A lens is considered to be thin if its thickness t is much less than the radii of curvature of both surfaces, as shown in Figure 2.19. In this case, the rays may be considered to bend once at the center of the lens. For the case drawn in the figure, light ray 1 is parallel to the optical axis, so the outgoing ray is bent once at the center of the lens and goes through the focal point. Another important characteristic of thin lenses is that light rays that pass through the center of the lens are undeviated, as shown by light ray 2.

Three RCTs showed statins decreased echo sPAP at rest [46–48] or during exercise [44], whereas another RCT showed no change [45]. Clinical and functional outcomes were infrequently assessed, and changes in dyspnoea, HRQoL, and functional capacity are inconsistent [44, 45, 47].

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In summary, PDE-5i significantly improved haemodynamics in COPD-PH patients, but this did not translate to clinical, functional, or HRQoL benefits (table 3).

Several important distances appear in the figure. As for a mirror, we define dodo to be the object distance, or the distance of an object from the center of a lens. The image distance didi is defined to be the distance of the image from the center of a lens. The height of the object and the height of the image are indicated by hoho and hihi, respectively. Images that appear upright relative to the object have positive heights, and those that are inverted have negative heights. By using the rules of ray tracing and making a scale drawing with paper and pencil, like that in Figure 2.22, we can accurately describe the location and size of an image. But the real benefit of ray tracing is in visualizing how images are formed in a variety of situations.

Step 5. Most quantitative problems require the use of the thin-lens equation and/or the lens maker’s equation. Solve these for the unknowns and insert the given quantities or use both together to find two unknowns.

We identified five categories of COPD-PH therapies, including supplemental oxygen (table 1), calcium-channel blockers (supplementary table S2), pulmonary arterial hypertension (PAH)-targeted therapy (table 2), statins (supplementary table S3), and miscellaneous therapies (supplementary table S4).

The left-hand side looks suspiciously like the mirror equation that we derived above for spherical mirrors. As done for spherical mirrors, we can use ray tracing and geometry to show that, for a thin lens,

Effects of supplemental oxygen therapy including long-term oxygen therapy (LTOT) and nocturnal oxygen therapy (NOT) in patients with COPD-associated pulmonary hypertension (PH)

Besides hypoxaemia, COPD-PH may also be driven through other potential mechanisms [60], including pathophysiologic features similar to PAH, including pulmonary micro-vessel rarefaction and endothelial dysfunction, for example decreased expression of endothelial nitric oxide synthetase (eNOS) [3, 4, 60]. Thus, PAH-targeted therapy may have a potential role in COPD-PH management. However, guidelines generally recommend against PAH-targeted therapy for mild to moderate WHO group 3 PH, including COPD-PH [13, 61].

June 12, 2024 answer of Camera Type For Short clue in NYT Crossword Puzzle. There is One Answer total, Slr is the most recent and it has 3 letters.

Data are mean±sem unless otherwise specified. 6MWD: 6-min walk distance (m); BDI: Borg dyspnoea index; BID: twice daily; BNP: brain natriuretic peptide; BODE index: Body mass index, Obstruction by FEV1, Dyspnoea by mMRC grade, and Exercise capacity by 6MWD; CCB: calcium channel blocker; CT: computed tomography; ERA: endothelin receptor antagonist; FEV1: forced expiratory volume in 1 s; FVC: forced vital capacity; GOLD: Global Initiative for Chronic Obstructive Lung Disease; HR: hazard ratio; HRQoL: health-related quality of life; IQR: interquartile range; ISWD: incremental shuttle walk distance; LTOT: long-term oxygen therapy; mMRC: modified Medical Research Council; mNYHA FC: modified New York Heart Association functional class; mPAP: mean pulmonary artery pressure; NT-proBNP: N-terminal propeptide of brain natriuretic peptide; PAAT: pulmonary artery acceleration time; PaCO2: partial pressure of carbon dioxide in arterial blood; PaO2: partial pressure of oxygen in arterial blood; PAWP: pulmonary arterial wedge pressure; PDE-5i: phosphodiesterase type 5 inhibitors; PH: pulmonary hypertension; PO: by mouth; PVR: pulmonary vascular resistance; RCT: randomised controlled trial; RHC: right heart catheterisation; RVEF: right ventricular ejection fraction; SGRQ: St George's Respiratory Questionnaire; SC: subcutaneous; sPAP: systolic pulmonary arterial pressure (mmHg); SpO2: transcutaneous pulse oximetry oxygen saturation (%); TID: three times a day; WHO: World Health Organization; WU: Wood unit (mmHg·L−1·min−1).

noun something that gives a minutely faithful representation, image, or idea of something else: Gershwin's music was a mirror of its time.

