General <i>q</i>-series transformations based on Abel's lemma on summation by parts and their applications

In this paper, we establish three new and general transformations with sixteen parameters and bases via Abel's lemma on summation by parts. As applications, we set up a lot of new transformations of basic hypergeometric series. Among include some new quadratic, cubic, and quartic transformations. Furthermore, we put forward the so-called (R,S)-type transformation with arbitrary degree to unify such multibasic transformations. A special (3,3)-type transformation and its example are presented.</p

Dynamic changes of anterior segment in patients with different stages of primary angle-closure in both eyes and normal subjects

<div><p>Purpose</p><p>To compare changes in anterior segment parameters under light and dark (light-to-dark) conditions among eyes with chronic primary angle-closure glaucoma (CPACG), fellow eyes with confirmed or suspect primary angle-closure (PAC or PACS), and age-matched healthy eyes.</p><p>Methods</p><p>Consecutive patients with CPACG in one eye and PAC/PACS in the fellow eye, as well as age-matched healthy subjects were recruited. Anterior segment optical coherence tomography measurements were conducted under light and dark conditions, and anterior chamber, lens, and iris parameters compared. Demographic and biometric factors associated with light-to-dark change in iris area were analyzed by linear regression.</p><p>Results</p><p>Fifty-seven patients (mean age 59.6±8.9 years) and 30 normal subjects matched for age (60.6±9.3 years) and sex ratio were recruited. In regards to differences under light–to-dark conditions, angle opening distance at 500 μm (AOD500μm) and iris area during light-to-dark transition were smaller in CPACG eyes than fellow PACS/PAC eyes and normal eyes (<i>P</i><0.017). Pupil diameter change was largest in normal eyes, and larger in PACS/PAC eyes than CPACG eyes (<i>P</i><0.017). There was an average reduction of 0.145 mm² in iris area for each millimeter of pupil diameter increase in CPACG eyes, 0.161 mm² in fellow PAC/PACS eyes, and 0.165 mm² in normal eyes. Larger iris curvature in the dark and diagnosis of PACG were significantly associated with less light-to-dark iris area changes.</p><p>Conclusions</p><p>Dynamic changes in iris parameters with light-to-dark transition differed significantly among CPACG eyes, fellow PAC/PACS eyes, and normal eyes. Greater iris curvature under dark conditions was correlated with reduced light-to-dark change in iris area and pupil diameter, which may contribute to disease progression.</p></div

Light-to-dark changes of anterior chamber parameters in CPACG eyes, fellow PAC/PACS eyes, and normal eyes.

<p>A: There was no difference in light-to-dark changes of ACDs among the three groups. B: There was no difference in light-to-dark changes of ACWs among the three groups. C: There was no difference in light-to-dark changes of ACAs among the three groups. D: The light-to-dark changes of AOD500μm in CPACG eyes were smaller than those in their fellow PACS/PAC eyes and normal eyes. There was no difference in the light-to-dark changes of AOD500μm between PACS/PAC eyes and normal eyes. E: The light-to-dark changes of ARA750μm in CPACG eyes were smaller than those in their fellow PACS/PAC eyes. There was no difference in the light-to-dark changes of ARA750μm between PACS/PAC eyes and normal eyes. CPACG: chronic primary angle closure glaucoma; PAC: primary angle closure; PACS: primary angle closure suspect; ACA: anterior chamber area; AOD500μm: angle opening distance 500 μm from the scleral spur; ARA750μm: angle recess area 750 μm from the scleral spur; ACD: anterior chamber depth; ACW: anterior chamber width; *: significant difference between PACG eyes and fellow eyes (<i>P</i><0.017); ‡: significant difference between PACG eyes and normal eyes (<i>P</i><0.017); Error bars: 95% confidence interval (95% CI).</p

Iris parameters under light/dark conditions and changes (Δ) in CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.

<p>Iris parameters under light/dark conditions and changes (Δ) in CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.</p

Anterior segment parameters under light and dark conditions and light-dark changes (Δ) in CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.

