Aquatic Ecodynamics (AED/AED2) model library

Science Modules / Pathogens

Overview

Understanding the fate and transport of pathogenic and indicator microbes within drinking water reservoirs is critical for managers to effectively reduce risk. Over the past decade several advances have been made for the simulating organism dynamics using coupled hydrodynamic-organism fate models. These have generally been used for simulating coliform bacteria (Hipsey et al., 2008), with applications also reported for Cryptosporidium (Hipsey et al., 2004) and viruses (Sokolova et al., 2012). In general, these models simulate organism concentrations within water bodies by accounting for external loading, advection and mixing process that occur within the lake interior, organism inactivation and sedimentation. A synthesis of relevant information from empirical and prior modelling studies is presented on the adjacent tab to define the model approach for river/reservoir or coastal systems, and summarises the implementation of the pathogen module within the AED2 model framework.

Organisms that can be simulated using the AED2 framework include:

  • Protozoa
  • • Cryptosporidium
    • Giardia
  • Bacteria
  • • E coli
    • Enterococci
    • Campylobacter (C. jejuni species)
  • Viruses
  • • Norovirus
    • Rotavirus

A table of parameters for each of the above groups and other common organism classes is provided below with indicative references, and additionally a example database of parameters configured in the appropriate input file format are available via the button below.

Goto Parameter Database

General Approach

The general balance equation for organism transport and fate is summarized in Hipsey et al., (2008) as:

Eq1

where C is the organic concentration (orgs m-3), t is time, xj is the distance in the j-th dimension (m), Uj is the velocity in the j-th dimension (m s-1), is the eddy-diffusivity and Cin and Cout are the inflow and outflow fluxes respectively (orgs m-3 s-1). This relates organism concentration through time to hydrodynamic characteristics within the lake (as captured by U, and ), and the environmental conditions experienced that influence organism fate (including temperature, salinity, light intensity, dissolved organic carbon, oxygen and pH). This comprehensive description is usually simplified for specific applications, based on justification of the dominant processes present in any particular lake and available data for model setup and validation. Within the TUFLOWFV-AED2 model framework, the 1st three terms on the RHS are solved via the finite volume scalar transport routines with TUFLOW-FV and the fourth and fifth terms are simulated by the aed2_pathogens module of the AED2 aquatic ecological modelling library. For this application the growth and predation terms suggested by Hipsey et al. (2008) are not considered directly since the likelihood of growth is small (Toze et al., 2012) and predation/grazing is factored into the die-off rate (described below). The remaining terms for simulation of organism resuspension and inactivation are described in detail next.

Natural Mortality

Natural mortality, or the ‘dark-death rate’, kd, is an important process determining the net rate of die off of protozoan, viral and bacterial organisms and has been reported to vary for specific organisms due to changes in temperature, salinity and pH. The reported die off rates in the literature however are widely variable, with a synthesis of numerous studies from a range of water bodies presented in Hipsey et al., (2008). For freshwater reservoirs, changes in salinity and pH are unlikely to be a significant driver of organism viability relative to the range presented Hipsey et al., (2008) and therefore a simple constant die-off rate that depends on temperature is appropriate:

Eq2

where is the rate of mortality in the dark at 20C and in freshwater. Since the AED2 implementation of the model to be applied with NPD does not include protozoan grazing as a separate term (as in Eq 1), the grazing effect needs to be embodied within the term. This effectively assumes a constant grazing pressure over time, and if chosen to be a low value this will essentially ensure conservative estimate of the die-off due to grazing. Empirical data from Wivenhoe dam shows the presence of native micro-organisms can increase the background die-off rate by 1.1-3.0x (eg Table 5 in Toze et al., 2012).

