Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Diagram of the experimental procedure. Porcine eyes were treated either topically or via intravitreal injection. The aqueous humor was collected using a syringe, while the vitreous humor was harvested after removal of the anterior segment. Ranibizumab and VEGF levels were detected using ELISA, and the optical density of the fluids was measured using a plate reader and then converted into a concentration using the respective standard curves. Figure created in https://BioRender.com/g17g888 .

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: Injection, Enzyme-linked Immunosorbent Assay, Concentration Assay

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Experimental results for treatment of ex vivo porcine eyes. Panels show ranibizumab (RBZ, first two columns ) and VEGF ( last two columns ) concentrations in the aqueous (Aq, columns 1 and 3 ) and vitreous (Vit, columns 2 and 4 ), at t = 20 min, 40 min, 1 h and 3.5 h. Top row : topical treatment (45 µL) with ranibizumab (1 mg mL −1 ) and CPP (100 mg mL −1 ). Ranibizumab is detected in significant quantities in the aqueous and appears to enter the vitreous, though it only has a significant effect in reducing aqueous VEGF levels, leaving vitreal VEGF levels unaffected. Middle row : intravitreal (invit.) treatment (45 µL) with ranibizumab (1 mg mL −1 ) and CPP (100 mg mL −1 ). As expected, vitreal ranibizumab levels are high, resulting in a significant reduction in vitreal VEGF levels. Bottom row : intravitreal treatment (45 µL) with ranibizumab only (1 mg mL −1 ). Interestingly, intravitreal treatment is more effective in reducing vitreal VEGF in the absence of CPPs. See Table 5 for numerical values of data points.

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: Ex Vivo

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Mathematical model fits to ex vivo porcine data. Panels show ranibizumab (R) concentrations in the aqueous (Aq, left column ) and vitreous (Vit, right column ), for topical drop administration with CPPs ( top row ) and for intravitreal injection without CPPs ( bottom row ). Top row : a single drop is applied at t = 0 h; simulations start at t = 0 h with r Tear (0) = r Dose = 2.07 × 10 4 pmol mL −1 , r Aq (0) = 0 pmol mL −1 and r Vit (0) = 0 pmol mL −1 ; fitting was performed for r Aq at t = 20 min, 40 min, and 3.5 h to the mean data points; Equations 3 – were solved with depleting tear ranibizumab concentration, constant tear volume, and in the absence of VEGF. Bottom row : a single injection is administered at t = 0 h; simulations start at t = 20 min (=1/3 h) with r Aq (1/3) = 4.73 × 10 −2 pmol mL −1 and r Vit (1/3) = 4.29 pmol mL −1 , equal to the mean data points at those times; fitting was performed for r Aq at t = 40 min, 1 h and 3.5 h to the mean data points; Equations 4 – were solved in the absence of VEGF. Reasonable fits are achieved in all cases except for vitreal ranibizumab with topical treatment. Model fit 1: β Tear-Aq, r = 5.93 × 10 −7 cm h −1 (this value is also used for model fit 2 in the topical case) and β Aq-Vit, r = 0.929 cm h −1 ; model fit 2: β Aq-Vit, r = 0.577 cm h −1 . All remaining parameters chosen as the default porcine values in Table 3 .

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: Ex Vivo, Injection, Concentration Assay

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Simulation results for treatment of an in vivo human eye, using a single mode of administration. Panels show VEGF (V) concentrations ( left column ) and ranibizumab (R) concentrations ( right column ) in the tear film (Tear), aqueous (Aq), and vitreous (Vit), as appropriate (insets show results over the full range of concentrations [ top right ], or with a logarithmic scale on the ordinate [ bottom row ]). Horizontal blue lines in the left column show untreated VEGF levels in the aqueous ( dotted ) and vitreous ( dash-dot ). Top row (topical drops): a single drop is applied at the start of hours 1 to 16 every day for the first 2 weeks; week 3 untreated. Middle row (drug-eluting contact lens): a series of four lenses are worn for 30 days at a time, starting on day 1, with a 1-day break between lenses; final 4 weeks untreated. Bottom row (intravitreal injections): administered at the start of weeks 1, 5, 9, and 13; simulation runs to 16 weeks. Drops suppress aqueous and vitreal VEGF levels to a fairly constant value during the period of administration; contact lenses suppress VEGF levels more strongly, with small transient increases in VEGF levels between lenses; injections reduce VEGF to by far the lowest levels, though VEGF returns to untreated values between injections. Equations 2 – were solved using the default human parameters in Table 3 .

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: In Vivo

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Simulation results for treatment of an in vivo human eye, using multiple modes of administration. Panels show VEGF (V) concentrations ( left column ) and ranibizumab (R) concentrations ( right column ) in the tear film (Tear), aqueous (Aq), and vitreous (Vit), as appropriate (insets show results over the full range of concentrations [ top right ], or with a logarithmic scale on the ordinate [ top left and bottom row ]). Horizontal blue lines in the left column show untreated VEGF levels in the aqueous ( dotted ) and vitreous ( dash-dot ). Top row (topical drops and intravitreal injections): a single drop is applied at the start of hours 1 to 16 every day for the first 16 weeks, while injections are administered at the start of weeks 1, 5, 9, and 13; simulation runs to 20 weeks, the final 4 untreated. Bottom row (drug-eluting contact lens and intravitreal injections): a series of four lenses are worn for 27 days at a time, starting on day 2, with a 1-day break between lenses, while injections are administered at the start of weeks 1, 5, 9, and 13 (on the days without contact lenses); simulation runs to 20 weeks, the final 4 untreated. Both drops and drug-eluting lenses suppress aqueous and vitreal VEGF levels between injections, preventing them from returning to untreated levels as in Figure 5 ( bottom row ). Equations 2 – were solved using the default human parameters in Table 3 .

