Simulating Photodynamic Inactivation (PDI) from chemical kinetics

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Antibiotic resistance is a developing medical crisis that is projected to surpass cancer in annual deaths by mid-21st century. Photodynamic Inactivation (PDI) escapes resistance evolution and may therefore be an essential antibiotic method to hamper the growing threat of resistant pathogens. The requisite rate of research to mitigate these somber projections requires computational tools that can improve and expedite experimental research in developing PDI treatments.

PDIpy is the first comprehensive software of PDI that simulates PDI biochemistry from a chemical kinetics model. PDIpy accepts user inputs of the simulated system, constructs and executes a Tellurium kinetic system, and processes and exports the results in spreadsheets and SVG figures. Investigation of the simulation data is further supported with a PDIpy function that parses the data based upon either a specified inactivation or time. The examples directory of the PDIpy GitHub exemplifies PDIpy through replicating experimental observations and conducting multiple sensitivity analyses. Users and developers are encouraged to critique, improve, and join the open-source project through GitHub issues or emailing afreiburger@uvic.ca, respectively.

Note

This project is under active development, and may therefore be subject to incompatible changes in the API. We seek to minimize these types of upgrades.

Installation

pdipy is installed in a command prompt, Powershell, Terminal, or Anaconda Command Prompt via pip:

pip install pdipy

Contents

Usage

from pdipy import PDI

# define the simulation conditions
pdi = PDI(
    solution_dimensions = {
        'area_sqr_cm':pi/4,
        'depth_cm': 46,
       },
       printing = False
       )
pdi.define_conditions(
    bacterial_specie = 'S_aureus',
    bacterial_cfu_ml = 3e7,
    photosensitizer = 'protoporphyrin IX',
    photosensitizer_characteristics = {
       'formula': {
           'value': 'C34_H34_N4_O4'
       },
       'dimensions':{
           'length (A)': length,
           'width (A)': width,
           'depth (A)': 4,
           'shape': 'rect',
       }
    },
    photosensitizer_molar = 18e-9,
    measurement = {'irradiance': 8},
    )

# execute and export the simulation
pdi.simulate(
   export_name = 'Bozja_et_al, 1E4 Lux',
   figure_title = '1E4 Lux, Protoporphyrin IX',
   display_ps_excitation = True,
)

# parse the data and evaluate the PDI object contents
value, unit = pdi.parse_data(log_reduction = 5)
print(dir(pdi))

Accessible content

Numerous entities are stored within the PDI object, and can be subsequently used in a workflow. The complete list of content within the PDI object can be identified and printed through the Python function dir(), while the following list highlights a few notable contents within the PDI object:

  • raw_data & processed_data Pandas.DataFrame: Pandas DataFrames that contain the raw and processed simulation data, respectively. These files are also exported through the export function.

  • model & phrasedml_str str: The kinetic model and its corresponding SED-ML plot, respectively, composed in a string that is read by Tellurium.

  • bacterium, photosensitizer, & light dict: Simulation parameters for the bacterium, photosensitizer, and light, respectively, in a for that is read by the code.

  • parameters, variables, & results dict: Input parameters, calculation variables, and simulation results, respectively, that are subsequently processed into DataFrames and exported as CSVs.

  • figure & ax MatplotLib.Pyplot.subplots: The MatPlotLib objects of the simulation figure, which allows the user to externally manipulate the figure without recreating a new figure from the raw or processed data.

  • chem_mw chemw.ChemMW: The ChemMW object from the ChemW module, which allows users to calculate the molecular weight from a string of any chemical formula or common name.

  • bacteria list: A list of all the predefined bacteria parameter files, from which a user can easily simulate via the PDI object.

  • light_parameters, photosensitizers, & solution dict: Dictionaries of the predefined options and parameters for the light sources, photosensitizers, and solution dimensions, respectively.

PDIpy API

PDI()

The simulation environment is defined:

import pdipy
pdi = pdipy.PDI(solution_dimensions = {}, surface_system = False, well_count = 24,
                verbose = False, jupyter = False, printing = True)

  • solution_dimensions dict: defines the physical dimensions of the simulated solution, which are used to calculate photonic density and photosensitizer volume proportion.

  • surface_system bool: specifies whether a photodynamic system with a surface-bound, cross-linked, photosensitizer will be simulated.

  • well_count int: specifies the petri dish well count that will be simulated, which begets default dimensions of the simulated solution.