Sunlight inactivation

Depending on the clarity of the water, the light climate of the lake can be a dominant factor influencing organism viability and this has been observed empirically in Wivenhoe Dam by Toze et al. (2012). Different organism types experience different sensitivity to different light bandwidths, with most organisms sensitive to UV-B and UV-A and some sensitive to light in the visible spectrum (Sinton eta l). Hipsey et al. (2008) formulated a multiple band-width model for organisms that included direct and indirect mechanisms for sunlight mediated inactivation by accounting for the effect of salinity, oxygen and pH on free radical formation. Here we use a simplified form that accounts only for direct sunlight denaturation as the indirect mechanism is more specific to MS2 phage relative to rotavirus for example (Verbyla et al., 2015). The implemented expression is therefore:

Eq3

where NB is the number of discrete solar bandwidths to be modeled, b is the bandwidth class {1, 2, … , NB}, kb is the freshwater inactivation rate coefficient for exposure to the bth class (m2 MJ-1), Ib is the intensity of the bth bandwidth class (Wm-2),  is a constant to convert units from seconds to days and J to MJ (= 8.6410-2). In AED2, the light intensity is computed for 3 distinct bandwidths, including UV-B, UV-A and PAR, and the attenuation of each through the reservoir water column is based on bandwidth specific light extinction coefficients, that account for the effect of turbidity and chromophoric dissolved organic matter (CDOM) on attenuation.

Sedimentation

Sedimentation of organisms occurs at a rate depending on the degree to which the population is attached to suspended particles. Within AED2, this is captured by simulating free and attached organisms and multiple groups of particles may be accounted for. If we assume a single dominant particle size and ignore the effect of salinity on the settling velocity, then the expression in Hipsey et al (2008) for the effective sedimentation velocity reduces to:

Eq4

where fa is the attached fraction, and V is the vertical velocity of organisms or sediment particles.

Resuspension

Resuspension of organisms accumulated within the sediment has been show to be a relatively important terms in environments where high currents or waves exist. In reservoirs this can occur in the lake margins or deeper in the lake where internal waves or river underflows increase the shear stress at the sediment. The amount of organisms that resuspend depends not only on the shear stress but also n the concentration of organisms in the surficial layers of the sediment. This may be modelled by accounting for the deposited organisms, decay within the sediment and resuspension rate, however, this is notoriously difficult given potentially complex dynamics of organisms in the sediment. Instead we assume that a standard background concentration exists within different sediment regions (based on depth and local geomorphology) and simulate resuspension rate as:

Eq5

where, is the rate of organism suspension (orgs m-2 s-1), which occurs when the critical shear stress is exceeded in the relative computational cell.



Variable Summary & Setup Options

Variable Name Description Units Variable Type Core/Optional
PTH_name Concentration of pathogens cfu/100mL pelagic optional
to be completed
Variable Name Description Units Variable Type Core/Optional
Parameter Name Description Units Parameter Type Default Typical Range Comment
num_pathogens number of pathogens to model 1-?
to be completed

An example nml block for the pathogens module is shown below.

&aed2_pathogens num_pathogens = 2 the_pathogens = 1,3 dbase = './the_path_to/aed2_pathogen_pars.nml' ! OPTIONAL VARS HERE resuspension num_ss ss_set ss_tau ss_ke sim_sedorgs oxy_variable epsilon tau_0 tau_0_min Ktau_0 extra_diag att_ts /

