**4. Major physicochemical phenomena used to mitigate the generation of AMD**

The AMDs characteristics vary from site to site, however, for simplicity and without loss of generality the pH usually ranges between acid (close to pH 1 to 3) and slightly acid (around pH 5) which after wastewater treatment needs to reach pH values between 6.5 and 9 to be adequately discarded [60]. The acidity stabilises a concentration of certain heavy metals in aqueous solutions such as copper, zinc, chromium among others and metalloids like arsenic. Several physicochemical phenomena used to remove ions from an aqueous phase are succinctly reviewed in this section from both thermodynamic and kinetic classic modelling standpoints.

### **4.1 Neutralisation: coupled or not with chemical precipitation**

Perhaps this is the most straightforward strategy to treat AMD wastewaters coming from mine sites. The idea is to remove from the aqueous phase dissolved species that might be toxic to human beings and the environment by adding salts with high saturation or solubility product constant (*Kps*) values but very small ones for the ions to be withdrawn. Considering that the AMD is acid, one of the priorities is to bring the pH of the water close to neutral and that is usually accomplished by dosing with an alkali reagent. The release of hydroxyl ions (*OH*� ð Þ *aq* ) to the aqueous solution enhances the hydrolysis of the metal ions promoting the generation of neutral species which will eventually precipitate. The most used reagent at an industrial scale is the quicklime which in presence of water is transformed into slaked lime [61]. In **Figure 9** a usual AMD containing a high concentration of acid (*H*3*O*þ ð Þ *aq* ), heavy metals (*Mn*þ ð Þ *aq* ) and sulphate (*SO*2� 4ð Þ *aq* ) is presented. When adding quicklime, ultimately dissolved calcium ions would react with sulphate forming anhydrite-like structures while hydroxyl ions would form metal hydroxides and simultaneous adjust the pH to neutral values. The precipitation of sparingly soluble species would follow two sequential steps namely nucleation and crystal growth being the former, in many cases, more energy consuming than the latter. That is the reason why seeds and/or surface roughness of different materials would be desirable to improve the precipitation thermodynamic spontaneity and kinetics [62].

### *4.1.1 Thermodynamics*

An initial concentration of metal is *CMe*,0 and of a counter ion (anion, which can be sulphate) is *Cci*,0. The flow rate of liquid enriched in these two ions is *Q*. For

**Figure 9.** *Sketch of the role of different ions formed during the dosing of quicklime to acidic aqueous solutions.*

computation purposes, the dose of leachate of a metal hydroxide (for simplicity, calcium hydroxide or slaked lime) of concentration *Cx* will be considered at a flow rate of *q*. Usually, as *Cx* is relatively high, the following flowrate relationship holds *q* ≪ *Q*. The reagent with higher solubility compared to that of the salt to be precipitated, undertake an ionisation reaction such as that presented in Eq. (13).

$$\text{M(OH)}\_{n'(s)} \longleftrightarrow \text{M}^{n'+}\_{(aq)} + n'\text{OH}^-\_{(aq)}\tag{13}$$

The mathematical condition required for the precipitation to occur is given by Eq. (13).

$$\frac{C\_x Q\_r}{Q} C\_{ci,0} > Kps^{(1)}\tag{14}$$

Then, the efficiency of the treatment can be computed using Eq. (14).

$$\rho = 100 \left\{ \frac{\mathcal{C}\_{\rm x} Q\_r}{2 \mathcal{C}\_{ci,0} Q} + \frac{1}{2} \left[ \sqrt{\left( \frac{\mathcal{C}\_{\rm x} Q\_r}{\mathcal{C}\_{ci,0} Q} - 1 \right)^2 - \frac{K p s^{(1)}}{\mathcal{C}\_{ci,0}^2}} - 1 \right] \right\} \tag{15}$$

The physical units of the different parameters in these equations need to be consistent. Plus, bear in mind that the efficiency of Eq. (15) is overestimated as only the major species were considered in this computation. Simultaneously, the precipitation of metals can be computed from Eq. (16). For the metal precipitation, Eq. (16) needs to be solved.

$$Kps^{(2)} = (\mathcal{C}\_{Me,0} - \mathcal{y})(n'\mathcal{C}\_x - n\mathcal{y})^n \tag{16}$$

Eq. (16) does admit an analytical solution only in very specific conditions, so it is better to solve it numerically. Although it looks like this strategy is quite promising as *Fundamentals and Practical Aspects of Acid Mine Drainage Treatment: An Overview from Mine… DOI: http://dx.doi.org/10.5772/intechopen.104507*

it would be able to remove sulphate, heavy metals and even neutralise the acidic conditions of the AMD, it is somehow misleading for at least four reasons [63, 64]:

During mine closure conditions this strategy is not directly recommended since the reagent dosing control is difficult to implement without personnel in place. However, the fundamentals behind this mechanism still hold. In the scenario of mine closure, the main idea would be to incorporate some sparingly soluble minerals with alkaline behaviour such as silicates, or others.

