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Biochemical Engineering Journal 79 (2013) 214– 220

Contents lists available at ScienceDirect

Biochemical Engineering Journal

journa l h om epage: www.elsev ier .com/ locate /be j

inetic models and process parameters for ultrasound-assistedxtraction of water-soluble components and polysaccharidesrom a medicinal fungus

i-Ching Cheung, Jian-Yong Wu ∗

epartment of Applied Biology and Chemical Technology, The Hong Kong Polytechnic University, Hung Hom, Kowloon, Hong Kong

r t i c l e i n f o

rticle history:eceived 2 July 2013eceived in revised form 5 August 2013ccepted 21 August 2013vailable online 30 August 2013

eywords:edicinal fungus

olysaccharide

a b s t r a c t

This study was on the kinetics and process parameters for ultrasound-assisted extraction (UAE) of water-soluble components and polysaccharides (PS) from the dry mycelium of a medicinal fungus, Cordycepssinensis Cs-HK1. Four process variables (factors) were evaluated at different levels, ultrasound inten-sity (2.44–44.1 W/cm2), temperature (40–70 ◦C), solid particle size (156.5–750 �m), and solid-to-liquidratio (1/30–1/70 g/mL). The experimental data of yields versus time in most cases were fitted closelyto two empirical kinetic models for solid–liquid extraction, parabolic diffusion equation (y = yo + y1t1/2)and power law (y = ˇtn) with high correlation coefficients (R2) of 0.95–0.99 for total extract yield, and0.90–0.96 for PS yield. The PS yield was increased more significantly than the total extract yield with the

ltrasonic extractioninetic model

ultrasound intensity. Reducing the particle size and increasing the extraction temperature led to a higheryield and extraction rate; increasing the solid-to-liquid ratio (or decreasing the liquid volume) increasedthe PS yield and extraction rate but had little influence on the total extract. Significant correlations werefound between extraction rate (dy/dt) and ultrasound power density (P/V), and between extract yield (y)and energy density (Pt/V). The kinetic and process parameters are useful for rational design and efficientoperation of UAE processes.

. Introduction

Edible and medicinal fungi or mushrooms have been widelypplied as the raw materials of functional foods and nutraceu-ical products because of their proven nutritive and medicinalroperties. Polysaccharides represent a major class of bioac-ive molecules from edible and medicinal fungi that haveotable antitumor, immunomodulatory and other medicinal prop-rties. Polysaccharide-rich water extracts of mushrooms haveeen applied to a wide range of functional food and cosmeticroducts, and some of the purified polysaccharide fractionsuch as �-glucans and polysaccharide-protein (PSP) complexesrom edible and medicinal fungi have found clinical applica-ions for immunotherapy and cancer treatment [1]. Solid–liquidxtraction is the first and important step for recovery and iso-ation of polysaccharides from the fungal materials (mycelia orruit bodies) in both commercial processes and research stud-

es.

Hot-water extraction (HWE) is the most common methodor extraction and isolation of water soluble components and

∗ Corresponding author. Tel.: +852 3400 8671; fax: +852 2364 9932.E-mail address: jian-yong.wu@polyu.edu.hk (J.-Y. Wu).

369-703X/$ – see front matter © 2013 Elsevier B.V. All rights reserved.ttp://dx.doi.org/10.1016/j.bej.2013.08.009

© 2013 Elsevier B.V. All rights reserved.