Thin lenses work quite well for monochromatic light (i.e., light of a single wavelength). However, for light that contains several wavelengths (e.g., white light), the lenses work less well. The problem is that, as we learned in the previous chapter, the index of refraction of a material depends on the wavelength of light. This phenomenon is responsible for many colorful effects, such as rainbows. Unfortunately, this phenomenon also leads to aberrations in images formed by lenses. In particular, because the focal distance of the lens depends on the index of refraction, it also depends on the wavelength of the incident light. This means that light of different wavelengths will focus at different points, resulting is so-called “chromatic aberrations.” In particular, the edges of an image of a white object will become colored and blurred. Special lenses called doublets are capable of correcting chromatic aberrations. A doublet is formed by gluing together a converging lens and a diverging lens. The combined doublet lens produces significantly reduced chromatic aberrations.

Although three rays are traced in this figure, only two are necessary to locate a point of the image. It is best to trace rays for which there are simple ray-tracing rules.

Single studies have reported on several miscellaneous, non-traditional potential therapies in patients with COPD-PH (supplementary table S4) [50–52]. Some therapies demonstrated improved pulmonary haemodynamics at rest (e.g. Dipyridamole [53], cicletanine [54], ACE inhibitors [55, 56], inhaled nitric oxide (iNO) [57]) or on exercise (e.g. Waon therapy [58]), reduced dyspnoea (e.g. Waon therapy [58]), and/or improved exercise capacity (e.g. iNO [57]), whereas many other therapies had no reported benefits. Combinations of such therapies may improve multiple parameters; for example, combination of azithromycin, simvastatin, and LTOT decreased RHC sPAP and increased 6MWD [59].

The effect of treatment with atorvastatin on systolic pulmonary artery pressure in COPD-associated pulmonary hypertension (PH). Note: PH was diagnosed by echocardiogram in all studies. IV: inverse variance.

Four retrospective cohort studies assessed the effects of multiple PAH-targeted therapies individually in RHC-defined COPD-PH [37–40], reporting haemodynamic improvement with no clinical or functional benefits [37, 38], or no effects at all [39, 40]. Three other retrospective cohort studies [41–43] reported no survival benefit of PAH-targeted therapies in various combinations in RHC-defined PH, but one found short-term clinical (improved New York Heart Association (NYHA) functional class) and functional (improved 6MWD) benefits up to 1 year which were not sustained at 2 years [41]. Three studies suggested greater improvements with PAH-targeted therapy in patients with more severe PH, including greater RHC-measured haemodynamic effects [37, 38, 41], and one showed clinical and functional benefits up to 1 year [41]. Risk of bias was high for six of seven studies of multiple PAH-targeted therapies, and unclear for one study, which limits confidence in the results.

There were inconsistent benefits in HRQoL in four RCTs using different measurement tools [29–31, 33]. Sildenafil improved mMRC dyspnoea [30, 31], 36-item Short Form survey (SF-36) score, and the multi-parameter COPD BODE index (body mass index, obstruction by FEV1, mMRC dyspnoea, and 6MWD) [30], but not HRQoL in an unspecified questionnaire [29]. Tadalafil had no effect using different scores (SF-36, SGRQ, MLHFQ) [33].

Chronic obstructive pulmonary disease (COPD) is a progressive and incurable disease that represents one of the five leading causes of death worldwide [1, 2]. COPD is characterised by exertional dyspnoea, functional limitation, poor health-related quality of life (HRQoL), recurrent exacerbations and hospitalisations, as well as shortened survival [1, 2]. The presence of pulmonary hypertension (PH) in patients with COPD is increasingly recognised as an important contributing factor to its clinical manifestations and adverse clinical outcomes including increased mortality [3, 4]. For example, severe PH and resulting right ventricular (RV) failure are associated with more severe dyspnoea and limited exercise capacity [5, 6]. Indeed, the presence of PH has a stronger association with mortality in COPD than forced expiratory volume in 1 s (FEV1) or gas exchange variables [7, 8]. Moreover, enlarged pulmonary artery diameter on computed tomography scan is independently associated with a higher risk of acute COPD exacerbations and related hospitalisations [8, 9].

Subgroups based on the method of PH diagnosis were defined a priori and a sensitivity analysis performed; patients diagnosed using right-heart catheterisation (RHC)-determined mPAP versus those diagnosed using non-invasive echocardiography by estimating systolic PAP (sPAP) or calculating mPAP. During data analysis, another subset of COPD-PH patients was identified; those with more severe PH and RV failure, often in the setting of only mild to moderate COPD without resting hypoxaemia. This subgroup was analysed separately. Details of statistical analysis are given in the supplementary material.

Focal Length Calculator · Effective Focal Length, EFL (mm): · Back Focal Length, BFL (mm): · Front Focal Length, FFL (mm): · Primary Principal Point, P (mm): ...

In summary, in COPD-PH patients with hypoxaemia, LTOT may mildly reduce severity of PH, slow PH progression over time, and reduce mortality, but without any other clinical or functional benefit (table 3). There are limited, conflicting data on NOT, with haemodynamic benefit in only one of two RCTs [22, 23], and no clinical benefits in either.