### *4.1.2 Kinetics*

There are several studies focused on determining the dissolution rate of solids, especially that of quicklime in water. The first stage of dissolution is usually modelled by Eq. (17) [65].

$$\frac{da\_i}{dt} = k(a\_{i, \text{sat}} - a\_i) \tag{17}$$

where *ai* is the activity of the ion "*i*" as a function of time, *ai*,*sat* is the activity of the ion "*i*" in saturation conditions, *t* represents the time, and *k* is a specific rate constant obtained per unit of volume that has been defined as a function of the diffusion coefficient of the ion being transferred from the solid surface to the aqueous solution bulk (*D*), the thickness of the diffusion layer (*δ*), and the specific surface *S V* as presented in Eq. (18) [66].

$$k = \left(\frac{\mathcal{S}}{V}\right)\frac{D}{\delta} \tag{18}$$

The classic shrinking core model with reaction control can also be used (Eq. 18) [67–69].

$$\mathbf{1} - (\mathbf{1} - a)^{\natural \downarrow} = k\_{ct} \mathbf{t} \tag{19}$$

where *α* represents the conversion of the reaction which corresponds to the volume fraction of solid that has been dissolved, and *kcc* is the kinetic rate constant when the process is governed by chemical control.

### **4.2 Adsorption: Chemisorption**

This mechanism aims at removing pollutants from an aqueous phase by fixing them onto a surface of a solid which is stable when immersed in the wastewater. The adsorption mechanism is one of the preferred reactions for wastewater treatment not only because low-cost adsorbents consisting of by-products or wastes from other industries may be used, but also because it may reach high removing efficiencies of dissolved molecules with final concentrations of a few parts per billion [69].  Different reactions between the adsorbent and the aqueous solution lead to the partial dissolution of the adsorbent affecting the local pH near its surface and its stability of the adsorbent suspension whenever forming small particles may occur [70].

There are several drawbacks behind the implementation of adsorption-based technologies. This technology requires optimising the contact between the solid phase and the aqueous phase containing the species to be adsorbed. Usually, piling up of adsorbent material in a column disposed of vertically or horizontally is preferred [71] but maintaining the permeability of the porous medium with time could become a challenge. It is also desirable to implement technologies using chemisorption rather than physisorption. Chemisorption has many advantages such as its specificity exemplified in **Figure 10** by the single and double binding shown for the metal and sulphate. That is, different adsorption sites would be used by different types of adsorbates reducing the competition for adsorption sites. Plus, the relatively high binding energy

**Figure 10.** *Diagram of adsorption processes used in wastewater treatment.*

*Fundamentals and Practical Aspects of Acid Mine Drainage Treatment: An Overview from Mine… DOI: http://dx.doi.org/10.5772/intechopen.104507*

associated with the adsorption process turns it quite irreversible from a kinetic standpoint which reduces the chances of pollutants desorption. Nevertheless, the main disadvantage would be that the eventual saturation of the adsorbent may be reached needing to move forward to a desorption stage to regenerate the adsorbent [72].

### *4.2.1 Thermodynamics*

The thermodynamics of the adsorption process is explained in terms of the adsorption isotherm [73]. The adsorption isotherm is usually plotted in a graph where the y-axis represents the maximum quantity of adsorbed species per unit of the dry mass of adsorbent (also known as specific adsorption) while the x-axis presents the concentration of the species in equilibrium with the specific adsorption measured. All the data is obtained experimentally at a constant temperature and solids percent. There are many mathematical models that can be used to describe the process having each of the conditions and assumptions that as much as possible must represent the specifics of the process under study. The most used adsorption isotherms cited by researchers are the Langmuir and Freundlich isotherms as Eqs. (20) and (21) [74].

$$q\_{i,eq,L} = \frac{\mathcal{S}\_m K\_L a\_{i,eq}}{\mathbf{1} + K\_L a\_{i,eq}} \tag{20}$$

where *qi*,*eq*,*L* corresponds to the volume (or mol) of adsorbate *i* at the surface of the adsorbent in equilibrium conditions, *ai*,*eq* is the equilibrium real concentration of the adsorbate in *molL*�1 , *KL* is the Langmuir isotherm constant commonly associated with the binding energy, *Sm* es the amount of adsorbate required to form a monolayer.

$$q\_{i,eq,F} = K\_F a\_{i,eq}{}^{\vee\_n} \tag{21}$$

where *KF* is the Freundlich empirical constant usually associated with the sorption capacity, and *n* is the sorption intensity.

### *4.2.2 Kinetics*

One general case to model adsorption kinetics is presented in Eq. (23) [75]

$$r = \frac{(kinetic\ factors)(process\ potential)}{(adsortion\ factor)}\tag{22}$$

wherein the numerator there is a description of the classic law of mass action and in the denominator, the inhibition of the adsorption rate procured by the blockage of surface sites of other species in the system is incorporated. For example, the mathematical model for adsorption kinetics of one species labelled with the underscore "*i*" can be described as in Eq. (24) in the case of chemical reaction control.

$$r = k\theta\_i = k \frac{K[a\_i]}{1 + K[a\_i] + \sum\_{j \neq i} K\_j[a\_j]} \tag{23}$$

where *k* is the specific kinetic constant, *θi* is the fractional occupancy of adsorption sites by the main species "*i*", *K* and *ai* are the Langmuir adsorption constant referred

**Figure 11.** *Redox reactions in wastewater treatment.*

to the main ion and its activity in the aqueous phase while *K j* and *a j* are their equivalent but for other ions competing for adsorption sites.