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: In Vivo

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Effect of dosing regimen on vitreal VEGF and ranibizumab levels. Panels show variation in the maximum/mean/minimum vitreal VEGF concentration, v Vit ( top row ), and maximum/mean/minimum total ranibizumab concentration, r Tot, Vit = r Vit + u Vit + 2 w Vit ( bottom row ), in response to variation in dosing frequency or duration ( first–third columns : circles show the corresponding values for the dosing regimens plotted in Fig. 5 ). Top row : horizontal green dash-dot lines show the untreated vitreal VEGF level. First column (topical drops only): the number of drops per day, n drop , is varied across all integer values between 1 and 16 inclusive, where the first drop of each day is administered at 0 h, with subsequent drops being administered in time increments of 16/ n drop h. Simulated for t ∈ [0, 12] weeks, with plotted values calculated over model outputs from the interval t ∈ [9, 12] weeks. Second column (drug-eluting contact lenses only): lenses are worn for n day days at a time, starting on day 1, with a 1-day break between lenses, where n day is varied across all integer values between 1 and 30 inclusive. Simulated for t ∈ [0, 124] days (enough for four full treatment cycles of 31 days: 30 days on and 1 day off), with plotted values calculated over the final treatment cycle (of n day days on and 1 day off). Third column (intravitreal injections only): the time between injections is varied across all integer values between 1 and 8 weeks inclusive, with the first injection being administered at the start of week 1. Fourth column (topical drops and intravitreal injections): injections are administered as in the third column, with the addition of four topical drops per day (the realistic maximum frequency ) at 4, 8, 12, and 16 h. Fifth column (drug-eluting contact lenses and intravitreal injections): injections are administered as in the third column, with the addition of drug-eluting contact lenses worn for 6 days a week (the longest duration that can be used across all interinjection intervals while allowing for a 1-day break between lenses) between days 2 and 7 of each week. Third to fifth columns : simulated for t ∈ [0, 32] weeks (enough for four full treatment cycles lasting the maximum interval of 8 weeks), with plotted values calculated over model outputs from the final treatment cycle (with duration equal to the time between injections). Increasing drop or injection frequency, or increasing the time interval for which drug-eluting contact lenses are worn, increases the maximum, mean, and minimum vitreal total ranibizumab concentrations and decreases the maximum, mean, and minimum vitreal VEGF concentrations. Combining injections with drops or contact lenses visibly reduces the maximum and mean vitreal VEGF concentrations compared to injections alone, while the effect on the minimum vitreal VEGF concentration and the maximum, mean, and minimum vitreal total ranibizumab concentrations is more subtle. Equations 2 – were solved using the default human parameters in Table 3 .

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: Concentration Assay, Injection

Journal: Investigative Ophthalmology & Visual Science

Article Title: Mathematical Models of Topically and Intravitreally Applied Ranibizumab

doi: 10.1167/iovs.66.11.45

Figure Lengend Snippet: Local sensitivity analysis. Panels show sensitivity of the maximum/mean/minimum vitreal VEGF (V) concentration ( left column ) and total vitreal ranibizumab (R Tot = R + VR + 2RVR) concentration ( right column ) to variation in model parameters over biologically realistic ranges (insets show full range of sensitivity values). Equations 2 – were solved for t ∈ [0, 12] weeks. Top row : topical drops, applied on the hour, every hour. Middle row : drug-eluting contact lens, worn continuously. Bottom row : intravitreal injections, administered at the start of weeks 1, 5, and 9. Parameters were varied individually, across 101 values uniformly distributed over the ranges given in Table 4 , with the remaining parameters being held at their default values given in Table 4 . For each parameter set, the maximum/mean/minimum vitreal values of V and R Tot were calculated over model outputs from the interval t ∈ [9, 12] weeks (see Supplementary Figs. S2 – ). Each sensitivity factor was then calculated as the maximum value obtained by the maximum/mean/minimum value of V or R Tot over the 101 values across which the parameter was varied, divided by the corresponding minimum value over that range. The dashed red horizontal line demarcates the sensitivity threshold (=1.5), above which sensitivity is considered significant. The model demonstrates sensitivity to the following parameters—drops: ( V Tear Norm , A Aq - Vit , k + , δ Aq , r , δ Vit , v , δ Vit , r , ϕ Vit , v , ψ Tear , ψ Aq ) ; contact lens: ( A Tear-Aq , k + , δ Aq, r , δ Vit, v , δ Vit, r , ϕ Vit, v , ψ Aq ), injections: ( V Vit , A Aq-Vit , k + , δ Aq, r , δ Vit, v , δ Vit, r , δ Vit, u , β Aq-Vit, r , ϕ Vit, v , ψ Aq ).

Article Snippet: A total of 1 mg of humanized anti-VEGF monoclonal antibody fragments (ranibizumab) was purchased already constituted in PBS from MedChem Express (CAT: HY-P9951A-1mg; Princeton, NJ, USA) and stored at −80°C.

Techniques: Concentration Assay