Skip to main content
Log in

Novel approach for estimating solubility of solid drugs in supercritical carbon dioxide and critical properties using direct and inverse artificial neural network (ANN)

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this work, a hybrid method based on neural network and particle swarm optimization (PSO) was applied to literature data to develop and validate a model that can predict with precision the solubility of binary systems (CO2 + solid drugs). ANN was used for modeling the nonlinear process. The PSO was used for two purposes: replacing the standard backpropagation in training the ANN and optimizing the process. The training and validation strategy has been focused on the use of a validation agreement vector, determined from linear regression analysis of the predicted versus experimental outputs, as an indication of the predictive ability of the neural network model. Statistical analysis of the predictability of the optimized neural network model trained with trainpso algorithm shows excellent agreement with experimental data. Furthermore, the comparison in terms of average relative deviation (AARD%) between the predicted results for each binary for the whole temperature and pressure range and results predicted by density-based models and a set of equations of state shows that the ANN–PSO model with optimized configuration, five neurons in input and hidden layers and one neuron in output layer (5-5-1) correlates far better the solubility of the solid drugs in scCO2. A control strategy was also developed by using the inverse artificial neural network method. The sensitivity analysis showed that all studied inputs have strong effect on the solubility and allowed the estimation of some solid properties from the solubility data with good accuracy without need to the group contribution methods.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11

Similar content being viewed by others

Abbreviations

AARD:

Average absolute relative deviation

ACO:

Ant colony optimization

ANN:

Artificial neural network

ANNi:

Inverse artificial neural network

b:

Bias of artificial neural model

br:

Bayesian regularization

I:

Relative importance

GA:

Genetic algorithm

lm:

Levenberg–Marquardt

MT:

Mendez-Santiago and Teja model

QLF:

Quasi-chemical lattice fluid

T:

Equilibrium temperature (K)

Tc:

Critical temperature (K)

P:

Pressure (MPa)

Pc:

Critical pressure (MPa)

PR:

Peng–Robinson

PSO:

Particle swarm optimization

R:

Regression coefficient

SAFT:

Statistical associating fluid theory

SRK:

Soave–Redlich–Kwong

V:

Output layer–hidden layer synaptic weights of artificial neural model

w:

Input layer–hidden layer synaptic weights of artificial neural model

ω:

Acentric factor

y 2 :

Solubility of solid drugs

calc:

Calculated property

exp:

Experimental property

h:

Hidden

o:

Output

2:

Solute (solid)

c:

Critical property

i:

Weight (i)

References

  1. Tabernero A, Vieira de Melo SA, Mammucari R, Martín del Valle EM, Foster NR (2014) Modelling solubility of solid active principle ingredients in sc-CO2 with and without cosolvents: a comparative assessment of semi empirical models based on Chrastil’s equation and its modifications. J Supercri Fluids 93:91–102

    Article  Google Scholar 

  2. Ayyildiz M, Çetinkaya K (2015) Comparison of four different heuristic optimization algorithms for the inverse kinematics solution of a real 4-DOF serial robot manipulator. Neural Comput Appl. doi:10.1007/s00521-015-1898-8

    Google Scholar 

  3. Duan S, Dong Z, Xiaofang H, Wang L, Li H (2015) Small-world Hopfield neural networks with weight salience priority and memristor synapses for digit recognition. J Neural Comput Appl. doi:10.1007/s00521-015-1899-7

    Google Scholar 

  4. Sakabe J, Uchida H, Shimoyama Y (2015) Mixed solid phase model using equation of state based on hole-theory for solubility prediction of pharmaceutical compound in supercritical CO2. J Supercrit Fluids 100:26–33

    Article  Google Scholar 

  5. Mohanraja M, Jayarajb S, Muraleedharan C (2012) Applications of artificial neural networks for refrigeration, air-conditioning and heat pump systems—a review. Renew Sustain Energy Rev 16(2):1340–1358

    Article  Google Scholar 

  6. Kalogirou SA (2001) Artificial neural networks in renewable energy systems applications: a review. Renew Sustain Energy Rev 5(4):373–401

    Article  Google Scholar 

  7. Ryan A, El Sayed M, Andrew SG, Tjong J, Saeid H (2015) Artificial neural network training utilizing the smooth variable structure filter estimation strategy. Neural Comput Appl. doi:10.1007/s00521-015-1875-2

    Google Scholar 

  8. Calero R, Stashenko E, Martínez JR, López-Giraldo J (2014) Formulation of a new generic density-based model for modeling solubility of polyphenols in supercritical carbon dioxide and ethanol. J Supercrit Fluids 85:116–122

    Article  Google Scholar 

  9. Chin-Sheng K, I-Cheng Y (2015) Using neural networks to integrate structural analysis package and optimization package. Neural Comput Appl. doi:10.1007/s00521-015-1878-z

