an assessment of the combined variable approach: 2...combined variable (cv) approach for any general...
TRANSCRIPT
An Assessment of the Combined Variable Approach: 2.0
Yuri Lawryshyn
IUVA Americas Conference, February, 2018
Objective• Main objective: to test the validity of the combined variable (CV) approach for any general case– Specifically: with all of the checks and balances of the proposed approach, can we find a case where a UV reactor passes all QA/QC criteria yet fails in a some potential real world application?
Approach of the Presentation• Theory
– Does the CV have any theoretical basis?• Numerical experiments to see if we can “break” the proposed validation methodology utilizing all proposed QA/QC– Theoretical “good” and “bad” reactors– CFD based “good” and “bad” reactors– Theoretical reactor where particle trajectories change with flow rate
– Bioassay uncertainty
Agenda• Summary of the proposed validation methodology
• Theory of the CV• Methodology• Results• Conclusions
– Proposed methodology (likely) has all of the required checks and balances to ensure appropriate application of the CV approach
Combined Variable Equation
Summary of Validation Methodology
• Bioassay test– Two different microorganisms
• E.g. T1 ( ~5mJ/cm ) and MS2 ( ~20mJ/cm )
– UVT range– Flow range– UVC power range (measure )
Summary of Validation Methodology• Analysis
– Use T1 data to fit parameters in the CV equation to predict MS2 within appropriate range (CV and
)– Use MS2 data to fit parameters in the CV equation to predict T1 within appropriate range (CV and
)– Use all data to fit parameters in the CV equation
• QA/QC for each of the above check plots for fit / issues:– as a function of CV for different UVTs– Actual as a function of Predicted
Summary of Validation Methodology
• Validated range based on bioassay test range of:– Flow rate– UVT– Combined variable–
Theory: Reactor Performance• Inactivation of the i‐th path:
• UV reactor performance:1
• UV system log inactivation
1
Theory: Reactor Performance• Note that
, ,
• If particle trajectories do not change with flow rate then
• where
• and the average normalized intensity per path is
1, ,
Theory: Combined Variable• Combined variable relationship
/
Theory: Combined Variable• Reactor performance
/
= · ·
• Combined variable equation
Methodology• Numerical experiments
– Good and bad theoretical reactors– Good and bad CFD modeled UV reactors– Good and bad theoretical reactors where variance of particle trajectories varies with flow rate
• utilize geometric Brownian motion (GBM) from stock modeling theory
– Bioassay uncertainty
Methodology• 3 flow rates: 0.25, 0.5, 1.0• 4 UVTs: 80%, 85%, 90%, 95%• 3 power levels: 40%, 70%, 100%• Leads to 36 bioassay tests
– Remove any points where:• 0.25• 6
• Test (all errors reported on absolute LogI):– CV vs LogI: T1 and MS2– T1 to predict MS2 and MS2 to predict T1– CV vs LogI: Combined (T1 and MS2)– Combined CV to predict Adenovirus
Methodology – Theoretical ReactorsReactor R1 Reactor R2
Dose path 1 radius 6.6 cm 7.5 cmDose path 1 weight 0.6 0.99Dose path 2 radius 10 cm 15 cmDose path 2 weight 0.4 0.01
Methodology – Theoretical Reactors
Methodology – CFD Reactors
Methodology – Variance ~ Flow
Methodology – Variance ~ Flow
Results• Good theoretical reactor• Bad theoretical reactor• Variance ~ Flow• Good / bad CFD reactor (summarized in table)
Results: Good Theoretical Reactor
Results: Good Theoretical Reactor
Results: Good Theoretical Reactor
Results: Bad Theoretical Reactor
Results: Bad Theoretical Reactor
Results: Bad Theoretical Reactor
Results: Variance ~ Flow
Results: Variance ~ Flow
Results: Variance ~ Flow
Results: Summary Table
• Limits: R2<0.95, LogI Error > 0.5
Min Max Min Max Min Max Min MaxGood Theoretical 1.00 1.00 ‐0.15 0.18 ‐0.07 0.10 1.00 ‐0.12 0.24 ‐0.02 0.10Bad Theoretical 0.99 0.98 ‐0.37 0.17 ‐0.30 0.20 0.98 ‐0.39 0.33 ‐0.41 0.18Variance ~ Flow 0.92 1.00 0.13 1.50 ‐2.19 0.05 0.93 ‐1.12 1.17 0.00 0.28Good CFD 1.00 1.00 ‐0.05 0.03 ‐0.04 0.02 1.00 ‐0.05 0.04 ‐0.02 0.03Bad CFD 1.00 1.00 ‐0.04 0.03 ‐0.11 0.07 1.00 ‐0.16 0.07 ‐0.19 0.06Good CFD (s=0.125) 1.00 0.99 ‐0.20 0.20 ‐0.30 0.18 0.99 ‐0.27 0.25 ‐0.30 0.23Good CFD (s=0.25) 0.99 0.97 ‐0.38 0.47 ‐0.32 0.30 0.98 ‐0.53 0.57 ‐0.55 0.82Bad CFD (s=0.125) 0.99 0.99 ‐0.09 0.48 ‐0.26 0.18 0.99 ‐0.24 0.40 ‐0.40 0.29Bad CFD (s=0.25) 0.97 0.94 ‐0.31 0.43 ‐0.56 0.33 0.97 ‐0.69 0.47 ‐0.56 0.32
T1 to MS2(LogI Error)
MS2 to T1(LogI Error)
Combined Fit (LogI Error)
Adenovirus Prediction(LogI Error)
T1 (R2)Combined Fit
(R2)MS2 (R2)
Results: Bad CFD with Uncertainty
Conclusions• CV approach appears viable if applied appropriately• Methodology work for all cases except where particle
trajectories varied with flow– This is outside the theoretical formulation assumptions– Extrapolation to a more resistant organism still worked
• Recommendations– Extrapolation on flow, CV and UVT should not be considered
– Effect of second order kinetics should be tested (tomorrow)