2018 : aed2_pathogen_pars.nml parameter formatting style

Goto aed2_pathogen_pars.nml Parameter Database
!------------------------------------------------------------------------------- ! aed2_pathogen_pars.nml : PATHOGEN PARAMETER DATABASE !------------------------------------------------------------------------------- ! p_name : [ string] - pathogen name ! coef_grwth_uMAX : [ real] - Max growth rate at 20C ! coef_grwth_Tmin : [ real] - Tmin and Tmax, f(T) ! coef_grwth_Tmax : [ real] - Tmin and Tmax, f(T) ! coef_grwth_T1 : [ real] - coef_grwth_T1 and coef_grwth_T2 ! coef_grwth_T2 : [ real] - coef_grwth_T1 and coef_grwth_T2 ! coef_grwth_Kdoc : [ real] - Half-saturation for growth, coef_grwth_Kdoc ! coef_grwth_ic : [ real] - coef_grwth_ic ! coef_mort_kd20 : [ real] - Mortality rate (Dark death rate) @ 20C and 0 psu ! coef_mort_theta : [ real] - Temperature multiplier for mortality: coef_mort_theta ! coef_mort_c_SM : [ real] - Salinity effect on mortality ! coef_mort_alpha : [ real] - Salinity effect on mortality ! coef_mort_beta : [ real] - Salinity effect on mortality ! coef_mort_c_PHM : [ real] - pH effect on mortality ! coef_mort_K_PHM : [ real] - pH effect on mortality ! coef_mort_delta_M : [ real] - pH effect on mortality ! coef_mort_fdoc : [ real] - Fraction of mortality back to doc ! coef_light_kb_vis : [ real] - Light inactivation ! coef_light_kb_uva : [ real] - Light inactivation ! coef_light_kb_uvb : [ real] - Light inactivation ! coef_light_cSb_vis : [ real] - Salinity effect on light inactivation ! coef_light_cSb_uva : [ real] - Salinity effect on light inactivation ! coef_light_cSb_uvb : [ real] - Salinity effect on light inactivation ! coef_light_kDOb_vis : [ real] - DO effect on light ! coef_light_kDOb_uva : [ real] - DO effect on light ! coef_light_kDOb_uvb : [ real] - DO effect on light ! coef_light_cpHb_vis : [ real] - pH effect on light inactivation ! coef_light_cpHb_uva : [ real] - pH effect on light inactivation ! coef_light_cpHb_uvb : [ real] - pH effect on light inactivation ! coef_light_KpHb_vis : [ real] - pH effect on light inactivation ! coef_light_KpHb_uva : [ real] - pH effect on light inactivation ! coef_light_KpHb_uvb : [ real] - pH effect on light inactivation ! coef_light_delb_vis : [ real] - exponent for pH effect on light inactivation ! coef_light_delb_uva : [ real] - exponent for pH effect on light inactivation ! coef_light_delb_uvb : [ real] - exponent for pH effect on light inactivation ! coef_pred_kp20 : [ real] - Loss rate due to predation and temp multiplier ! coef_pred_theta_P : [ real] - Loss rate due to predation and temp multiplier ! coef_sett_fa : [ real] - Attached fraction in water column ! coef_sett_w_path : [ real] - Sedimentation velocity (m/d) at 20C (-ve means down) for NON-ATTACHED orgs ! coef_resus_epsilonP : [ real] - Pathogen resuspension rate ! coef_resus_tauP_0 : [ real] - Critical shear stress for organism resuspension &pathogen_data pd%p_name = 'crypto', 'ecoli', 'totalcoli' pd%coef_grwth_uMAX = 0, 3, 2.4 pd%coef_grwth_Tmin = 4, 4, 4 pd%coef_grwth_Tmax = 35, 35, 35 pd%coef_grwth_T1 = 0.008, 0.008, 0.008 pd%coef_grwth_T2 = 0.1, 0.1, 0.1 pd%coef_grwth_Kdoc = 0, 0.3, 0.3 pd%coef_grwth_ic = 1.0E-9, 1.0E-9, 1.0E-9 pd%coef_mort_kd20 = 0.03, 0.48, 0.34 pd%coef_mort_theta = 1.08, 1.08, 1.11 pd%coef_mort_c_SM = 0, 2.0E-10, 2.0E-7 pd%coef_mort_alpha = 0, 6.1, 4.2 pd%coef_mort_beta = 0, 0.25, 0.25 pd%coef_mort_c_PHM = 0, 50, 50 pd%coef_mort_K_PHM = 0, 6, 6 pd%coef_mort_delta_M = 0, 4, 4 pd%coef_mort_fdoc = 0, 0.5, 0.5 pd%coef_light_kb_vis = 0, 0.097, 0.097 pd%coef_light_kb_uva = 0, 1.16, 1.16 pd%coef_light_kb_uvb = 0, 36.4, 36.4 pd%coef_light_cSb_vis = 0.0067, 0.0067, 0.0067 pd%coef_light_cSb_uva = 0.0067, 0.0067, 0.0067 pd%coef_light_cSb_uvb = 0.0067, 0.0067, 0.0067 pd%coef_light_kDOb_vis = 0.5, 0.5, 0.5 pd%coef_light_kDOb_uva = 0.5, 0.5, 0.5 pd%coef_light_kDOb_uvb = 0.5, 0.5, 0.5 pd%coef_light_cpHb_vis = 10, 10, 10 pd%coef_light_cpHb_uva = 10, 10, 10 pd%coef_light_cpHb_uvb = 10, 10, 10 pd%coef_light_KpHb_vis = 5, 5, 5 pd%coef_light_KpHb_uva = 5, 5, 5 pd%coef_light_KpHb_uvb = 5, 5, 5 pd%coef_light_delb_vis = 3, 3, 3 pd%coef_light_delb_uva = 3, 3, 3 pd%coef_light_delb_uvb = 3, 3, 3 pd%coef_pred_kp20 = 0, 0.2, 0.2 pd%coef_pred_theta_P = 1, 1.04, 1.04 pd%coef_sett_fa = 0, 0.94, 0.81 pd%coef_sett_w_path = -2.5E-6, -5.0E-7, -5.0E-7 pd%coef_resus_epsilonP = 0.01, 0.01, 0.01 pd%coef_resus_tauP_0 = 0.01, 0.01, 0.01 /