According to the Preferred Reporting Items for Systematic Reviews and Meta-Analyses (PRISMA) guidelines, we searched MEDLINE and Embase databases from 1947 to 30 September 2020, using the search terms “pulmonary hypertension” AND “chronic obstructive airway disease or chronic obstructive pulmonary disease or COPD” AND “treatment or management”.

We also reviewed bibliographies, identifying additional relevant studies. Titles and abstracts were screened, and full-text articles were reviewed independently and in duplicate (R. Arif and S. Mehta) in order to identify studies meeting the predefined inclusion and exclusion criteria (supplementary table S1): studies of 10 or more patients reporting the effects of at least 4 weeks of treatment on pulmonary haemodynamics, survival, or other clinical outcomes in patients with COPD-PH. Risk of bias was assessed using the Newcastle Ottawa Scale for observational studies and the Cochrane Collaboration tool for randomised controlled trials (RCTs). Disagreements were resolved by consensus.

The haemodynamic benefit of LTOT varied, with small reductions (3–5 mmHg) in mPAP in four of eight studies [15, 16, 19, 21], and/or PVR in three [19–21], but no reported change in CO (three studies). Even in the absence of actual improvement in the severity of PH, LTOT may be associated with less progression of PH over time [14, 16]. For example, a progressive increase in mPAP in control patients was completely attenuated in LTOT patients in the Medical Research Council (MRC) trial [14].

In summary, combination PAH-targeted therapy does not improve survival but may offer some transient clinical and/or functional benefits. Patients with objective “response” to therapy, including improved mNYHA FC or PVR, may have improved survival [39].

Step 7. Check to see if the answer is reasonable. Are the signs correct? Is the sketch or ray tracing consistent with the calculation?

Data collection was performed independently by at least two authors (R. Arif, A. Pandey and Y. Zhao). The data extracted included: study characteristics, patients demographics and comorbidities, method of PH diagnosis, intervention type, dosage and frequency, duration of and loss to follow-up, as well as outcomes, including clinical outcomes (e.g. survival), cardiopulmonary haemodynamics (e.g. mean pulmonary artery pressure (mPAP)), pulmonary vascular resistance (PVR), cardiac output (CO), and others) as listed in supplementary table S1.

We retrieved and screened 4577 reports, and an additional 26 records were identified through other sources (figure 1). 4557 studies were excluded, leaving 46 studies reporting treatment of COPD-PH, including 23 RCTs (1159 patients) and 23 non-RCTs (1187 patients). Patients ranged from 35–85 years in age and were predominantly male in the majority of studies (range 32–100%). Lung function varied widely (FEV1 13–94% predicted), but most patients had moderate to severe COPD, many with hypoxaemia at rest.

Consider the thick bi-convex lens shown in Figure 2.24. The index of refraction of the surrounding medium is n1n1 (if the lens is in air, then n1=1.00n1=1.00) and that of the lens is n2n2. The radii of curvatures of the two sides are R1andR2R1andR2. We wish to find a relation between the object distance dodo, the image distance didi, and the parameters of the lens.

The main purpose of using neutral density (i.e., ND) filters is to reduce the amount of light that can pass through the lens. As a result, if a shutter speed is ...

Based on strong benefits in the treatment of PAH, 15 reports describe potential benefits of PAH-targeted therapies, including oral phosphodiesterase type 5 inhibitors (PDE-5i), oral endothelin receptors antagonists (ERAs), and prostanoids, in patients with COPD-PH (table 2).

PRISMA flow diagram of identification of relevant articles for inclusion in systematic review and quantitative analysis. PH: pulmonary hypertension.

Chronic obstructive pulmonary disease-associated pulmonary hypertension (COPD-PH) is an increasingly recognised condition which contributes to worsening dyspnoea and poor survival in COPD. It is uncertain whether specific treatment of COPD-PH, including use of medications approved for pulmonary arterial hypertension (PAH), improves clinical outcomes. This systematic review and meta-analysis assesses potential benefits and risks of therapeutic options for COPD-PH.

Ray tracing for thin lenses is very similar to the technique we used with spherical mirrors. As for mirrors, ray tracing can accurately describe the operation of a lens. The rules for ray tracing for thin lenses are similar to those of spherical mirrors:

COPD-PH is believed to be largely the result of hypoxaemia. As such, LTOT could be effective in the treatment of hypoxaemic COPD-PH. The data suggest mild improvements in severity of PH, some evidence for slowing progression of PH, and importantly, improved survival. However, oxygen did not normalise mPAP and there were no other symptomatic or functional clinical benefits reported. As for NOT, the limited available data shows no clear benefits in COPD-PH patients with either daytime or isolated nocturnal hypoxaemia. We did not find studies that assessed the long-term effect of supplemental oxygen in COPD-PH patients with exertional hypoxaemia.

