and Purpose
Most studies assessing outcomes in intervention trials for patients with claudication use pain-free walking time or distance and peak walking time or distance as primary outcomes. These variables provide information about important functional outcomes. However, this practice relies on analysis of observed scores without consideration of the underlying latent pain continuum. It discards much data reported in trials, does not allow description of the pain experience in real time, and does not permit comparison of pain trajectories from pretest to posttest or between intervention groups.
The aim of this secondary analysis was to use a trajectory perspective to describe and model the observed patterns of pain during TM testing in participants who took part in the ETC Study (Treat-Jacobson et al., 2009). Measurements were obtained at baseline and after 12 weeks of supervised exercise training. It was hypothesized that there would be different patterns of pain response to walking during the TM tests among individuals and also that treatments would differentially affect patterns of pain response (trajectories) at the 12-week testing compared with baseline. A hierarchical generalized latent variable model with a cumulative logit link function (Raudenbush & Bryk, 2002) was used to evaluate this proposition.
The ETC Study was a single-center, randomized, controlled pilot study comparing the relative efficacy of AE training, TM training, combination training, and UC in improving walking distance in patients with lifestyle-limiting claudication. Results of this study indicated significant improvement in the peak walking distance from baseline to 12 weeks in all exercise groups compared with the UC group. There was also a significant improvement in pain-free walking distance after 12 weeks of exercise training only in the AE group compared with the UC group (Treat-Jacobson et al., 2009).
Sample and Procedures
Details of the study sample are reported elsewhere (Treat-Jacobson et al., 2009). In brief, study participants were recruited from the Twin Cities metropolitan area and were included if they had lifestyle-limiting claudication, with PAD confirmed through an abnormal resting and postexercise ankle brachial index (Hirsch et al., 2006). All participants were medically stable and able to complete 12 weeks of supervised exercise training safely. The sample comprised 41 participants who were predominantly male (71%) and Caucasian (85%) with moderately severe PAD (the mean ankle brachial index of the more severely diseased leg was 0.67). The parent study was powered at 90% to detect a 30% improvement in maximum walking duration, based on previous studies. Most participants had medical histories that included hypertension, dyslipidemia, diabetes, cigarette smoking, or coronary heart disease. There were no statistical differences between groups in baseline demographics, health status, or current medications.
Participants in the exercise groups performed 60 minutes of supervised exercise (TM walking, AE, or a combination of both modalities) three times weekly for 12 weeks according to a standard protocol. All participants performed a symptom-limited, graded, cardiopulmonary TM exercise test (GXT) at baseline and after 12 weeks of study participation. Participants continued with the TM test until they reported a maximal level of unbearable pain, at which point the test was stopped.
The AE group (n = 10) began exercising at one work level (10 W) below the maximal level achieved during their baseline AE test at a rate of 50 cycles per minute. Participants worked against this load intermittently for periods of 2 minutes of exercise, followed by 2 minutes of rest, for a total of up to 60 minutes. After 3 weeks of training, exercise intensity was increased to the work level in watts achieved during the baseline arm ergometry test. Exercise time was progressively increased in each cycle by 1 minute every 2-3 weeks during the training period and rest periods were decreased to 1 minute, for a maximal volume of 5 minutes of exercise and 1 minute of rest for 60 minutes (50 minutes of exercise). The TM group (n = 11) initially began exercising at 2 mph at a 0% grade. They walked until their claudication pain became moderately severe (4 of 5 on claudication scale), and they then stopped, sat down, and rested until the pain subsided. This exercise-rest cycle was repeated throughout each 60-minute exercise session. When a participant was able to walk 8 minutes at the initial workload without having to stop because of moderately severe claudication, the TM grade was increased by increments of 0.5% until an 8%-10% grade was achieved. Subsequently, exercise intensity was increased during training sessions by increasing the TM speed by increments of 0.1 to 0.2 mph as tolerated. Combination group participants (n = 12) completed both upper and lower body training at each session. After a 5-minute warm-up period, sessions consisted of 20 minutes of intermittent arm ergometry exercise utilizing a protocol similar to the AE group, followed by 40 minutes of intermittent TM walking, utilizing a protocol similar to that of the TM group, for a total of 60 minutes of training per session. The UC group participants (n = 8) were provided with standardized walking instructions for patients with claudication and were instructed to continue the prescribed usual medical care for their PAD.