<p>Anterior segment parameters under light and dark conditions and light-dark changes (Δ) in CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.</p

Relationship between mean PD change and I-area change after physiological mydriasis in CPACG eyes, fellow PAC/PACS eyes, and normal eyes.

<p>The I-area decreased with increasing pupil size in all three groups. A: For CPACG eyes, the linear regression equation of the scatter plot was y = 0.015–0.127x. B: For fellow PAC/PACS eyes, the linear regression equation of the scatter plot was y = 0.101–0.094x. C: For normal eyes, the linear regression equation of the scatter plot was y = 0.037–0.144x. CPACG: chronic primary angle closure glaucoma; PAC: primary angle closure; PACS: primary angle closure suspect; PD: pupil diameter; I-area: iris area.</p

Light-to-dark changes of iris parameters in CPACG eyes, fellow PAC/PACS eyes, and normal eyes.

<p>A: The light-to-dark changes of PDs were largest in normal eyes and least in CPACG eyes. B: The light-to-dark changes of I-areas were largest in normal eyes and least in CPACG eyes. C: There was no significant difference in iris curvature changes in response to light among normal eyes, PACS/PAC eyes, and CPACG eyes. D: There was no significant difference in the light-to-dark changes of IT500μm among normal eyes, PACS/PAC eyes, and CPACG eyes. E: The light-to-dark changes of IT750μm were smaller in CPACG eyes than in normal eyes. There was no significant difference between PACS/PAC eyes and CPACG eyes in the iris thickness. F: The light-to-dark changes of IT1000μm were smaller in CPACG eyes than in normal eyes. There was no significant difference between PACS/PAC eyes and CPACG eyes in the iris thickness. CPACG: chronic primary angle closure glaucoma; PAC: primary angle closure; PACS: primary angle closure suspect; PD: pupil diameter; I-area: iris area; IC: iris curvature; IT500μm/IT750μm/IT1000μm: iris thicknesses 500 μm/750 μm/1000 μm from the iris root. *: significant difference between PACG eyes and fellow eyes (<i>P</i><0.017); †: significant difference between fellow PAC/PACS eyes and normal eyes (<i>P</i><0.017); ‡: significant difference between PACG eyes and normal eyes (<i>P</i><0.017); Error bars: 95% confidence interval (95% CI).</p

Demographic and biometric characteristics of CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.

<p>Demographic and biometric characteristics of CPACG patients (CPACG eyes <i>vs</i> fellow PAC/PACS eyes) and normal subjects.</p

Light-to-dark changes of lens parameters in CPACG eyes, fellow PAC/PACS eyes, and normal eyes.

<p>A: There was no difference in light-to-dark change of LVs among the three groups. B: There was no difference in light-to-dark change of LTs among the three groups. CPACG: chronic primary angle closure glaucoma; PAC: primary angle closure; PACS: primary angle closure suspect; LV: lens vault; LT: lens thickness; Error bars: 95% confidence interval (95% CI).</p

Determinations of AOD500μm, IT500μm/750μm/1000μm, IC, LT, ARA750μm, and I-area by AS-OCT.

<p>A: Iris thickness at 500, 750, and 1000 μm (IT500μm, IT750μm, and IT1000μm, respectively) were defined as the perpendicular distance from the point at iris pigment epithelium anterior to the iris surface at 500, 750, and 1000 μm from the iris root, respectively. B: Iris area (I-area) was defined as the cross-sectional area of the iris. C: Iris curvature (IC) was defined as the maximum perpendicular distance between the iris pigment epithelium and the line connecting the most peripheral to the most central point of the epithelium. D: Lens thickness (LT) was defined as the maximum perpendicular distance between the anterior and posterior poles of the lens. E: Angle opening distance at 500 μm (AOD500μm) was defined as the perpendicular distance from the point anterior to the scleral spur to the anterior iris surface at 500 μm from the scleral spur. F: Angle recess area at 750 μm (ARA750μm) was defined as the enclosed triangular area demarcated by the anterior iris surface, trabecular meshwork, and corneal endothelium to a distance of 750 μm from the scleral spur.</p