polysaccharides from medicinal fungi [2,3] and other sources suchas plants and animals. HWE is also a common or standard pro-cedure for preparation of herbal decoctions in traditional Chinesemedicine. However, HWE has two potential drawbacks for extract-ing bioactive products, the high extraction temperature, which isunfavorable for heat sensitive constituents and the long extrac-tion time, which causes high energy consumption and low processefficiency. To overcome these drawbacks of HWE, alternative tech-niques have been developed such as the application of microwave,power ultrasound and high-pressure [4]. Ultrasonic or ultrasound-assisted extraction (UAE) is one of the most widely exploredprocesses for more efficient extraction of bioactive products atlower temperatures than HWE [5,6]. In UAE, high power ultrasoundis applied to the sample liquid either directly with an ultrasonicprobe inserted into the sample liquid or indirectly through waterin an ultrasonic bath. The enhancement of extraction by the son-ication is mostly attributed to the hydrodynamic events associatedwith acoustic cavitation, particularly the shock waves and shearforces resulting from the rupture of cavitation bubbles. At a highintensity, the forces can cause the disruption of fungal cell walls to

release the cell contents into the extracting solvent [5,7]. UAE hasbecome a common laboratory procedure for a long time, thoughits industrial application in large scale is still limited and underdevelopment.

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Many studies have shown that UAE improved the extractionfficiency (shorter time) and also attained higher bioactivity ofhe extracted products than HWE [4,8]. A previous study by ourroup has shown that the UAE was more effective and favor-ble for extraction of polysaccharide-protein (PSP) complexes at aower temperature than HWE from two edible mushrooms, retain-ng higher protein content and higher antioxidant activities [9].owever, most previous studies on UAE have been focused on theptimization of the experimental conditions or process factors andualitative description of their effects, and very few on the quanti-ative relationships between the extraction kinetics and the processactors, particularly ultrasound power and energy.

Cordyceps (Ophiocordyceps) sinensis, generally called the Chineseaterpillar fungus, is a well-known and one of the most valuableedicinal fungi in traditional Chinese medicine [10,11]. Because

f the limited supply and high price of natural Cordyceps fruitody-caterpillar complexes, mycelial fermentation has been widelypplied for commercial production of fungal biomass and polysac-harides by Cordyceps fungi. Present study was to establish theelationship between the UAE kinetics and the process factors forxtraction of water-soluble components and polysaccharides (PS)rom the mycelial biomass of C. sinensis fungus Cs-HK1 and to iden-ify the ultrasonic power and energy parameters for predicting thextraction rate and yield. Modeling the extraction kinetics is usefulot only for predicting the rate and yield but also for understand-

ng the major process factors and their effects on the extractionrocess.

. Materials and methods

.1. Fungal material

C. sinensis species Cs-HK1 was chosen as the representativeedicinal fungus for the kinetic study. The Cs-HK1 fungus was pre-

iously isolated in our lab from the fruiting body of a wild C. sinensisrganism (China General Microbiological Culture Collection Centeregistration No. 6004). The Cs-HK1 mycelial fermentation was per-

ormed in the liquid medium and conditions as reported by Leungt al. [12]. After 6 to 7 days of liquid fermentation, the myceliumiomass was separated from the liquid medium by filtration andhen dried at 50 ◦C in an oven. The dry mycelium biomass wastored in sealed plastic bags at room temperature (23 ± 2 ◦C) beforese.

.2. Ultrasonic processors and power measurement

The ultrasound-assisted extraction (UAE) experiments wereerformed with two 20 kHz ultrasonic processors, one with a max-

mum output power of 130 W (Model VCX-130, Sonics & Materialsnc., Newton, USA) and the other of 900 W (Model CTXNW-2B, Hongiang Long Biotechnology Developing Co., Ltd., Beijing, China). A2 mm-diameter probe was used with the former processor and a5 mm-diameter probe for the latter. The power level in these ultra-onic processors was controlled by adjusting the amplitude ratio%). The actual power P (in W) transferred into the extraction liquidwater) at a given amplitude was determined by the calorimetric

ethod [13]. The measurement was performed in an insulatedolycarbonate flask filled with 100 ml of water and sonicated withhe probe horn for 15–20 min, during which water temperatureas recorded. The actual power was derived from the following

quation,

= CpW(dT

dt)t=0

(1)

here Cp is the heat capacity (4.18 kJ/kg ◦C) and W the mass ofater used for extraction (100 g), and (dT/dt)t = 0 the initial slope

eering Journal 79 (2013) 214– 220 215

of temperature (T) versus time (t) plot. The plots of temperatureversus t within the initial 5-min period were close to linear for bothprocessors (Supplemental data). The actual power was roughly pro-portional to the amplitude shown in the processor panels. Theultrasound intensity I (in W/cm2) is represented by the power perunit area of probe tip (=�r2),