Pain Measurement Over Time During TM Testing
During the baseline and 12-week GXTs, participants rated pain severity every 30 seconds using a 6-point scale (0 = no pain; 1 = mild claudication pain, onset of pain; 3 = moderate pain; and 5 = severe pain, wherein the test is stopped). There were no verbal descriptors at scores of 2 or 4. Participants rated their pain by pointing to the number on the scale or by raising the corresponding number of fingers. Time walked prior to initial onset of mild pain, times at which the participant progressed to each pain stage, and stopping time were recorded. This method is employed commonly across PAD clinical trials.
A person-period data set (Singer & Willett, 2003) was used to organize trial information. Treatment was dummy coded so that baseline GXT records were indicated when all treatment codes were equal to 0. Interaction variables were computed by multiplying treatment by time at each observation for each person. As illustrated for one person in Table 1, each record in the person-period data set had 11 explicit variables: an identifier (i = ID), an outcome (PAIN, measured on the ordinal NRS using integers from 0 to 5), and 9 predictors (time [in seconds], 4 dummy-coded treatment variables [TM, CB, AE, and UC], and 4 computed treatment-by-time interaction variables [TMSEC, CBSEC, AESEC, and UCSEC]).
Graphing Pain Responses Over Time
Observed pain trajectories were plotted with X = time in seconds from 0 up to 1,560 (26 minutes; just beyond the duration of the longest test). Y values were the integers from 0 to 5 (scores on the NRS pain rating scale). Straight lines were used to connect adjacent points to create the observed pain trajectory. The discrete, ordered categories of the scale in combination with the monotonic increasing nature of claudication pain resulted in graphs with a stair-step appearance. One participant's scores for pain during the GXT at baseline and 12-week posttest are shown in Figure 1.
Modeling Pain Responses
The analytic goal was to use ordinal NRS scores to construct a person-oriented model suitable for evaluating the hypotheses about individual variation in pain trajectories and impact of treatment and treatment-by-time interactions on pain trajectories at 12 weeks compared with individual baseline. Let R be a response m on the NRS. The cumulative log odds, defined as the natural logarithm of the odds ratio given by (Prob[R ≤ m]) / (Prob[R > m]), are at the heart of the model. Using the symbol ηmti to represent the cumulative log odds of NRS response m at measurement t for person i, a set of hierarchical logistic regression equations (Hedecker & Gibbons, 2006; Hosmer & Lemeshow, 1989) specifies the ηmti as time-based functions of random effects (due to individuals; Level 2) and fixed effects (due to thresholds on the latent pain continuum, treatment, and treatment-by-time interaction; Level 1). Variables and parameters of the model are defined in Table 2. (η5ti is not modeled because the cumulative probability is 1 by definition). The full Level 1 model is as follows:
The Level 1 model reflects the ordinal nature of the NRS response options, the measurement protocol incorporated into the person-period data set, and the randomized design rendered in the dummy-coded treatments. The first threshold on the latent pain continuum (d0 in Equation 1a) is shown for completeness but is set to 0 to identify the model. At baseline, only the first three terms in each equation are nonzero and determine individual pain trajectories. The treatment effects and the treatment-by-time interaction effects come into play at 12 weeks, offsetting pain trajectories from individualized baseline models.
The Level 2 model, associated with the Level 1 random coefficients B0i and B1i, is
where G00 and G10 are the grand means for B0i and B1i (Equations 1a-1e). The residual terms R0i and R1i reflect individual variation around the grand means. Variance in intercepts (τ00), slopes (τ11), and the intercept-slope covariance (τ01) is estimated assuming multivariate normality.