  • verbose & printing bool: specifies whether simulation details and simulation results, respectively, will be printed. These are valuable for troubleshooting.

  • jupyter bool: specifies whether the simulation is being conducted in a Jupyter Notebook, which allows display() to illustrate data tables and figures.

define_conditions()

The characteristics of the simulated system are concisely defined in a single function:

pdi.define_conditions(bacterial_specie = 'S_aureus', bacterial_characteristics = {},
      bacterial_cfu_ml = 1e6, biofilm = False, photosensitizer = 'A3B_4Zn',
      photosensitizer_characteristics = {}, absorbance_nm = {}, transmittance = {},
      photosensitizer_molar = None, surface_system = False, photosensitizer_g = 90e-9,
      cross_linked_sqr_m = 0.0191134, area_coverage = False,
      light_source = None, light_characteristics = {}, measurement = {})

  • bacterial_specie str: specifies one of the bacteria in the pdipy/parameters/bacteria directory, where S. aureus is imported by default. These imported parameters are overwritten by the bacterial_characteristics, and can be used complementarily. The PDIpy parameter files directory of these docs detail the contents and syntax of these files.

  • bacterial_characteristics dict: provides custom characteristics of the simulated bacterium that supplant imported characteristics from the bacterial_specie argument. The expected dictionary keys shape, membrane_thickness_nm, cell_mass_pg, "cell_volume_fL, eps_oxidation_rate_constant, cellular_dry_mass_proportion_biofilm, doubling_rate_constant, and biofilm_oxidation_fraction_lysis are all themselves dictionaries that follow a simple structure:

{
         "value": 0.268,
         "reference": "A. G. O’DONNELL, M. R. NAHAIE, M. GOODFELLOW, D. E. MINNIKINI, and V. HAJEK. Numerical Analysis of Fatty Acid Profiles in the Identification of Staphylococci. Journal of General Microbiology (1989). 131, 2023-2033. https://doi.org/10.1099/00221287-131-8-2023",
         "notes": "All saturated SCFAs were summed from Table 2 for all S. aureus entries."
}

The reference and notes keys are optional, yet may be important for provenance and reproducibility of the simulation results. The final key of bacterial_characteristics is membrane_chemicals, which characterizes the chemicals that constitutes the bacterial membrane such as BCFA for branch-chain, and SCFA for straight-chain, saturated fatty acids. The sub-structure of these values are exemplified by the following content for the "SCFA" entry for S. aureus:

{
    "density_gL": {
         "value": 0.94,
         "reference": ["https://pubchem.ncbi.nlm.nih.gov/compound/Stearic-acid#section=Density"],
         "notes": "The density for all saturated fatty acids is estimated as stearic acid."
         },
    "formula": [
         "C20_H38_O2",
         "C18_H34_O2",
         "C16_H30_O2"
         ],
        "proportion": {
             "value": 0.268,
             "reference": "A. G. O’DONNELL, M. R. NAHAIE, M. GOODFELLOW, D. E. MINNIKINI, and V. HAJEK. Numerical Analysis of Fatty Acid Profiles in the Identification of Staphylococci. Journal of General Microbiology (1989). 131, 2023-2033. https://doi.org/10.1099/00221287-131-8-2023",
             "notes": "All saturated SCFAs were summed from Table 2 for all S. aureus entries."
         }
 }

  • bacterial_cfu_ml float: specifies the bacterial concentration for simulations of solution-based photosensitizers.

  • biofilm bool: specifies whether a biofilm will be simulated.

  • photosensitizer str: names the simulated photosensitizer, where predefined names will load the stored parameter values from pdipy/parameters/photosensitizers.json. The PDIpy parameter files directory of these docs detail the contents and syntax of these files.