I = P

�r2(2)

2.3. Ultrasound-assisted extraction of fungal mycelium

The Cs-HK1 mycelium was ground into powder with an elec-tric mill and then screened through mesh sieves into differentmean particle sizes. The sample powder was suspended in distilledwater in a 250-ml plastic centrifuge bottle during the ultrasonicextraction. The mass of sample was fixed at 3 g for all experimentsand the volume of water varied from 90 to 210 mL for the desiredsolid–liquid ratio (1/30–1/70 g solid/mL liquid). The sample powderwas suspended in water for 30 min at room temperature (23 ± 2 ◦C)(without stirring) before ultrasonic treatment in all experiments toensure an equal starting point. UAE was performed for a selectedperiod of 10 to 80 min with the ultrasonic probe, which was dippedinto the liquid about 2 cm deep. The sample bottle was immersedin a water bath to maintain a constant extraction temperature dur-ing UAE. The liquid extract was separated from the solid residue bycentrifugation after the extraction. The solid residue was dried at50 ◦C for 2 days and its weight was measured, and deducted fromthe initial solid mass to attain the mass of water-soluble extract.Polysaccharide (PS) was isolated from the water extract by ethanolprecipitation (80% final concentration) at 4 ◦C for overnight. Theprecipitated PS was recovered by centrifugation and freeze-dried.The total extract/PS yield attained from UAE was given by,

y = m − mo

M(3)

where mo and m are the mass of total water extract/PS at the begin-ning of UAE (after 30-min suspension in water) and at a given timeof UAE, respectively, and M is the initial mass of mycelium sample(3 g).

Water extraction (WE) (maceration) was performed at 40 ◦Cwith solid–liquid ratio of 1/30 (g/mL) and mean particle size of156.5 �m for comparison with the UAE of the Cs-HK1 mycelia atthe same conditions. The solid sample (3 g) was suspended in 90 mLwater in a 250-mL centrifugal bottle and placed in a water bath for10–80 min.

2.4. Kinetic models of solid–liquid extraction for UAE

The extraction of fungal mycelium with water is a case ofsolid–liquid extraction. Many theoretical and empirical kineticmodels have been developed for solid–liquid extraction, andapplied to the extraction of food and medicinal products in waterand other solvents [14,15] and also to ultrasonic extraction pro-cesses [16,17]. Because of their simplicity and satisfactory fit toexperimental data, the empirical models have been more widelyused in previous studies on UAE [16,17]. The applicability of a modelto the experimental data of a UAE process is very dependent on thesolid properties. As shown in a recent study by our group on UAEof water soluble components and polysaccharides from differentmedicinal fungi [18], the kinetic characteristics and the suitable

models are dependent on the fungal species and the morphologicalform (mycelium or fruit body). The total water extract and PS yieldsof UAE from fungal mycelia of C. sinensis Cs-HK1 and two othermedicinal fungi were fitted most closely to the parabolic diffusion

216 Y.-C. Cheung, J.-Y. Wu / Biochemical Engineering Journal 79 (2013) 214– 220

Table 1Comparison of the total extract and PS yields by UAE and water extraction (WE) at 40 ◦C (solid–liquid ratio: 1/30 g/mL; mean particle size: 156.5 �m).