The model was estimated using HLM 6.0 (Raudenbush & Bryk, 2002). Model-based standard errors were used to evaluate statistical significance of the estimates. The estimated cumulative log odds ηmti were exponentiated to obtain odds ratios. Additional transformations produced the probabilities of responding in each category over time that were used to create smooth, model-based individualized pain trajectories in continuous time for each person at baseline and at 12 weeks. In the model, larger function values for ηmti are associated with greater odds of responding in lower NRS categories, reflecting less pain. Thus, a negative rate of change in the cumulative log odds (i.e., B1i < 0) indicates that the probability of responding in lower NRS categories decreases as pain increases.
Pain Response Graphs
Shorter trajectories were uniformly steep, showing quick onset of pain and rapid ascent to maximum pain. Longer trajectories showed wider variation in patterns of pain over time. Selected baseline observed trajectories with varying total walking times are displayed (see Figure, Supplemental Digital Content 1, http://links.lww.com/NRES/A47).
Treatment Effects on Pain Trajectories
Graphs of self-reported pain at baseline were compared with 12-week reports to search for common patterns of exercise training effects. The differences identified visually in duration of walking at each level of pain are shown in Figure 2: (a) at highest pain levels, (b) at every pain step, (c) at onset and lower pain levels, (d) at onset only, and (e) no difference (the 12-week trajectory resembled the baseline trajectory). For some participants, no obvious pattern of effect was visually detectable. Baseline and posttest trajectories of self-reported pain were then sorted into treatment groups and reexamined (see Figure, Supplemental Digital Content 2, http://links.lww.com/NRES/A48). Participants in the TM and combination treatment groups demonstrated all five patterns of difference between pretest and the 12-week GXT. The AE group showed one striking quality: At 12 weeks, no AE participant walked longer at moderate and severe pain levels. Instead, AE participants demonstrated delays in onset to pain and increased walking at mild to lower pain levels. Most UC participants appeared to demonstrate no difference in pain trajectories. The TM group participants with shorter baseline walking times seemed less likely to have improvement at the lower end of the pain scale (mild to moderate pain) than those with longer baseline walking times.
The Trajectory Model
Model parameters and derived odds ratios are listed in Table 3. Graphs based on estimated parameters were used to portray most statistical results; transformations are described in figure legends.
Parameter estimates for the intercept and slope terms (G00 and G10) were significant (i.e., as expected, the log odds of an NRS response of 0 at the outset of the baseline test were high, and as time passed, the probability of responding in lower rather than higher NRS category decreased). The thresholds were significant and ordered with varying differences in distance between adjacent thresholds. The modeled ηmti values are linear functions of time (see Figure, Supplemental Digital Content 3, which shows the modeled ηmti, http://links.lww.com/NRES/A49). The estimated probability of responding in a higher versus lower NRS category is also presented (see Figure, Supplemental Digital Content 4, http://links.lww.com/NRES/A50), which illustrates the increase as the baseline GXT progressed.
Treatment Effects at 12 Weeks
Treatment effects (on intercepts) were all significant (including UC); treatment-by-time interaction effects (on slopes) were significant for TM and combination groups as well (Table 3). The typical baseline pain trajectory for all participants and typical pain trajectories estimated at 12 weeks for each treatment group, derived from model parameters and transformations to the cumulative probabilities for responding to each NRS category over time are shown in Figure 3 (see also Figure, Supplemental Digital Content 5, http://links.lww.com/NRES/A51). Patterns in these typical pain trajectories are consistent with findings of improved walking at lower levels of pain after AE training and longer walking through higher levels of pain after TM and combination training and show the pain trajectory throughout the GXT as well.