    Google Scholar 

  10. Chapman WG, Gubbins KE, Jackson G, Radosz M (1989) SAFT: equation of state solution model for associating fluid. Fluid Phase Equilib 52:31–38

    Article  Google Scholar 

  11. Chapman WG, Gubbins KE, Jackson G, Radosz M (1990) New reference equation of state for associating liquids. Ind Eng Chem Res 29:1709–1721

    Article  Google Scholar 

  12. Huang SH, Radosz M (1990) Equation of state for small, large, polydisperse, and associating molecules. Ind Eng Chem Res 29:2284–2294

    Article  Google Scholar 

  13. Gross J, Sadowski G (2001) Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40:1244–1260

    Article  Google Scholar 

  14. Gross J, Sadowski G (2000) Application of perturbation theory to a hard-chain reference fluid: an equation of state for square-well chains. Fluid Phase Equilib 168:183–199

    Article  Google Scholar 

  15. Gross J, Vrabec J (2006) An equation-of-state contribution for polar components: dipolar molecules. AlChE J 52(3):1194–1204

    Article  Google Scholar 

  16. Gross J, Sadowski G (2001) Perturbed-chain SAFT: an equation of state based on a perturbation theory for chain molecules. Ind Eng Chem Res 40(4):1244–1260

    Article  Google Scholar 

  17. Gross J, Sadowski G (2002) Application of the perturbed-chain SAFT equation of state to associating systems. Ind Eng Chem Res 41(22):5510–5515

    Article  Google Scholar 

  18. Selvi V, Umarani R (2010) Comparative analysis of ant colony and particle swarm optimization techniques. Int J Comput Appl 5(4):0975–8887

    Google Scholar 

  19. Simon ST, Macnaughton JS, Tomaske LD, Foster R (1993) Solubility of naproxen in supercritical carbon dioxide with and without cosolvents. Ind Eng Chem Res 23:1471–1481

    Google Scholar 

  20. Chen YM, Chen YP (2009) Measurements for the solid solubilities of antipyrine, 4-aminoantipyrine and 4-dimethylaminoantipyrine in supercritical carbon dioxide. Fluid Phase Equilib 282:82–87

    Article  Google Scholar 

  21. Chen YM, Lin PC, Tang M, Chen YP (2010) Solid solubility of antilipemic agents and micronization of gemfibrozil in supercritical carbon dioxide. J Supercrit Fluids 52:175–182

    Article  Google Scholar 

  22. Khimeche K, Alessi P, Kikicand I, Dahmani A (2007) Solubility of diamines in supercritical carbon dioxide: experimental determination and correlation. J Supercrit Fluids 41:10–19

    Article  Google Scholar 

  23. Zhen H, Yu-hua G, Miao H, Teng LJ (2014) Solubility of progesterone in supercritical carbon dioxide and its micronization through RESS. Powder Technol 258:66–77

    Article  Google Scholar 

  24. Li S, Varadarajan GS, Hartland S (1991) Solubilities of theobromine and caffeine in supercritical carbon dioxide: correlation with density-based models. Fluid Phase Equilib 68:263

    Article  Google Scholar 

  25. Cortesi A, Kikic I, Alessi P, Turtoi G, Garnier S (1999) Effect of chemical structure on the solubility of antioxidants in supercritical carbon dioxide: experimental data and correlation. J Supercrit Fluids 14:139

    Article  Google Scholar 

  26. Knez Ž, Markočič E, Leitgeb M, Primožič M, Hrnčič MK, Škerget M (2014) Industrial applications of supercritical fluids: a review. Energy 77:235–243

    Article  Google Scholar 

  27. Beckman EJ (2004) Supercritical and near-critical CO2 in green chemical synthesis and processing. J Supercrit Fluids 28:121–191

    Article  Google Scholar 

  28. Ashwini E, Devtalu V, Bari Manoj M, Barhate SD (2013) A review on: novel solubility enhancement technique hydrotropy. Indo Am J Pharm Res 3(6):4670–4679

    Google Scholar 

  29. Pfohl O, Petkov S, Brunner G (1998) High pressure fluid-phase equilibria containing supercritical fluids. In: 8th International conference on properties and phase equilibria for product and process design. Noordwijkerhout, Netherlands

  30. Nannoolal Y, Rarey J, Ramjugernath D (2008) Estimation of pure component properties Part 3. Estimation of the vapour pressure of non-electrolyte organic compounds via contribution and group interactions. Fluid Phase Equilib 269:117–133

    Article  Google Scholar 

  31. Marrero J, Gani R (2001) Group-contribution based estimation of pure component properties. Fluid Phase Equilib 183–184:183–208

    Article  Google Scholar 

  32. Plumb A, Rowe RC, York P, Brown M (2005) Optimisation of the predictive ability of artificial neural network (ANN) models: a comparison of three ANN programs and four classes of training algorithm. Eur J Pharm Sci 25:395