Time (min) Total extract yield (g/g) PS yield (g/g)

UAE WE UAE WE

10 0.540 ± 0.026 0.443 ± 0.020 0.122 ± 0.011 0.081 ± 0.00520 0.588 ± 0.051 0.450 ± 0.076 0.145 ± 0.016 0.081 ± 0.00640 0.615 ± 0.033 0.462 ± 0.052 0.154 ± 0.026 0.083 ± 0.010

± 0.03

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80 0.658 ± 0.035 0.488

ote: Yield in this table is m/M, inclusive of mo attained before UAE (different from

odel (R2 > 0.98) and less well to the power-law model (R2 > 0.92)18], Parabolic diffusion:

= yo + y1t1/2 (4)

ower law : y = ˇtn (5)

here y is the total extract or PS yield and t the time of extrac-ion; in Eq. (4), yo is the initial washing-out yield at t = 0 and y1 ishe diffusion coefficient for the diffusion of solute molecules fromhe interior of particles to the solvent; in Eq. (5), is a constantelated to extraction rate and the power-law exponent (<1). Thesewo models were applied in this study to fit the experimental dataf UAE.

.5. Experimental variables (process factors) of UAE

With a given solid material and an extracting solvent (Cs-HK1ungal mycelium extraction with water in this study), particle size,olid–liquid ratio and temperature are three of the most significantactors affecting solid–liquid extraction processes [14]. These arelso identified as the major factors on UAE of bioactive natural prod-cts [19,20] and polysaccharides from mushrooms [21] and fungalycelia [22]. In addition to these factors for solid–liquid extraction,

ltrasound power (P) applied to the system will have a significantnfluence on the UAE process and kinetics. Therefore the UAE exper-ments in this study were performed with four variables (factors),ltrasound power intensity (3 levels: 2.44, 21.7, 44.1 W/cm2, cor-esponding to 30.7, 272.7, 856.6 kW/m3 power density in 90 mLiquid), temperature of the extraction liquid (3 levels: 40, 55, 70 ◦C),olid-to-liquid ratio (3 levels: 1/30, 1/50, 1/70 g/ml) and mean parti-le size of sample powder (2 levels: 156.5, 750 �m). All experimentsere conducted by with one factor variable and the other threexed (one-factor-at-a-time test) in a set of experiments.

All experiments were performed in triplicate and the resultsere represented by means and standard deviation (SD). The

xperimental data, total water extract yield or PS yield from theater extract versus time of UAE for each fungal species, were fitted

o the kinetic models by linear regression (using Microsoft Excel),nd to derive the model constants and the correlation coefficientsR2).

. Results and discussion

.1. Enhancement of polysaccharide extraction by ultrasound

Table 1 shows the total extract and PS yields attained by UAEnd water extraction (40 ◦C) for various extraction periods. At allhe time points, the total extract and PS yields by UAE were notablyigher than those by water extraction. With 80-min UAE, for

nstance, the total extract yield was increased by 35% (net increase.17 g/g) and the PS yield was increased by double compared with

hose of water extraction. The results proved the enhancement ofxtraction by the application of power ultrasound. The more sig-ificant increase in the PS yield suggests that the UAE was moreffective or favorable for the extraction of high molecular weight

1 0.180 ± 0.028 0.085 ± 0.004

)).

constituents than low molecular constituents contained in the totalextract. As most polysaccharides exist as the structural componentsof cell walls, high-intensity ultrasound may cause the breakup ofcell walls through cavitation to release the wall constituents intothe extracting solvent [7–9]. Water at a relatively low temperature(∼40 ◦C) does not cause significant disruption of the cell walls andis not effective to extract the cell wall polymers.