Variance in B0i and B1i was significant (Table 3; also see Supplemental Digital Content 6, http://links.lww.com/NRES/A52), indicating meaningful interindividual differences in pain trajectories. The correlation between intercepts and slopes was small but positive, indicating that earlier onset of pain was associated with quicker advancement to unbearable pain.
Modeled Individual Trajectories
Individual functions for the cumulative log odds (Equations 1a-1e) were transformed and used to plot expected mean responses on the NRS over time at baseline and 12 weeks. Selected modeled individual pain trajectories are shown as overlays to observed scale scores at baseline and 12 weeks in Figure 4. There was wide-ranging individuality in the set of modeled pain trajectories during the GXTs. The constant treatment effect on the cumulative log odds at 12 weeks was incorporated in the pain trajectories via nonlinear transformation of model parameters to create individualized pain trajectories. The modeled trajectories appear consistent with the observed data (i.e., the area between the observed and modeled curves is generally small).
Pain trajectories were studied during GXTs at baseline and after 12 weeks of randomly assigned supervised exercise training or UC for claudication. Scores on a 6-point ordinal NRS for pain obtained every 30 seconds during each test were graphed to obtain observed individual pain trajectories, which were smoothed and summarized with a hierarchical generalized linear model. Visual inspection of observed trajectories showed a wide range of pain experiences over time. Common differences noted between baseline and 12-week tests involved trajectory segments at the beginning of the test (time to onset of pain and low pain levels), the middle of the test (pattern of increase to higher pain levels), and the end of the test (moderate to severe pain) and appeared related to treatment. The model provided information about the impact of time on use of the NRS response options by patients with PAD during the GXT. At 12 weeks, fixed effects for all treatments (including UC) and treatment-by-time effects (for TM and combination groups) were significant. Individual parameters for predicting the cumulative log odds for each rating scale category combined with fixed effects show posttraining trajectories as offsets from personal baselines. Findings are discussed in terms of the personal claudication experience, understanding treatment impact, and implications for design and analysis in future research studies.
Personal Claudication Experiences
Model-based pain trajectories create a visual image of the claudication experienced by individual patients with PAD. The pain trajectory describes the gripping progressive intensity of the unpleasant sensory experience of claudication. The modeled trajectory pictures claudication as a dynamic phenomenon that complements classic functional walking outcomes of pain-free walking time or distance and total walking time or distance. The trajectory approach extends possibilities for understanding the impact of claudication by providing information about the pain itself, rather than the consequences of pain. The visual summary can be used to debrief clinic patients about their pain experience, point out various ways in which pain can be mitigated across the trajectory, and tailor exercise interventions to maximize effectiveness for individual patients (Thorne & Morley, 2009).
Understanding Treatment Impact
Improvement in walking ability through delayed onset of pain, slower increase of pain, and ability to walk at higher levels of pain after PAD exercise training are thought to be functions of local mechanisms (i.e., changes in skeletal muscle metabolism) or systemic mechanisms (i.e., change in vascular and cardiac function). It is postulated that those who perform non-ischemia-inducing aerobic arm exercise derive the benefits through systemic rather than local mechanisms. Conversely, individuals who perform ischemia-inducing TM exercise training are hypothesized to derive benefit primarily through local skeletal muscle adaptations (Stewart et al., 2002).
Differential association of treatment modality with local and systemic physiological responses may underlie the pattern of effects seen on pain trajectories. Arm ergometry training affected pain trajectories toward the start of the test, extending the time during which the probabilities of reporting low levels of pain remained high. After the onset of pain, however, the course to maximum pain was similar to the individual baseline. The cumulative log odds as a function of time were unchanged from baseline after AE training, so that once pain took hold, the course was similar to the individual baseline. Pain trajectories of participants in the TM group at 12 weeks were more likely to show increased ability to walk longer with more severe pain. This outcome reflects the training protocol, whereby participants walked into moderately severe pain, rested, and then repeated these bouts for 1 hour during each exercise session. Based on descriptive analysis, the TM group participants who were at the lower end of the functional continuum at baseline with short steep pain trajectories seemed more likely to walk longer at more severe pain levels after training. Those with longer trajectories and gradual appearance of pain at baseline appeared to show increases at onset and mild pain, similar to the AE group. This is likely due to their ability to tax the central cardiovascular system to a greater degree before reaching moderately severe claudication, thus generating a systemic response during training. Combination training created a significant but muted effect on the cumulative log odds at t = 0 and an effect similar to TM exercise over time. From a mechanistic perspective and compared with AE, the 12-week training may have allowed only partial systemic conditioning, resulting in less change in the pain trajectory early in the test.