  • photosensitizer_characteristics dict: defines characteristics of the simulation photosensitizer, which supplant the characteristics from the photosensitizer parameter. The expected structure of the dictionary are keys with dictionary substructure according to the following example:

{
               "e_quantum_yield": {
                       "value": 0.6,
                       "reference": "Singlet Oxygen Yields and Radical Contributions in the Dye-Sensitised Photo-oxidation in methanol of esters of polyunsaturated fatty acids _oleic, linoleic, linolenic, and arachidonic) Chacon et al., 1988"
               },
               "so_specificity": {
                       "value": 0.8,
                       "reference": null
               },
               "formula": {
                       "value": "C76_H48_N16_F12_Zn",
                       "reference": null
               },
               "excitation_nm": {
                       "value": [
                               [400, 430],
                               [530, 625]
                                ],
                       "reference": null
               },
               "ps_decay (ns)": {
                   "value": 1.5,
                   "reference": "Akimoto et al., 1999, 'Ultrafast ... Porphyrins'"
               },
               "ps_rise (fs)": {
                   "value": 50,
                   "reference": "Anderssonet al., 1999, 'Photoinduced ... State' ; Gurzadyan et al., 1998, 'Time-resolved ... Zn-tetraphenylporphyrin'"
               },
               "ps_charge_transfer (ns)": {
                   "value": 100,
                   "reference": "Kupper et al., 2002, 'Kinetics ... Oxygen'"
               },
               "photobleaching_constant (cm^2/J)": {
                       "value": 1.74e-7,
                       "reference": "“Photobleaching kinetics, photoproduct formation, and dose estimation during ALA induced PpIX PDT of MLL cells under well oxygenated and hypoxic conditions” by Dysart et al., 2005",
                       "notes": "The 0.015 value from literature is divided by 8.64e4 -- the quantity of seconds in a day -- to yield a sensible value. A similar value is discovered from “PHOTOBLEACHING OF PORPHYRINS USED IN PHOTODYNAMIC THERAPY AND  IMPLICATIONS FOR THERAPY” by Mang et al., 1987"
                       },
               "dimensions": {
                       "shape": "disc",
                       "length_A": 32.8,
                       "width_A": 32.8,
                       "depth_A": 1.5,
                       "notes": "The depth is atomic thickness, as quantified by this paper https://www.nature.com/articles/ncomms1291."
               }
}

The value sub-key in the dictionary substructures, where it is present, is the only necessary sub-key for each parameter.

  • absorbance_nm & transmittance dict: define the absorbance or transmittance, respectively, of the simulated PS at the simulated concentrations or area coverage. The absence of these parameters triggers the estimation of the photon absorption from first principles and several assumptions.

  • photosensitizer_molar float: specifies the photosensitizer molar concentration for simulations of a solution-based photosensitizer.

  • surface_system bool: signals whether the photosensitizer is surface-bound upon a material substratum.

  • photosensitizer_g float: specifies the mass of photosensitizer that is surface-bound in cross-linked simulations.

  • cross_linked_sqr_m float: defines the square-meters area that is coated with the bound photosensitizer. This must be provided in tandem with the photosensitizer_g parameter.

  • area_coverage float: specifies the fraction of a substratum area that is covered with the surface-bound photosensitizer.

  • light_source str: names the simulated light source, where predefined names will load the stored parameter values from pdipy/parameters/light_source.json. The PDIpy parameter files directory of these docs detail the contents and syntax of these files.

  • light_characteristics dict: specifies custom characteristics of the light source, which overwrite characteristics that are specified from the light_source option. The expected structure of the dictionary are keys with dictionary substructure according to the following example:

{
   "visible_proportion": {
     "value": 0.1,
     "reference": "Macisaac et al., 1999"
   },
   "lumens_per_watt": {
     "value": 3,
     "reference": "Michael F. Hordeski. Dictionary Of Energy Efficiency Technologies. Fairmont Press. ISBN: 9780824748104"
   }
 }

where the value sub-key in the dictionary substructures is the only necessary sub-key for each parameter.

  • measurement dict: provides the unit and quantity of the photonic intensity measurement of the light source in a key-value pair. The supported unit options are: irradiance in mW/cm2, exposure in J/cm2, lux in lumen/m2, and lumens in lumens.

simulate()

The aforementioned system specifications are refined into chemical parameters and are executed in a Tellurium kinetic model:

pdi.simulate(export_name = None, export_directory = None, figure_title = None,
           y_label = 'log10', exposure_axis = False, total_time = 720, timestep = 3
           experimental_data = {'x':[], 'y':[]}, display_fa_oxidation = False,
           display_ps_excitation = False, display_inactivation = True, export_content = True)

  • export_name & export_directory str: specify the name and directory, respectively, to which the simulation contents will be saved, where None defaults to a folder name with simulation parameters PDIpy-<photosensitizer_selection>-<bacterial_specie>-<count> within the current working directory.