3.2. Effects of process factors on UAE yields

Fig. 1 shows the UAE time courses of total extract andpolysaccharide yields with respect to the four process variablesin an overall period of 80 min. In most of these figures, theyields increased with UAE time more rapidly in the early period(10–20 min) and slower in later period (after 20 min). The increasein ultrasound intensity from 2.44 to 44.1 W/cm2 (or power den-sity from 30.7 to 856.6 kW/m3) resulted in increases in both totalextract and PS yields (Fig. 1a), proving the enhancing effect ofultrasound on the extraction. Both yields also increased with theincrease in temperature from 40 to 70 ◦C (Fig. 1b) and the decreasein particle size from 156.5 to 750 �m (Fig. 1c). Increasing tem-perature promotes diffusion mass transfer, and reducing particlesize increases the mass transfer area, contributing to the enhancedextraction. However, temperature increase from 55 to 70 ◦C ledto a notable increase in the PS yield but not in the total extractyield. This was due probably to that the dissolution of PS from themycelia with water was more dependent on a higher temperaturethan the dissolution of low molecular weight components. Increas-ing the solid–liquid ratio or reducing the liquid volume resultedin a higher PS yield but no significant change in the total extractyield (Fig. 1d). As the liquid volume increases at a fixed ultrasoundpower (P), the power per volume (P/V) decreases, leading to lowerPS yield. For the total extract, the yield is probably more dependenton the concentration-difference driving force that increases withthe liquid volume (dilution effect). The decrease of PS yield shownin Fig. 1d with time from 40 to 80 min at 1/70 solid–liquid ratio maybe attributable to the degradation of the PS extracted into the liq-uid by the mechanical force from acoustic cavitation, which tendsto be more intense in a liquid with low solid content and low PSconcentration [7].

3.3. Kinetic models for UAE

Table 2 shows the model constants and correlation coefficients(R2) obtained from linear regression fit of the experimental datato the two kinetic models. The total extract yields in all conditionswere fitted closely to the two models as indicated by the high R2

values in the range of 0.937–0.999. The PS yields also fitted closelyto the models with R2 values in the range of 0.934–0.977 in mostconditions. Fig. 2 shows the plots of experimental data with thelinearized parabolic model (y versus t½) against four experimen-

tal variables, including ultrasound intensity (Fig. 2a), temperature(Fig. 2b), mean particle size (Fig. 2c) and solid–liquid ratio (Fig. 2d),which demonstrate a close fit of experiment data to the kineticmodel in most cases. However, the regression results do not show

Y.-C. Cheung, J.-Y. Wu / Biochemical Engineering Journal 79 (2013) 214– 220 217

0

0.05

0.1

0.15

0.2

0 20 40 60 80 10 0

Tota

l extr

act yie

ld (

g/g

)

UAE time (min )

2.44 W/cm^ 2

21.7 W/cm^ 2

44.1 W/cm^2

0

0.04

0.08

0.12

0.16

0.2

0 20 40 60 80 10 0

Tota

l extr

act

yie

ld (

g/g

)

UAE time (min)

40C

55C

70C

(b)

0

0.01

0.02

0.03

0.04

0 20 40 60 80 100

PS

yie

ld (

g/g

)

UAE time (min)

(a)

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Tota

l extr

act

yie

ld (

g/g

)

UAE time (min)

156.5μm

750μm

(c)

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PS

yie

ld (

g/g

)

UAE time (min )

(c)

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PS

yie

ld (

g/g

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UAE time (min )

(d)

0

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Tota

l extr

act

yie

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UAE time (min)

1:30

1:50

1:70

(d)

0

0.01

0.02

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0.04

0.05

0.06

0 20 40 60 80 10 0

PS

yie

ld (

g/g

)

UAE time (min)

(b)

(a)

W/cm2

W/cm2

W/cm2

ºC

ºC

ºC

Fig. 1. Time courses of total extract yield (left) and PS yield (right) in UAE of fungal mycelia performed with four process variables: (a) ultrasound intensity (W/cm2); (b)temperature (◦C); (c) mean solid particle size (�m); (d) solid–liquid ratio (g/mL). (The other three variables were fixed at the levels as noted in Table 1; error bars for standarddeviation or SD at n = 3).

aptv(

significant trend of the model constants yo, y1, and n with the

rocess variables. The lack of correlation was probably attributedo the empirical nature of the models and the complex effect ofarious factors on the extraction process, plus experimental errorsin the control of experimental conditions and the measurement

of extract yields). The power-law constant and exponent n var-

ied from 0.0241 to 0.0836 and 0.154 to 0.354 respectively for thetotal extract yields, and from 0.0081 to 0.0195 and 0.172 to 0.399respectively for most of the PS yields (except for the two PS yieldswith poor fit R2 < 0.8) (Table 2).