Lenses are found in a huge array of optical instruments, ranging from a simple magnifying glass to a camera’s zoom lens to the eye itself. In this section, we use the Snell’s law to explore the properties of lenses and how they form images.

Interestingly, an objective “response” to PAH-targeted therapy (PDE-5i or ERA), as characterised by improved mNYHA FC or PVR (>20% fall), was predictive of better survival [39]. Furthermore, some COPD patients with more severe PH, generally defined as mPAP≥35 mmHg, may respond better to PAH-targeted therapy [37, 38, 41]. A subset of COPD patients with this severe precapillary PH and possibly RV failure, often in the setting of only mild to moderate COPD has been labelled, and may reflect a “vascular” phenotype [65] that may be at particularly high risk of long-term PH-related morbidity and mortality [5, 66]. This group of patients may have a genetic predisposition to PH, similar to heritable PAH, which may become manifest in the context of COPD, either driven by hypoxaemia, cigarette smoke, airway or systemic inflammation [60, 65], or simply due to concurrent COPD and unrelated PAH. This subset of COPD patients merits further study and may benefit clinically from referral to expert PH centres for further assessment and consideration of treatment [4, 13].

In summary, based on limited evidence, CCBs may mildly improve haemodynamics with no evidence to suggest any clinical or survival benefits, and they are generally poorly tolerated (table 3).

The effect of treatment with phosphodiesterase type 5 inhibitors (PDE-5i) on 6-min walk distance in patients with COPD-associated pulmonary hypertension (PH). Note: PH was diagnosed either by right heart catheterisation (Vitulo 2017) or by echocardiogram in the other studies. IV: inverse variance.

Step 1. Determine whether ray tracing, the thin-lens equation, or both would be useful. Even if ray tracing is not used, a careful sketch is always very useful. Write symbols and values on the sketch.

As noted in the initial discussion of Snell’s law, the paths of light rays are exactly reversible. This means that the direction of the arrows could be reversed for all of the rays in Figure 2.18. For example, if a point-light source is placed at the focal point of a convex lens, as shown in Figure 2.20, parallel light rays emerge from the other side.

A convex or converging lens is shaped so that all light rays that enter it parallel to its optical axis intersect (or focus) at a single point on the optical axis on the opposite side of the lens, as shown in part (a) of Figure 2.18. Likewise, a concave or diverging lens is shaped so that all rays that enter it parallel to its optical axis diverge, as shown in part (b). To understand more precisely how a lens manipulates light, look closely at the top ray that goes through the converging lens in part (a). Because the index of refraction of the lens is greater than that of air, Snell’s law tells us that the ray is bent toward the perpendicular to the interface as it enters the lens. Likewise, when the ray exits the lens, it is bent away from the perpendicular. The same reasoning applies to the diverging lenses, as shown in part (b). The overall effect is that light rays are bent toward the optical axis for a converging lens and away from the optical axis for diverging lenses. For a converging lens, the point at which the rays cross is the focal point F of the lens. For a diverging lens, the point from which the rays appear to originate is the (virtual) focal point. The distance from the center of the lens to its focal point is the focal length f of the lens.

Of six studies assessing functional capacity [28–33], sildenafil improved 6-min walk distance (6MWD) in two RCTs [28, 31] and one cohort study [32] but had no effect in two other RCTs [29, 30]. The one study of tadalafil showed a similar lack of benefit [33]. The pooled analysis of 6MWD showed no clear benefit with a trend towards improvement (figure 3). PDE-5i were generally well-tolerated with expected side-effects and did not worsen hypoxaemia.

Six studies (n=459) assessed effects of PDE-5i, including sildenafil (5 studies) [28–32] and tadalafil [33]. In five studies, PH was echo-defined using variable thresholds (sPAP >30–40 mmHg) [28, 29, 31, 33], whereas a single study variably defined PH by RHC (mPAP >30–35 mmHg), depending on FEV1% predicted [30]. Three studies had a low risk of bias, one RCT was unclear [28], and two had a high risk of bias [31, 32]. All five studies assessing haemodynamics reported benefits of PDE-5i. Sildenafil improved echo-sPAP [28, 31], echo-calculated mPAP [32], and RHC-mPAP [30], and tadalafil improved both echo-sPAP and calculated mPAP [33]. Pooled analyses showed favourable effects on both sPAP and mPAP (figure 2).