2014 : aed2_pathogen_pars.nml style parameters (note: not compatible with the online parameter database)

!----------------------------------------------------------------! ! coef_grwth_uMAX !-- Max growth rate at 20C ! coef_grwth_Tmin, coef_grwth_Tmax !-- Tmin and Tmax, f(T) ! coef_grwth_T1, coef_grwth_T2 !-- coef_grwth_T1 and coef_grwth_T2 ! coef_grwth_Kdoc !-- Half-saturation for growth, coef_grwth_Kdoc ! coef_grwth_ic !-- coef_grwth_ic ! coef_mort_kd20 !-- Mortality rate (Dark death rate) @ 20C and 0 psu ! coef_mort_theta !-- Temperature multiplier for mortality: coef_mort_theta ! coef_mort_c_SM, coef_mort_alpha, coef_mort_beta !-- Salinity effect on mortality ! coef_mort_c_PHM, coef_mort_K_PHM, coef_mort_delta_M !-- pH effect on mortality ! coef_mort_fdoc !-- Fraction of mortality back to doc ! coef_light_kb_vis, coef_light_kb_uva, coef_light_kb_uvb !-- Light inactivation ! coef_light_cSb_vis, coef_light_cSb_uva, coef_light_cSb_uvb !-- Salinity effect on light inactivation ! coef_light_kDOb_vis, coef_light_kDOb_uva, coef_light_kDOb_uvb !-- DO effect on light ! coef_light_cpHb_vis, coef_light_cpHb_uva, coef_light_cpHb_uvb !-- pH effect on light inactivation ! coef_light_KpHb_vis, coef_light_KpHb_uva, coef_light_KpHb_uvb !-- pH effect on light inactivation ! coef_light_delb_vis, coef_light_delb_uva, coef_light_delb_uvb !-- exponent for pH effect on light inactivation ! coef_pred_kp20, coef_pred_theta_P !-- Loss rate due to predation and temp multiplier ! coef_sett_fa !-- Attached fraction in water column ! coef_sett_w_path !-- Sedimentation velocity (m/d) at 20C (-ve means down) for NON-ATTACHED orgs !----------------------------------------------------------------! ! p_name coef_grwth_uMAX, coef_grwth_Tmin, coef_grwth_Tmax, coef_grwth_T1, coef_grwth_T2, coef_grwth_Kdoc, coef_grwth_ic, coef_mort_kd20, coef_mort_theta, coef_mort_c_SM, coef_mort_alpha, coef_mort_beta, coef_mort_c_PHM, coef_mort_K_PHM, coef_mort_delta_M, coef_mort_fdoc, coef_light_kb_vis, coef_light_kb_uva, coef_light_kb_uvb, coef_light_cSb_vis, coef_light_cSb_uva, coef_light_cSb_uvb, coef_light_kDOb_vis, coef_light_kDOb_uva, coef_light_kDOb_uvb, coef_light_cpHb_vis, coef_light_cpHb_uva, coef_light_cpHb_uvb, coef_light_KpHb_vis, coef_light_KpHb_uva, coef_light_KpHb_uvb, coef_light_delb_vis, coef_light_delb_uva, coef_light_delb_uvb, coef_pred_kp20, coef_pred_theta_P, coef_sett_fa, coef_sett_w_path &pathogen_data pd = 'crypto', 0.0, 4.0, 35.0, 0.008, 0.1, 0.0, 1e-9, 0.03, 1.14, 0.00, 0.0, 0.00, 0.0, 0.0, 0.0, 0.0, 0.000, 2.13, 33.7, 0.0067, 0.0067, 0.0067, 0.5, 0.5, 0.5, 10.0, 10.0, 10.0, 5.0, 5.0, 5.0, 3.0, 3.0, 3.0, 0.0, 1.00, 0.00, -2.\5e-6, 'ecoli', 0.0, 4.0, 35.0, 0.008, 0.1, 0.3, 1e-9, 0.48, 1.08, 2e-10, 6.1, 0.25, 50.0, 6.0, 4.0, 0.5, 0.097, 1.16, 36.4, 0.0067, 0.0067, 0.0067, 0.5, 0.5, 0.5, 10.0, 10.0, 10.0, 5.0, 5.0, 5.0, 3.0, 3.0, 3.0, 0.0, 1.04, 0.94, -0.5e-6, 'fcoli', 0.0, 4.0, 35.0, 0.008, 0.1, 0.3, 1e-9, 0.71, 1.06, 2e-3, 1.8, 0.25, 50.0, 6.0, 4.0, 0.5, 0.097, 1.16, 36.4, 0.0067, 0.0067, 0.0067, 0.5, 0.5, 0.5, 10.0, 10.0, 10.0, 5.0, 5.0, 5.0, 3.0, 3.0, 3.0, 0.0, 1.04, 0.81, -0.5e-6, 'ent', 0.0, 4.0, 35.0, 0.008, 0.1, 0.3, 1e-9, 0.45, 1.04, 0.00, 0.0, 0.25, 50.0, 6.0, 4.0, 0.5, 0.882, 1.16, 17.2, 0.0067, 0.0067, 0.0067, 0.5, 0.5, 0.5, 10.0, 10.0, 10.0, 5.0, 5.0, 5.0, 3.0, 3.0, 3.0, 0.0, 1.04, 0.81, -0.5e-6, 'totalcoli', 0.0, 4.0, 35.0, 0.008, 0.1, 0.3, 1e-9, 0.34, 1.11, 2e-7, 4.2, 0.25, 50.0, 6.0, 4.0, 0.5, 0.097, 1.16, 36.4, 0.0067, 0.0067, 0.0067, 0.5, 0.5, 0.5, 10.0, 10.0, 10.0, 5.0, 5.0, 5.0, 3.0, 3.0, 3.0, 0.0, 1.04, 0.81, -0.5e-6, /