218 Y.-C. Cheung, J.-Y. Wu / Biochemical Engineering Journal 79 (2013) 214– 220

0

0.05

0.1

0.15

0.2

0 2 4 6 8 10

Tota

l extr

act

yie

ld (

g/g

)

t 1/2

2.44 W/cm^2 21.7 W/cm ^2

44.1 W/cm^2

0

0.01

0.02

0.03

0.04

0 2 4 6 8 10

PS

yie

ld (

g/g

)

t1/2

(a)

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0.15

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0.25

0 2 4 6 8 10

Tota

l extr

act

yie

ld (

g/g

)

t 1/2

156.5 um

750 m

(c)

0

0.02

0.04

0.06

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0 2 4 6 8 10

PS

yie

ld (

g/g

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t1/2

(c)

0

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0.1

0.12

0 2 4 6 8 10

Tota

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ld (

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t 1/2

1/70 1/5 0

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0.02

0.03

0.04

0 2 4 6 8 10

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yie

ld (

g/g

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t1/2

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0

0.05

0.1

0.15

0.2

0 2 4 6 8 10

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l extr

act

yie

ld (

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t1/2

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70

(b)

0

0.01

0.02

0.03

0.04

0.05

0.06

0 2 4 6 8 10

PS

yie

ld (

g/g

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t 1/2

(b)

(a)

W/cm2 W/cm

2

W/cm2

ºCºC

ºC

µm

µ

F (marku m); (s

d

tcps

ig. 2. Fitting of UAE experimental data (left: total extract yields; right: PS yields)

ltrasound intensity (W/cm2); (b) temperature (◦C); (c) mean solid particle size (�hown in Fig. 1).

Table 2 also shows the rate constant, k = ˇn, which is from theerivative of power law Eq. (5),

dy

dt= ktn−1 (6)

In most cases, k value for the total extract yield increased with

he increase in ultrasound intensity and the decrease in parti-le size, and k value for the PS yield increased with ultrasoundower and extraction temperature, and the decrease in particleize. Solid–liquid ratio had a significant effect on the PS extraction

ers) to linearized parabolic diffusion model (lines) with four process variables: (a)d) solid–liquid ratio (g/mL). (Error bars for SD at n = 3; experimental data same as

rate but only slight effect on total extraction rate. Ultrasound powerand temperature also had more significant effect on the PS extrac-tion rate than the total extraction rate. Most of the factor effectson the rate followed the same trends as on the yields of extraction(Fig. 1).

3.4. Kinetic characteristics of UAE process

There are two major differences between the two kinetic mod-els (Eqs. (4) and (5)), an initial yield yo and a fixed exponent 1/2

Y.-C. Cheung, J.-Y. Wu / Biochemical Engineering Journal 79 (2013) 214– 220 219

Table 2Kinetic model constants and correlation coefficients for the total extract and PS yields of UAE derived from linear regression of experimental data.

UAE conditions Parabolic diffusion (Eq. (2)) Power-law (Eq. (3))y0, g/g y1, min−1/2 R2

n k = ˇn R2

Total extract yieldPower intensitya (W/cm2) 2.44 0.0231 0.0078 0.969 0.0241 0.300 0.0072 0.937

21.7 0.0363 0.0074 0.995 0.0317 0.265 0.0084 0.99944.1 0.0487 0.0110 0.950 0.0414 0.289 0.0122 0.980

Mean particle sizeb (�m) 156.5 0.0535 0.0193 0.960 0.0484 0.354 0.0171 0.964750 0.0487 0.0110 0.950 0.0414 0.289 0.0120 0.980