In our systematic review, PAH-targeted therapy in patients with COPD-PH had inconsistent effects, including limited clinical benefits (for example, symptoms, functional capacity, HRQoL) but no assessment of hospitalisation or survival. Overall, our findings are similar to other analyses [4, 62, 63]. Some PAH-targeted medications may offer benefits, as PDE-5i (sildenafil and tadalafil) significantly improved pulmonary haemodynamics, and sildenafil improved mMRC [30, 31], BODE index, and SF-36 [30]. In our pooled analysis, 6MWD increased slightly but not significantly with PDE-5i treatment (+16 m; figure 3), which was less than the significant pooled effect of sildenafil on 6MWD (+29 m) in another review of COPD-PH [64]. Differences include our inclusion of a negative trial on tadalafil, possibly due to an ineffective small dose [33], and exclusion of several positive studies from China. Comparatively, there are fewer studies of other PAH-targeted therapies such as ERAs, but similar overall limited clinical benefits despite some haemodynamic effects. Combination PAH-targeted therapy is now standard of care in PAH [13, 61], but there are limited data in COPD-PH to suggest any benefit.

The three rays cross at a single point on the opposite side of the lens. Thus, the image of the tip of the arrow is located at this point. All rays that come from the tip of the arrow and enter the lens are refracted and cross at the point shown.

Ray tracing allows us to get a qualitative picture of image formation. To obtain numeric information, we derive a pair of equations from a geometric analysis of ray tracing for thin lenses. These equations, called the thin-lens equation and the lens maker’s equation, allow us to quantitatively analyze thin lenses.

(where the three lines mean “is defined as”). This is exactly the same equation as we obtained for mirrors (see Equation 2.8). If m>0m>0, then the image has the same vertical orientation as the object (called an “upright” image). If m<0m<0, then the image has the opposite vertical orientation as the object (called an “inverted” image).

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This review supports guideline recommendations for LTOT in hypoxaemic COPD-PH patients as well as recommendations against treatment with PAH-targeted medications. Effective treatment of COPD-PH depends upon research into the pathobiology and future high-quality studies comprehensively assessing clinically relevant outcomes are needed.

Supplemental long-term oxygen therapy (LTOT) mildly reduced mean pulmonary artery pressure (PAP), slowed progression of PH, and reduced mortality, but other clinical or functional benefits were not assessed. Phosphodiesterase type 5 inhibitors significantly improved systolic PAP (pooled treatment effect −5.9 mmHg; 95% CI −10.3, −1.6), but had inconsistent clinical benefits. Calcium channel blockers and endothelin receptor antagonists had limited haemodynamic, clinical, or survival benefits. Statins had limited clinical benefits despite significantly lowering systolic PAP (pooled treatment effect −4.6 mmHg; 95% CI −6.3, −2.9).

An object much farther than the focal length f from the lens should produce an image near the focal plane, because the second term on the right-hand side of the equation above becomes negligible compared to the first term, so we have di≈f.di≈f. This can be seen in the plot of part (a) of the figure, which shows that the image distance approaches asymptotically the focal length of 1 cm for larger object distances. As the object approaches the focal plane, the image distance diverges to positive infinity. This is expected because an object at the focal plane produces parallel rays that form an image at infinity (i.e., very far from the lens). When the object is farther than the focal length from the lens, the image distance is positive, so the image is real, on the opposite side of the lens from the object, and inverted (because m=−di/dom=−di/do). When the object is closer than the focal length from the lens, the image distance becomes negative, which means that the image is virtual, on the same side of the lens as the object, and upright.

Specific medical treatment of COPD-PH may also offer clinical benefits, including improved dyspnoea, functional capacity, and long-term outcomes. Thus, we conducted a systematic review and meta-analysis for benefits and risks of treatment options for COPD-PH.

In conclusion, this systematic review identifies the large number of studies assessing multiple treatments for patients with COPD-PH and highlights the limited evidence base. This review supports recent guidelines which recommend LTOT in hypoxaemic COPD-PH patients but do not recommend other treatments for COPD-PH, including PAH-targeted medications. Development of future therapies depends upon new ideas on the pathobiology of COPD-PH, as well as higher-quality studies on more homogeneous populations, including patients with more severe PH or a “vascular” phenotype, using a standardised RHC diagnosis of PH and comprehensive assessment of outcomes.

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We searched Medline and Embase for relevant publications until September 2020. Articles were screened for studies on treatment of COPD-PH for at least 4 weeks in 10 or more patients. Screening, data extraction, and risk of bias assessment were performed independently in duplicate. When possible, relevant results were pooled using the random effects model.

where f is the focal length of the thin lens (this derivation is left as an exercise). This is the thin-lens equation. The focal length of a thin lens is the same to the left and to the right of the lens. Combining Equation 2.18 and Equation 2.19 gives

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We use ray tracing to investigate different types of images that can be created by a lens. In some circumstances, a lens forms a real image, such as when a movie projector casts an image onto a screen. In other cases, the image is a virtual image, which cannot be projected onto a screen. Where, for example, is the image formed by eyeglasses? We use ray tracing for thin lenses to illustrate how they form images, and then we develop equations to analyze quantitatively the properties of thin lenses.