Examples

pending ......



Publications & References

Auer, M. T., and S. L. Niehaus (1993), Modeling fecal coliform bacteria – I. Field and laboratory determination of loss kinetics, Water Res., 27, 693-701.

Bertrand, I. et al. (2012), The impact of temperature on the inactivation of enteric viruses in food and water: a review, Journal of Applied Microbiology, 112(6), 1059–1074.

Bae, J., and K. J. Schwab (2008), Evaluation of Murine Norovirus, Feline Calicivirus, Poliovirus, and MS2 as Surrogates for Human Norovirus in a Model of Viral Persistence in Surface Water and Groundwater, Applied and Environmental Microbiology, 74(2), 477–484.

Cervantes, A. A. (2012), Resuspension of E. coli Under Controlled Flows and Stream Bottom Sediments, MSc Thesis , Iowa State University. 167 pp

Silva, A. K. D., F. S. L. Guyader, J.-C. L. Saux, M. Pommepuy, M. A. Montgomery, and M. Elimelech (2008), Norovirus Removal and Particle Association in a Waste Stabilization Pond, Environ. Sci. Technol., 42(24), 9151–9157.

Dai, X., and J. Boll (2006), Settling velocity of Crytposporidium parvum and Giardia lamblia, Water Res., 40, 1321-1325.

Gerba, C. P., and G. E. Schaiberger (1975), Effect of particulates on virus survival in seawater, J. Water Pollut. Control Fed., 47, 93-103.

Ge, Z., R. L. Whitman, M. B. Nevers, M. S. Phanikumar, and M. N. Byappanahalli (2012), Nearshore hydrodynamics as loading and forcing factors for Escherichia coli contamination at an embayed beach, Limnol. Oceanogr., 57(1), 362–381, doi:10.4319/lo.2012.57.1.0362.

Hipsey, M. R., J. P. Antenucci, J. D. Brookes, M. D. Burch, R. H. Regel, and L. Linden (2004), A three dimensional model of Cryptosporidium dynamics in lakes and reservoirs: a new tool for risk management, Intl. J. River Basin Management, 2, 181-197.