Temperaturec (±3 ◦C) 40 0.0487 0.0110 0.950 0.0414 0.289 0.0120 0.98055 0.0855 0.0089 0.969 0.0725 0.1860 0.0135 0.98070 0.0962 0.0078 0.995 0.0836 0.154 0.0129 0.992

Solid to liquid ratiod (g/mL) 1/70 0.0460 0.0069 0.974 0.0403 0.222 0.0089 0.9641/50 0.0455 0.0064 0.992 0.0387 0.221 0.0085 0.9991/30 0.0363 0.0074 0.995 0.0317 0.265 0.0084 0.999

PS yieldPower intensitya (W/cm2) 2.44 0.0131 0.0006 0.869 0.0121 0.0897 0.0011 0.763

21.7 0.0088 0.0022 0.954 0.0082 0.282 0.0023 0.94344.1 0.0189 0.0017 0.902 0.0156 0.175 0.0023 0.950

Mean particle sizeb (�m) 156.5 0.0168 0.0094 0.959 0.0178 0.399 0.0071 0.952750 0.0189 0.0017 0.902 0.0156 0.175 0.0023 0.950

Temperaturec (±3 ◦C) 40 0.0189 0.0017 0.902 0.0156 0.175 0.0023 0.95055 0.0179 0.0023 0.976 0.0160 0.1943 0.0031 0.93470 0.0257 0.0025 0.979 0.0216 0.195 0.0042 0.939

Solid to liquid ratiod (g/mL) 1/70 0.0135 −0.0008 0.619 0.0195 −0.243 −0.0047 0.4631/50 0.0101 0.0008 0.971 0.0081 0.172 0.0014 0.9771/30 0.0088 0.0022 0.954 0.0082 0.282 0.0023 0.943

(Mass of extract in water before UAE (mo in Eq. (1)): 0.327 ± 0.0161 total extract and 0.0235 ± 0.0059 PS, except for the cases with mean particle size of 156.5 �m,mo = 0.436 ± 0.0029 total extract and 0.0792 ± 0.0055 PS).

a Temperature = 40 ◦C; mean particle size = 750 �m; solid-to-liquid ratio = 1/30 (corresponding power densities: 30.7, 272.7, 856.6 kW/m3).b Temperature = 40 ◦C; power intensity = 44.1 W/cm2; solid-to-liquid ratio = 1/30.c Mean particle size = 750 �m; power intensity = 44.1 W/cm2; solid-to-liquid ratio = 1/30.d ◦ 2.

ietesatwlimoaufdmc(tmmiy

3p

ypsH

(Fig. 4a) with an R2 > 0.80; while the PS yield had a relatively poorcorrelation to E/V, with a R2 > 0.75 (Fig. 4b).

y = 0.0011x + 1.314 6R² = 0.960 8

y = 0.0007x + 0.777 8R² = 0.940 1

y = 0.0005x + 0.460 4R² = 0.912 3

y = 0.0003x + 0.272 7R² = 0.88 1

0

0.5

1

1.5

2

2.5

0 20 0 40 0 60 0 80 0 100 0

dy/d

t of to

tal extr

act

yie

ld (

x10

3,

g/g

/min

)

US po wer den sity, P/ V (kW/ m3)

Temperature = 40 C; mean particle size = 750 �m; power intensity = 21.7 W/cm

n the parabolic model but zero initial yield (at t = 0) and variablexponent n in the power-law model. The parabolic model assumeshat the overall mass transfer process involved in the solid–liquidxtraction is divided into two major steps, an initial washing-outtep for dissolution of the solute molecules on the solid surface and

diffusion step for the transfer of solute molecules from inside ofhe solid particle into the liquid solvent [23]. Compared with theashing out step, the diffusion step is much slower and the rate

imiting step for most solid–liquid systems, which should be mainlynfluenced and enhanced by the ultrasound power. It is probably

ore meaningful and realistic to ignore or eliminate the washing-ut yield from the kinetic models of UAE as in this study. In contrast,