Estimates of the prevalence of PH in COPD (COPD-PH) vary widely (20–91%) [5, 10, 11], with increasing prevalence with greater severity of COPD [4]. For example, the most severe Global Initiative for Chronic Obstructive Lung Disease (GOLD) stage IV COPD is associated with mild-moderate PH in up to 90% of patients [5]. PH in a patient with COPD could be due to a broad range of underlying conditions, such as left-heart disease [12], concomitant interstitial lung diseases or sleep disordered-breathing, or chronic thromboembolic PH. Management of associated cardiac and respiratory conditions can improve the clinical status and outcomes in COPD-PH patients [4, 13].

The image is real and on the opposite side from the object, so di>0di>0 and do′>0do′>0. The second surface is convex away from the object, so R2<0R2<0. Equation 2.15 can be simplified by noting that do′=|di′|+tdo′=|di′|+t, where we have taken the absolute value because di′di′ is a negative number, whereas both do′do′ and t are positive. We can dispense with the absolute value if we negate di′di′, which gives do′=−di′+tdo′=−di′+t. Inserting this into Equation 2.15 gives

Data are mean±sem, unless otherwise specified. AHI: apnoea-hypopnoea index; CO: cardiac output; FEV1: forced expiratory volume in 1 s; mPAP: mean pulmonary artery pressure; OSA: obstructive sleep apnoea; PaO2: partial pressure of oxygen in arterial blood; PVR: pulmonary vascular resistance; RCT: randomised controlled trial; REM: rapid eye movement; RHC: right heart catheterisation; RVH: right ventricular hypertrophy; SaO2: arterial oxygen saturation (%); SpO2: transcutaneous pulse oximetry oxygen saturation (%); SVI: stroke volume index; TPR: total pulmonary resistance; WU: Wood unit (mmHg·L−1·min−1).

The thin-lens equation and the lens maker’s equation are broadly applicable to situations involving thin lenses. We explore many features of image formation in the following examples.

RV: right ventricular; HRQoL: health-related quality of life; LTOT: long-term oxygen therapy; NOT: nocturnal oxygen therapy; CCB: calcium channel blocker; PDE: phosphodiesterase; ERA: endothelin receptor antagonist. Clinically relevant effects: +: significant; +/−: uncertain; 0: none; NA: not assessed.

Concerns over potential risks of PAH-targeted therapies worsening ventilation/perfusion matching and hypoxaemia because of non-selective widespread pulmonary vasodilation are not supported by any evidence for any adverse effect on oxygenation [29–31, 33, 34]. Expected side-effects of PAH-targeted therapy were observed, for examplec flushing, headache, diarrhoea, but did not lead to high rates of medication discontinuation.

To derive the thin-lens equation, we consider the image formed by the first refracting surface (i.e., left surface) and then use this image as the object for the second refracting surface. In the figure, the image from the first refracting surface is Q′Q′, which is formed by extending backwards the rays from inside the lens (these rays result from refraction at the first surface). This is shown by the dashed lines in the figure. Notice that this image is virtual because no rays actually pass through the point Q′Q′. To find the image distance di′di′ corresponding to the image Q′Q′, we use Equation 2.11. In this case, the object distance is dodo, the image distance is di′di′, and the radius of curvature is R1R1. Inserting these into Equation 2.3 gives

No studies assessed clinical or functional patient outcomes other than mortality benefits of LTOT. Survival was assessed in four studies (n=480), of which three (n=408) reported improved survival [14, 20, 21], but one study found no effect [17]. Pulmonary haemodynamic improvement may be associated with greater survival [20, 21], but this was not consistently observed [22].

Conflict of interest: S. Mehta reports grants or contracts from Altavant Pharmaceuticals, Eiger Pharmaceuticals, Ikaria Pharmaceuticals, Janssen Pharmaceuticals, Reata Pharmaceuticals, and United Therapeutics; consulting fees from Acceleron Pharmaceuticals, Janssen Pharmaceuticals and Natco Pharmaceuticals; payment or honoraria for lectures, presentations, speakers bureaus, manuscript writing or educational events from Bayer Pharmaceuticals, Janssen Pharmaceuticals, Natco Pharmaceuticals and SpecialtyRx Pharmacy; payment for expert testimony from Bergeron Clifford LLP, Lerner Law and St. Lawrence Barristers LLP; support for attending meetings and/or travel from Janssen Pharmaceuticals; participation on a data safety monitoring or advisory board for Ozmosis Research; board directorship for the Pulmonary Hypertension Association of Canada (unpaid position); and receipt of equipment, materials, drugs, medical writing, gifts or other services from Janssen Pharmaceuticals, all outside the submitted work.