  • figure_title & y_label str: specify the title and y-axis label of the simulation figure, respectively. The y-axis label is general to support multiple overlaid plots in the same figure. The value of None defaults to a figure title of Cytoplasmic oxidation and inactivation of < bacterial_specie >.

  • exposure_axis bool: specifies whether the x-axis of the simulation figure will be defined with cumulative exposure J/cm2over the simulation or in minutes of simulation time, where the latter is default.

  • total_time float: specifies the total simulated time in minutes. This parameter is over-ridden when the predicted oxidation proportion reaches a signularity, at which point the simulation is determined to conclude.

  • timestep int: specifies the timestep value in minutes of the simulation.

  • display_fa_oxidation, display_ps_excitation, & display_inactivation bool: determine whether the fatty acid oxidation, the photosensitizer excitation, or the inactivation proportions, respectively, will be plotted in the figure.

  • export_content bool: specifies whether the simulation content will be exported.

parse_data()

The inactivation predictions can be easily investigated through this function:

value, unit = pdi.data_parsing(log_reduction = None, target_hours = None)

  • log_reduction float: inquires at what time the specified log-reduction is achieved

  • target_hours float: inquires what log-reduction is achieved that the specified time

Returns value float: The value of the search inquiry, reported in the respective units.

Returns unit str: The units of the search inquiry result, being either log-reduction or hours.

PDIpy parameter files

Parameters may be more succinctly provided through comprehensive JSON files, which are automatically imported by the code, than through function arguments; although, these parameter sources are complementary. Each JSON file pertains to a distinct category of simulation parameters, which are individually detailed in the following sections.

photosensitizers

The chemical attributes of the simulated photosensitizer are articulated in the following format:

{
       "A3B_4Zn": {
               "e_quantum_yield": {
                       "value": 0.6,
                       "reference": "Singlet Oxygen Yields and Radical Contributions in the Dye-Sensitised Photo-oxidation in methanol of esters of polyunsaturated fatty acids _oleic, linoleic, linolenic, and arachidonic) Chacon et al., 1988"
               },
               "so_specificity": {
                       "value": 0.8,
                       "reference": null
               },
               "so_quantum_yield":{
                       "value": 0.48,
                       "reference": null
               },
               "formula": {
                       "value": "C76_H48_N16_F12_Zn",
                       "reference": null
               },
               "excitation_nm": {
                       "value": [
                               [400, 430],
                               [530, 625]
                                ],
                       "reference": null
               },
               "ps_rise (fs)": {
                       "value": 50,
                       "reference": "Anderssonet al., 1999, 'Photoinduced ... State' ; Gurzadyan et al., 1998, 'Time-resolved ... Zn-tetraphenylporphyrin'"
               },
               "ps_decay (ns)": {
                       "value": 1.5,
                       "reference": "Akimoto et al., 1999, 'Ultrafast ... Porphyrins'"
               },
               "ps_charge_transfer (ns)": {
                       "value": 100,
                       "reference": "Kupper et al., 2002, 'Kinetics ... Oxygen'"
               },
               "photobleaching_constant (cm2/(J*M))": {
                       "value": 600,
                       "reference": "Dysart et al., 2005, 'Calculation of Singlet Oxygen Dose ... and Photobleaching During mTHPC Photodynamic Therapy of MLL Cells'"
               },
               "dimensions": {
                       "shape": "disc",
                       "length_A": 32.8,
                       "width_A": 32.8,
                       "depth_A": 1.5,
                       "notes": "The depth is atomic thickness, as quantified by this paper https://www.nature.com/articles/ncomms1291."
               }
       }

  • e_quantum_yield, so_specificity, & so_quantum_yield float: quantum yields of the photosensitizer (PS). The e_quantum_yield and so_specificity quantum yields correspond to the excitation of a PS after collision with a photon and the generation of singlet oxygen (SO) by that excited PS, respectively. The so_quantum_yield quatum yield is the collective probability, and thus the product, of the two aforementioned quantum yields, and is disaggregated into estimates of the first two quantum yields by simply taking its square-root.

  • formula str: defines the chemical formula of the PS, where underscores may optionally separate elements to improve readability.

  • excitation_nm 2D-array: specifies the excitation range(s) of the photosensitizer in nanometers.

  • ps_rise (fs) & ps_decay (ns) float: specifies the excitation and fluorescence times in units of femtoseconds and nanoseconds, respectively, for the PS.