Traditional analysis of pain response to walking in patients with claudication focuses on the points of onset and maximal pain, without taking into account the data on the pain experience between those two points. The trajectory perspective fills this gap in time, highlighting the individual effect. However, the model and its statistical foundations are considerably more complex and lack the familiarity of classic approaches, which prompts the question, "Was it worth the effort?“ This secondary analysis was started by plotting observed pain trajectories (Figures 1 and 2; see Supplemental Digital Content 1, http://links.lww.com/NRES/A47). Experienced investigators saw new types of information in their data and found that thinking about the observed pain trajectories generated novel ideas about treatment effectiveness, mechanisms, and individual responses. Conceiving of cumulative log odds that varied continuously over time for individuals was challenging, as was working through the transformations to obtain the pain trajectories. With time, links between the model and key aspects of the scientific problem became evident, confirming the value of the approach. It is also relevant to a wide variety of problems in nursing research characterized by change over time in an outcome with ordinal measurement.
Power considerations in studies of individual change involve the duration, timing, and frequency of observations as well as sample size (Raudenbush & Bryk, 2002). In studies of claudication interventions, time itself is nested and temporal factors within GXT and between GXTs need to be considered. Within GXTs, past research has shown the utility of using symptom-limited tests, which individualizes duration and also provides information about peak walking time or distance. Patients were able to report the pain scores on the 6-category rating scale every 30 seconds even as they were exerting themselves to the utmost during the test. After 12 weeks of training, the scores they reported depicted individual change across the duration of a given test. However, it is important to determine whether functional changes occur at different rates among individuals and in response to different modes of exercise training. Employment of increased frequency of GXT testing, especially during the training period, is needed to better understand the rate of response both within individuals and within treatment groups. Larger sample sizes would permit identification of an even wider array of individual patterns of response and predictors of patterns of change.
The trajectory perspective on claudication offers new avenues for research. Because claudication is associated with diminished quality of life, improvement in functional ability and sense of well-being is a key motivation for recommending time-consuming and challenging exercise interventions. Concurrent examination of trajectories of quality of life over time and claudication experiences can provide information about the personal costs and benefits of undertaking exercise training. Advances in real-time monitoring of skeletal muscle tissue oxygenation using near infrared spectroscopy permits measurement of the proportion of oxygenated and deoxygenated hemoglobin in skeletal muscle at rest and during walking exercise (Gardner et al., 2008). Combining tissue oxygenation measures with modeled pain trajectories obtained using data from a GXT protocol has potential for unlocking information about mechanisms of action associated with various exercise modalities as well as understanding the links between tissue damage from ischemia and subjective pain experiences.
All exercise training modalities studied improved walking ability, and experimental effects created a wide range of posttraining pain trajectories that reflect individual baseline functioning. The physiological, functional, and psychosocial characteristics that predict individual response to a walking versus upper body exercise program are as yet undetermined. Further exploration of baseline functional status, ability to tolerate discomfort, and previous experience with aerobic exercise is warranted. Future studies with larger samples may help elucidate these individual predictors and permit more effective tailoring of interventions to address the unique needs and characteristics of each patient. The trajectory perspective embedded in the hierarchical, generalized linear model is a useful and illuminating way to highlight these effects.
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