Effects of pulmonary arterial hypertension-targeted therapies in patients with COPD-associated pulmonary hypertension (COPD-PH)

To find the object distance for the object Q formed by refraction from the second interface, note that the role of the indices of refraction n1n1 and n2n2 are interchanged in Equation 2.11. In Figure 2.24, the rays originate in the medium with index n2n2, whereas in Figure 2.15, the rays originate in the medium with index n1n1. Thus, we must interchange n1n1 and n2n2 in Equation 2.11. In addition, by consulting again Figure 2.24, we see that the object distance is do′do′ and the image distance is didi. The radius of curvature is R2R2 Inserting these quantities into Equation 2.11 gives

In COPD-PH patients, long-term oxygen therapy (LTOT) may have haemodynamic and clinical benefits. The evidence base consists of eight reports (n=596; 72–100% men), including one RCT [14], two randomised parallel group studies comparing LTOT versus nocturnal oxygen therapy (NOT), and four case series [15–18] (table 1). All patients underwent RHC which documented the presence and severity of baseline PH. Most studies report outcome data over longer than 1 year (range 2–6 years), but two studies were <8 weeks in duration [15, 19]. Most LTOT studies had an unclear or high risk of bias in at least one domain; only one study had a low risk of bias (supplementary tables S5 and S6) [20], which limits our confidence in the effects of LTOT in COPD-PH.

The effect of treatment with phosphodiesterase type 5 inhibitors (PDE-5i) on mean pulmonary artery pressure (mPAP; upper panel) and systolic pulmonary artery pressure (sPAP; lower panel) in COPD-associated pulmonary hypertension. Note: mPAP was measured by right heart catheterisation (Vitulo 2017) or estimated from echo measurement of sPAP (Goudie 2014). IV: inverse variance.

Our systematic review focuses on the effect of various therapeutic options in COPD-PH. We identified studies that focused on treatment of COPD-PH for at least 4 weeks and captured haemodynamics and clinical outcomes including survival. Overall, many treatments improve PH haemodynamics and some may improve survival, but few are associated with improved symptoms, functional capacity, or HRQoL. For example, supplemental LTOT mildly reduces PH haemodynamic severity, may slow PH progression over time, and reduces mortality. However, other clinical and functional benefits of LTOT were not assessed. Similarly, PAH-targeted therapy using sildenafil improved PH haemodynamics, but had uncertain clinical and functional benefits. In contrast, other PAH-targeted medications, such as ERAs, had inconsistent effects, as did other therapies including CCBs and statins.

In the thin-lens approximation, we assume that the lens is very thin compared to the first image distance, or t≪di′t≪di′ (or, equivalently, t≪R1andR2t≪R1andR2). In this case, the third and fourth terms on the left-hand side of Equation 2.17 cancel, leaving us with

Free-electron laser ... A free-electron laser (FEL) is a fourth generation light source producing extremely brilliant and short pulses of radiation. An FEL ...

After locating the image of the tip of the arrow, we need another point of the image to orient the entire image of the arrow. We chose to locate the image base of the arrow, which is on the optical axis. As explained in the section on spherical mirrors, the base will be on the optical axis just above the image of the tip of the arrow (due to the top-bottom symmetry of the lens). Thus, the image spans the optical axis to the (negative) height shown. Rays from another point on the arrow, such as the middle of the arrow, cross at another common point, thus filling in the rest of the image.

which is called the lens maker’s equation. It shows that the focal length of a thin lens depends only of the radii of curvature and the index of refraction of the lens and that of the surrounding medium. For a lens in air, n1=1.0n1=1.0 and n2≡nn2≡n, so the lens maker’s equation reduces to

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The presence of PH in COPD patients is associated with worsening morbidity and mortality. These findings support guideline recommendations for LTOT in hypoxaemic COPD-PH patients as well as recommendations against treatment using PAH-targeted medications. https://bit.ly/3Al4rLb

Consider a thin converging lens. Where does the image form and what type of image is formed as the object approaches the lens from infinity? This may be seen by using the thin-lens equation for a given focal length to plot the image distance as a function of object distance. In other words, we plot

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When solving problems in geometric optics, we often need to combine ray tracing and the lens equations. The following example demonstrates this approach.

To see a concrete example of upright and inverted images, look at Figure 2.27, which shows images formed by converging lenses when the object (the person’s face in this case) is place at different distances from the lens. In part (a) of the figure, the person’s face is farther than one focal length from the lens, so the image is inverted. In part (b), the person’s face is closer than one focal length from the lens, so the image is upright.

2022519 — Apertur is a light object designed to communicate a sensation of unlimited space to the viewer. Dimensions: 52 x 52 x 11.5 cm

Two placebo-controlled RCTs assessed the effects of bosentan in severe COPD. In a non-blinded study in RHC-diagnosed moderate to severe PH, bosentan had mild haemodynamic benefit associated with improved exercise capacity and limited symptomatic benefit [34]. In contrast, bosentan had inconsistent haemodynamic effects, uncertain clinical benefits (6MWD fell slightly, HRQoL improved), and reduced PaO2 in mild echo-defined PH [35]. Ambrisentan treatment in a case series (n=24) of RHC-diagnosed severe PH decreased brain natriuretic peptide (BNP) with no change in 6MWD [36]. Two studies had a high risk of bias and one RCT had a low risk of bias [35].