  • ps_charge_transfer (ns) float: specifies the average time after a photon collision when the excited PS relays excitation energy to another molecule, ideally tripley oxygen.

  • photobleaching_constant (cm2/(J*M)) float: specifies the rate constant of the oxygen-dependent photobleaching reaction for the PS.

  • dimensions dict: specifies the physical dimensions of the PS molecule in angstroms and the approximate shape of the simulated PS, which are used in the absence of absorption data for the PS at the simulated concentration to calculate the molecular volume and then estimate the absorption properties of the chemical in the system.

The reference and notes keys are optional, and other keys of metadata may be added as well at the user’s discretion.

wells

The dimensions of the solution in which the PDI simulation is conducted may be described through the wells.json file, in addition to the function argument. The default entries of this file reflect standard dimensions of individual wells in the 6-, 12-, 24-, 48-, and 96-well bioassay plates; however, any solution can be defined that provides the area_sqr_cm, depth_cm, and extinction_coefficient (1/m) parameters.

{
       "12": {
               "area_sqr_cm": 3.85,
               "depth_cm": 1.766,
               "extinction_coefficient (1/m)":0.013,
               "dimensions_reference":"https://ca.vwr.com/assetsvc/asset/en_CA/id/25423331/contents/vwr-essential-products-for-tissue-culture.pdf",
               "coefficient_reference":"The effect of photocarrier generating light on light scattering in the Sea. Lorenzen, 1972"
       }
}

Other key:value pairs may be defined to specify references or other notes about the system. A sample entry in the wells.json file is provided below:

  • area_sqr_cm float: specifies the area on the bottom of the simulated solution, in units of cm2.

  • depth_cm float: specifies the depth (height) of the simulated solution, in units of cm.

  • extinction_coefficient (1/m) float: specifies the rate constant for the scattering of light through the solution, as a function of depth, via the light attenuation equation: remaining fraction = e(-k*z).

bacteria

This folder contains a different JSON file for each bacterial specie. The only bacterium that is specified by default is Staphylococcus aureus (S_aureus.json), however, other organisms can be defined by replicating the structure of the default parameter file. The values of each sub-dictionary are stored in the value key.