    Article  Google Scholar 

  33. Faúndez CA, Quiero FA, Valderrama JO (2010) Phase equilibrium modeling in ethanol + congener mixtures using an artificial neural network. Fluid Phase Equilib 292:29–35

    Article  Google Scholar 

  34. Si-Moussa C, Hanini S, Derriche R, Bouhedda M, Bouzidi A (2008) Prediction of high-pressure vapor liquid equilibrium of six binary systems, carbon dioxide with six esters, using an artificial neural network model. Braz J Chem Eng 25(1):183–199

    Article  Google Scholar 

  35. Battiti R (1996) Reactive search: towards self-tuning heuristics. In: Rayward-smith VJ, Osman IH, Reeves CR, Smith GD (eds) Modern heuristic search methods, chap 4. Wiley, New York, NY, pp 61–83

    Google Scholar 

  36. Kennedy J, Eberhart R, Shi Y (2001) Swarm intelligence. Morgan Kaufmann, San Francisco, CA

    Google Scholar 

  37. Pazuki GR, Dashtizadeh A, Taghikhane V, Ghotbi C (2006) A new two-parameter cubic equation of state for predicting phase behaviour of pure compounds and mixtures. Fluid Phase Equilib 242:19–28

    Article  Google Scholar 

  38. Slokar YM, Zupanb J, Marechal AM (1999) The use of ANN for modeling of the H2O2/UV decoloration process: part I. Dyes Pigm 42:123–135

    Article  Google Scholar 

  39. Garson GD (1991) Interpreting neural network connections weights. Al Expert: Miller Freeman, Inc, San Francisco, p 46

    Google Scholar 

  40. El Hamzaoui Y, Hernández JA, Silva-Martínez S, Bassam A, Álvarez A, Lizama-Bahena C (2011) Optimal performance of COD removal during aqueous treatment of alazine and gesaprim commercial herbicides by direct and inverse neural network. Desalination 277:325–337

    Article  Google Scholar 

  41. Hernández JA, Rivera W, Colorado D, Moreno-Quintanar G (2012) Optimal COP prediction of a solar intermittent refrigeration system for ice production by means of direct and inverse artificial neural networks. Sol Energy 86:1108–1117

    Article  Google Scholar 

  42. Laidi M, Hanini S (2013) Optimal solar COP prediction of a solar-assisted adsorption refrigeration system working with activated carbon/methanol as working pairs using direct and inverse artificial neural network. Int J Refrig 36:247–257

    Article  Google Scholar 

  43. Hattab N, Motelica-Heino M (2014) Application of an inverse neural network model for the identification of optimal amendment to reduce copper toxicity in phytoremediated contaminated soils. J Geochem Explor 136:14–23

    Article  Google Scholar 

  44. Mohanraj M, Jayaraj S, Muraleedharan C (2015) Applications of artificial neural networks for thermal analysis of heat exchangers—a review. Int J Therm Sci 90:150–172

    Article  Google Scholar 

  45. Hernández JA (2009) Optimum operating conditions for heat and mass transfer in food stuffs drying by means of neural network inverse. Food Control 20:435–438

    Article  Google Scholar 

  46. Coimbra P, Duarte CM, De Sousa HC (2006) Cubic equation-of-state correlation of the solubility of some anti-inflammatory drugs in supercritical carbon dioxide. Fluid Phase Equilib 239:188–199

    Article  Google Scholar 

  47. Coimbra P, Fernandes D, Ferreira P, Gil MH, De Sousa HC (2008) Solubility of Irgacure 2959 photoinitiator in supercritical carbon dioxide: Experimental determination and correlation. J supercrit Fluids 45:277–281

    Article  Google Scholar 

  48. Stassi A, Betteni R, Gazzaniga A, Giordano F, Schiraldi A (2000) Assessment of solubility of ketoprofen and vanillic acid in supercritical CO2 under dynamic condition. J Chem Eng Data 45:161–165

    Article  Google Scholar 

  49. Housaindokht MR, Bozorgmehr MR (2008) Calculation of solubility of methimazole, phenazopyridine and propranolol in supercritical carbon dioxide. J Supercrit Fluids 43:390–397

    Article  Google Scholar 

  50. Li JH, Huang Z, Wei JL, Xu L (2013) A new optimization method for parameter determination in modeling solid solubility in supercritical CO2. Fluid Phase Equilib 25:117–124

    Article  Google Scholar 

  51. Burgos GI, Brennecke S, Stadtherr MA (2004) Solubility measurement and modeling of molecules of biological and pharmaceutical interest with supercritical CO2. Fluid Phase Equilib 220(1):57–69

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to A. Abdallah el hadj.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Abdallah el hadj, A., Laidi, M., Si-Moussa, C. et al. Novel approach for estimating solubility of solid drugs in supercritical carbon dioxide and critical properties using direct and inverse artificial neural network (ANN). Neural Comput & Applic 28, 87–99 (2017). https://doi.org/10.1007/s00521-015-2038-1

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-015-2038-1

Keywords

Navigation