The presence and severity of PH in COPD patients is a significant contributor to clinical morbidity, including worse dyspnoea, functional capacity, and HRQoL [5, 6, 30], as well as being a prognostic marker for more frequent exacerbations and worse survival. However, there are no specific treatments for COPD-PH, and current guidelines for management of WHO group 3 PH, including COPD-PH, simply suggest LTOT for resting hypoxaemia and optimisation of underlying chronic cardiopulmonary conditions [4, 13].

In summary, statins are well-tolerated, significantly reduced sPAP (figure 4) but had no clinical or functional benefits.

We have seen that rays parallel to the optical axis are directed to the focal point of a converging lens. In the case of a diverging lens, they come out in a direction such that they appear to be coming from the focal point on the opposite side of the lens (i.e., the side from which parallel rays enter the lens). What happens to parallel rays that are not parallel to the optical axis (Figure 2.23)? In the case of a converging lens, these rays do not converge at the focal point. Instead, they come together on another point in the plane called the focal plane. The focal plane contains the focal point and is perpendicular to the optical axis. As shown in the figure, parallel rays focus where the ray through the center of the lens crosses the focal plane.

Among other treatment options, CCBs may mildly improve haemodynamics, but there is no evidence to suggest any clinical or survival benefits, and they are generally poorly tolerated. Statins reduced sPAP (mPAP in one study) but had limited clinical benefits. Although the statin effect in PH could be mediated through systemic vascular and/or left-ventricular effects rather than direct pulmonary vascular action, a multiple regression analysis suggested statins reduce mPAP independent of pulmonary artery wedge pressure [49]. Statins may also prevent COPD progression and improve PH by reducing C-reactive protein and other inflammatory factors [67]. Several other therapies (e.g. iNO, Waon, cicletanine) improved pulmonary haemodynamics with minimal clinical benefits.

Statins are widely used in COPD due to the prevalence of cardiovascular diseases and were used for treatment of COPD-PH in six studies (n=394; supplementary table S3), including five RCTs using echo-defined PH [44–48] and one RHC-defined PH cohort study [49]. Only one study had low risk of bias [44], but the other five studies had an unclear risk of bias.

Limitations of this review include paucity of RHC diagnosed PH, as only some studies reported RHC-mPAP, whereas most studies only reported echo-estimated sPAP ± calculated mPAP. A systemic vascular effect of a putative treatment could result in apparent pulmonary haemodynamic benefit as assessed simply by echocardiogram, for example, a decrease in sPAP with statins. Moreover, studies used various thresholds for both RHC and echo measurements to define presence of PH. In addition, study populations exhibited marked heterogeneity, including severity of COPD and presence of hypoxaemia. There was also treatment heterogeneity, as studies used various doses and duration of therapy, and in some studies of combination PAH-targeted therapies, specific combinations were not clearly defined. Most importantly, very few studies provided a comprehensive assessment of the potential benefits of PAH-targeted therapies, including multi-parameter characterisation of haemodynamic, clinical, and functional benefits.

The word “lens” derives from the Latin word for a lentil bean, the shape of which is similar to a convex lens. However, not all lenses have the same shape. Figure 2.17 shows a variety of different lens shapes. The vocabulary used to describe lenses is the same as that used for spherical mirrors: The axis of symmetry of a lens is called the optical axis, where this axis intersects the lens surface is called the vertex of the lens, and so forth.

The image is virtual and on the same side as the object, so di′<0di′<0 and do>0do>0. The first surface is convex toward the object, so R1>0R1>0.

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Consider an object some distance away from a converging lens, as shown in Figure 2.22. To find the location and size of the image, we trace the paths of selected light rays originating from one point on the object, in this case, the tip of the arrow. The figure shows three rays from many rays that emanate from the tip of the arrow. These three rays can be traced by using the ray-tracing rules given above.

Four studies defining PH using mPAP threshold of 20 mmHg, including two RCTs (n=80) [24, 25] and two case series [26, 27], evaluated effects of calcium channel blockers (CCBs) over at least 8 weeks (supplementary table S2). All studies had an unclear or high risk of bias in at least one domain. Two small studies found no RHC-assessed haemodynamic benefit of nifedipine [25, 26], but felodipine decreased echo-calculated mPAP and total pulmonary resistance (TPR) as well as increased CO in a case-series [27]. Only one study assessed symptoms, reporting decreased dyspnoea scores, but found no difference in survival [24]. Another study reported no change in exercise capacity [27]. Side-effects of CCBs were common and many patients required dose reduction (50%) and/or withdrawal of therapy (7–27%).

For a thin diverging lens of focal length f=−1.0cmf=−1.0cm, a similar plot of image distance vs. object distance is shown in part (b). In this case, the image distance is negative for all positive object distances, which means that the image is virtual, on the same side of the lens as the object, and upright. These characteristics may also be seen by ray-tracing diagrams (see Figure 2.26).

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