{
   "membrane_chemicals": {
     "BC_SFA": {
       "density_gL": {
         "value": 0.9,
         "reference": ["https://pubchem.ncbi.nlm.nih.gov/compound/Stearic-acid#section=Density", "https://pubchem.ncbi.nlm.nih.gov/compound/445639"],
         "notes": "The density is estimated to be between stearic acid and oleic acid"
       },
       "formula": ["C18_H34_O2","C16_H30_O2"],
       "proportion": {
         "value": 0.662,
         "reference": "A. G . O’DONNELL, M. R . NAHAIE, M. GOODFELLOW, D. E. MINNIKINI, and V . HAJEK. Numerical Analysis of Fatty Acid Profiles in the Identification of Staphylococci. Journal of General Microbiology (1989). 131, 2023-2033. https://doi.org/10.1099/00221287-131-8-2023",
         "notes": "All BCFAs were summed from Table 2 for all S. aureus entries."
       }
     },
     "SC_SFA": {
       "density_gL": {
         "value": 0.94,
         "reference": ["https://pubchem.ncbi.nlm.nih.gov/compound/Stearic-acid#section=Density"],
         "notes": "The density for all saturated fatty acids is estimated as stearic acid."
       },
       "formula": ["C20_H38_O2","C18_H34_O2","C16_H30_O2"],
       "proportion": {
         "value": 0.268,
         "reference": "A. G. O’DONNELL, M. R. NAHAIE, M. GOODFELLOW, D. E. MINNIKINI, and V. HAJEK. Numerical Analysis of Fatty Acid Profiles in the Identification of Staphylococci. Journal of General Microbiology (1989). 131, 2023-2033. https://doi.org/10.1099/00221287-131-8-2023",
         "notes": "All saturated SCFAs were summed from Table 2 for all S. aureus entries."
       }
     },
     "SC_UFA": {
       "density_gL": {
         "value": 0.94,
         "reference": ["https://pubchem.ncbi.nlm.nih.gov/compound/Stearic-acid#section=Density"],
         "notes": "The density for all saturated fatty acids is estimated as stearic acid."
       },
       "formula": ["C20_H38_O2","C18_H34_O2","C16_H30_O2"],
       "proportion": {
         "value": 0.07,
         "reference": "A. G. O’DONNELL, M. R. NAHAIE, M. GOODFELLOW, D. E. MINNIKINI, and V. HAJEK. Numerical Analysis of Fatty Acid Profiles in the Identification of Staphylococci. Journal of General Microbiology (1989). 131, 2023-2033. https://doi.org/10.1099/00221287-131-8-2023",
         "notes": "All saturated SCFAs were summed from Table 2 for all S. aureus entries."
       }
     }
   },
   "membrane_thickness_nm": {
     "value": 4,
     "reference": "W.Rawicz, K.C.Olbrich, T.McIntosh, D.Needham, E.Evans (2000). Effect of Chain Length and Unsaturation on Elasticity of Lipid Bilayers. Biophysical Journal, 79(1), 328–339. https://doi.org/10.1016/S0006-3495(00)76295-3  ; “The electrical capacity of suspensions with special reference to blood” by Fricke, 1925"
   },
   "cell_mass_pg": {
     "value": 1.048,
     "reference": "Lewis, C. L., Craig, C. C., & Senecal, A. G. (2014). Mass and density measurements of live and dead Gram-negative and Gram-positive bacterial populations. Applied and environmental microbiology, 80(12), 3622–3631. https://doi.org/10.1128/AEM.00117-14"
   },
   "cell_volume_fL": {
     "value": 0.9357,
     "reference":  "Lewis, C. L., Craig, C. C., & Senecal, A. G. (2014). Mass and density measurements of live and dead Gram-negative and Gram-positive bacterial populations. Applied and environmental microbiology, 80(12), 3622–3631. https://doi.org/10.1128/AEM.00117-14"
 },
   "eps_oxidation_rate_constant":{
     "value": 37.75,
     "reference": null,
     "notes": "This rate constant was empirically determined after calibrating the predictions with the Beirao et al., 2014 paper that constituted one of our examples"
 },
   "cellular_dry_mass_proportion_biofilm":{
         "value": 0.1,
         "reference": "The biofilm matrix; Flemming et al.; 2010"
 },
   "doubling_rate_constant":{
         "value": 0.00038441,
         "reference": "Baines et al.; mBio; 2015"
 },
   "biofilm_oxidation_fraction_lysis":{
         "value": 0.0014125,
         "note": "empirically derived through training with Beirao et al."
 }
}

  • membrane_chemicals dict: specifies the fatty acid constituent the phospholipids of the bacterial cytoplasmic membrane. Each fatty acid (FA) entry is defined with sub-dictionaries of its chemical formula, its density_gL density, and its proportion of total FAs in the cytoplasmic membrane.

  • membrane_thickness_nm dict: specifies the thickness of the cytoplasmic membrane in nanometers.

  • cell_mass_pg & cell_volume_fL dict: specifies the mass and volume of the bacterial cell in picograms and femtoliters, respectively.

  • eps_oxidation_rate_constant dict: defines the rate constant of oxidizing the extracellular polymeric substance for biofilm simulations of this organism.

  • cellular_dry_mass_proportion_biofilm dict: defines the ratio of biofilm mass that is comprised of cellular dry mass.

  • doubling_rate_constant dict: specifies the rate constant at which the bacteria doubles

  • biofilm_oxidation_fraction_lysis dict: specifies the threshold of membrane oxidation that manifests in cellular lysis.

The reference and notes keys are optional in each sub-dictionary, as are other keys of metadata at the user’s discretion.

light

The emission spectrum and visual intensity per energy input of the simulated light source are defined through the light.json file, complementarily to the function argument. The default light sources are incandescent, LED, and fluorescent; however, other light sources can be defined by emulating the same syntactic structure. The values of each sub-dictionary are stored in the value key.

{
 "incandescent": {
   "visible_proportion": {
     "value": 0.1,
     "reference": "Macisaac et al., 1999"
   },
   "lumens_per_watt": {
     "value": 3,
     "reference": "Michael F. Hordeski. Dictionary Of Energy Efficiency Technologies. Fairmont Press. ISBN: 9780824748104"
   }
 }
}

  • visible_proportion dict: specifies proportion of the emission spectrum that resides within the visible region.

  • lumens_per_watt dict: specifies the visual lumens that are emitted per watt of energy. This is used to convert between parameterized light intensity in units of lux or lumens into watts, which is the necessary unit for subsequent PDIpy calculations.