recent report on UAE kinetics of plant components suggests thatltrasound mainly enhanced the washing-out step but not the dif-usion step [24]. As the yield y of total extract and PS from UAE hadeducted the extract yield attained during the 30 min of sampleixing with water before UAE (Eq. (3)) which was quite signifi-

ant (up to 50% of the maximum yield y), yo was small in this studyaccounting for 10% or less of y). This may be the main reason whyhe power-law model was a better fit than the parabolic diffusion

odel to most of the experimental data in this study but parabolicodel was better in the previous study [18], in which UAE started

mmediately after the sample was added to water and the initialields were quite high (accounting for 50% or more of y).

.5. Correlation of extraction rate and yield with ultrasonicower/energy

The result of ultrasonic treatment (e.g., improved extraction

ield and/or rate) is a function of the power (P) and exposureeriod (t). These two variables can be combined into a total ultra-onic energy, the product of power and exposure period, E = P × t.ere, we introduce two scalable ultrasonic process parameters

independent of the volume of liquid, i.e. the power and energyper volume (V) of liquid, P/V (power density) or and E/V (energydensity). The extraction rate for total extract represented by Eq.(6) at various conditions showed a significant and linear correla-tion to P/V (Fig. 3) with R2 > 0.80 and the slope of line, representingthe enhancing effect of ultrasound power on the extraction rate,decreased with time. Based on regression analysis, the experimen-tal data of total extract yield showed a significant correlation to E/V

Fig. 3. Correlation of extraction rate (dy/dt, y = total extract yield) with ultrasoundpower per unit volume of liquid or US power density P/V over various extractionperiods (�10 min � 20 min � 40 min • 80 min) (experimental data of total extractyields from Table 2 at constant temperature 40 ◦C and mean particle size 750 �m).

220 Y.-C. Cheung, J.-Y. Wu / Biochemical Engineering Journal 79 (2013) 214– 220

y = 0.0304x0.176 4

R² = 0.8065

0

0.05

0.1

0.15

0 100 0 200 0 300 0 400 0 500 0

To

tal extr

act yie

ld (

g/g

)

US energy density, E/V (kJ/m3)

y = -2E-09x2 + 1E-05x + 0.0125R² = 0.7545

0

0.01

0.02

0.03

0.04

0 50 0 100 0 150 0 200 0 250 0

PS

yie

ld (

g/g

)

US energy density, E/V (kJ/m3)

(a) (b)

F E perP

4

rpeasstTvpd

A

ea

A

t

R

[

[

[

[

[

[

[

[

[

[

[

[

[

[

Oxford, 1991.[24] P.S. Milic, K.M. Rajkovic, O.S. Stamenkovic, V.B. Veljkovic, Kinetic modeling

ig. 4. Correlations of total extract yield (a) and PS yield (b) with ultrasound energyS yields from Table 2 at temperature 40 ◦C and mean particle size 750 �m).

. Conclusions

The UAE kinetics of water soluble components and polysaccha-ides from a medicinal fungus at various operating conditions andarticle sizes can be adequately represented by two empirical mod-ls, parabolic diffusion and power-law. According to the modelingnalysis, power ultrasound mainly enhanced the slow diffusiontep of extraction and only affected the initial washing-out steplightly. The models provide the quantitative relationship betweenhe extract yield and extraction time, and the ultrasound power.he rate of extraction can be correlated to the ultrasound power perolume of liquid and the yield correlated to the ultrasound energyer volume of liquid. These scalable parameters may be useful foresign, operation and scaling-up of UAE processes.

cknowledgements

This work was supported by grants from the Hong Kong Gov-rnment UGC (GRF Projects PolyU 5036/10P and PolyU 5033/11P)nd The Hong Kong Polytechnic University.

ppendix A. Supplementary data

Supplementary data associated with this article can be found, inhe online version, at http://dx.doi.org/10.1016/j.bej.2013.08.009.

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