Hipsey, M. R., J. D. Brookes, R. H. Regel, J. P. Antenucci, and M. D. Burch (2006), In situ evidence for the association of total coliforms and Escherichia coli with suspended inorganic particles in an Australian reservoir, Water Air Soil Pollut., 170, 191-209.

Hipsey, M. R., J. P. Antenucci, and J. D. Brookes (2008), A generic, process-based model of microbial pollution in aquatic systems, Water Resour. Res., 44, W07408.

King, B. J., D. Hoefel, D. P. Daminato, S. Fanok, and P. T. Monis (2007), Solar UV dramatically reduces Cryptosporidium parvum oocyst infectivity in environmental waters, Appl. Environ. Microbiol., in review.

King, B. J., A. R. Keegan, P. T. Monis, and C. P. Saint (2005), Environmental temperature controls Cryptosporidium oocyst metabolic rate and associated retention of infectivity, Appl. Environ. Microbiol., 71, 3848-3857.

Meng, Z.-D., C. Burch, R. Heath, and I. Gust (1987), Physicochemical stability and inactivation of human and simian rotaviruses, Applied and Environmental Microbiology, 53(4), 727–730.

Medema, G. J., F. M. Schets, P. F. M. Teunis, and A. H. Havelaar (1998), Sedimentation of free and attached Cryptosporidium oocysts and Giardia cysts in water, Appl. Environ. Microbiol., 64, 4460-4466.

Pandey, P. K., M. L. Soupir, and C. R. Rehmann (2012), A model for predicting resuspension of Escherichia coli from streambed sediments, Water Res., 46(1), 115–126.

Payment, P., E. Morin, and M. Trudel (1988), Coliphages and enteric viruses in the particulate phase of river water, Can. J. Microbiol., 34, 907-910.

Rodríguez, S., and R. Araujo (2012), Effect of environmental parameters on the inactivation of the waterborne pathogen Campylobacter in a Mediterranean river, J Water Health, 10(1), 100–10.

Romero, O. C., A. P. Straub, T. Kohn, and T. H. Nguyen (2011), Role of Temperature and Suwannee River Natural Organic Matter on Inactivation Kinetics of Rotavirus and Bacteriophage MS2 by Solar Irradiation, Environ. Sci. Technol., 45(24), 10385–10393

Searcy, K. E., A. I. Packman, E. R. Atwill, and T. Harter (2005), Association of Cryptosporidium parvum with suspended particles: Impact on oocyst sedimentation, Applied and Environmental Microbiology, 71(2), 1072–1078.

Sidhu, J. P. S., and S. Toze (2012), Assessment of pathogen survival potential during managed aquifer recharge with diffusion chambers, J Appl Microbiol, 113(3), 693–700.

Sinton, L. W., C. H. Hall, P. A. Lynch, and R. J. Davies-Colley (2002), Sunlight inactivation of fecal indicator bacteria and bacteriophages from waste stabilization pond effluent in fresh and saline waters, Appl. Environ. Microbiol., 68, 1122-1131.

Sinton, L., C. Hall, and R. Braithwaite (2007), Sunlight inactivation of Campylobacter jejuni and Salmonella enterica, compared with Escherichia coli, in seawater and river water, Journal of Water and Health, 5(3), 357–9,.

Sokolova, E., J. Åström, T. J. R. Pettersson, O. Bergstedt, and M. Hermansson (2012), Estimation of pathogen concentrations in a drinking water source using hydrodynamic modelling and microbial source tracking, J Water Health, 10(3), 358–13,.

Toze, S., Hodgers, L., Palmer, A., Sidhu, J., Page, D., Williams, M., Kookana, R., Bartkow, M., Sedlak, D., Stratton, H., Ahmed, W., Schroeder, S. and Christie, M. (2012). Natural Attenuation of Pathogens and Trace Contaminants in South East Queensland Waterways. Urban Water Security Research Alliance Technical Report No. 87.

Verbyla, M. E., and J. R. Mihelcic (2015), A review of virus removal in wastewater treatment pond systems, Water Res., 71(C), 107–124.

Walker, F. R., and J. R. Stedinger (1999), Fate and transport model of Cryptosporidium, J. Environ. Eng., 125, 325-333.

Yang, Y., and M. W. Griffiths (2013), Comparative Persistence of Subgroups of F-Specific RNA Phages in River Water, Applied and Environmental Microbiology, 79(15), 4564–4567

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