**6. Results**

a standard healthy base. Thus, the daily active energy expenditure should be at least 11

**•** GrS (n=25)-children and adolescents who participated in their daily PA at school according

**•** GrR (n=28)-children and adolescents who participated in their daily PA during a rehabili‐

The first group of subjects (GrS) were asked to wear an accelerometer for 7 consecutive days, starting on the day immediately after they had received monitors at school. The second group (GrR) was monitored during the second week of a summer camp for children and adolescents

Blood samples were collected in the morning using venipuncture after overnight fast. To analyze the children and adolescents' glycemia, the measurements of glucose concentrations, and doses of insulin were repeated 6-8 times per day. The analyses of all individual daily insulin doses were compared to differences in glucose concentrations (Medtronic MiniMed Paradigm 715). Glycated hemoglobin (HbA1c) concentrations were checked (Ames DCA-2000TM Immunoassay Analyzer-normal range: 4.2-6.5%) before and at about two weeks

For each subject the mean insulin dose and the average blood glucose concentrations were monitored in the morning, afternoon, and evening. Moreover, all incidents of hypo-and hyperglycemia were monitored and recorded and so was the time of their occurrence.

Food intake was recorded and compared to dietary recommendations for all study subjects

**GrR (n=28)**

**GrS (n=25)**

Age [yr] 11.5 (3.4) 12.2 (1.5) Body height [m] 1.67 (0.1) 1.55 (0.1) Body mass [kg] 56.0 (9.6) 45.0 (1.0) BMI [kg/m2] 19.8 (1.8) 18.9 (2.3) BMI Centiles[centiles] 51.1 (22.1) 54.5 (23.2) HgA1c [%] 7.16 (0.38) 7.02 (0.3)

**Table 1.** Anthropometric and physiologic features of the study population (mean, SD)

kcal/kg/day in boys and 9 kcal/kg/day in girls on most days within a week [83].

to their educational program and own lifestyle

tation summer camp.

**4. Biochemical assessments**

after the end of the study.

[32, 84].

**Variables**

with diabetes.

76 Glucose Homeostasis

Considering the aim of the study, PA measurements were conducted in two groups:

We studied the effects of energy intake and physical activity on glycaemic control in children and adolescents suffering from diabetes type 1. The variables associated with glucose homeo‐ stasis (e.g. daily insulin doses, energy intake, and glycated hemoglobin (HbA1c) were compared during daily activities and in response to exercise/sports participation in a sample of children and adolescents with T1DM.

The assessment of nutritional status of all children and adolescents who participated in the study showed normal body mass and normal BMI percentile values (57.5 ± 20.5 and 52.7 ± 24.9, respectively). Before the study all children had similar levels of hemoglobin A1c (HbA 1c). Anthropometric features of the two study groups (GrS vs. GrR) were similar for all subjects (Table 1.) Children from the GrS accumulated an average of 8904 ± 981 steps/day while the average activity-induced energy expenditure was 248 ± 40 kcal/day and the relative energy expenditure was 6.06 ± 0.86 kcal/kg/day. The mean number of steps per day during daily PA at school (GrS) was low compared to recommended values (Fig.1).

Analysis of variance revealed a significant effect of physical activity programme during diabetes camp on daily steps (F=44.0; p<0.001) and daily energy expenditure (F=21.0; p<0.001). The two-week adherence to a structured exercise programme increased children and adoles‐ cents physical activity. Diabetic children who participated in the camp (GrR) accumulated an average of 14378 ± 1699 steps/day, corresponding to 466 ± 48 kcal/day; the relative energy expenditure was 10.4 ± 0.85 kcal/kg/day. A comparison of the study subjects who took part in their daily PA at school according to their educational program (GrS) and participants of the camp for diabetics (GrR) revealed significant differences regarding steps per day (p<0.001) and daily energy expenditure (p<0.01) between these groups (Table 2).

T1DM children participated in the camp exhibited a higher tolerance of physical exercise on each day of the investigations (Fig. 1). The average daily dose of insulin (Ins/kg) was similar for all subjects, and no significant differences were observed in GrS compared to GrR. No differences were observed in mean daily serum glucose levels between GrS vs GrR groups (p>0.05) (Table 2). However, based on the measurements of blood glucose concentrations during the day, several incidents of hypo-and hyperglycemia were observed. Two-way ANOVA revealed a significant effect of physical activity levels on hyperglycemic but not hypoglycemic incidents (GrS vs GrR; F=1014.7 p<0.001). GrR exhibited a trend to higher number of hypoglycemic events between 10.00 to 12.00 hours compared to GrS (Fig. 2).The number of hyperglycemic events differed depending on the day of the study (F=442.0, p<0.001). Higher risk of hyperglycemia was noted in children with T1DM who participated in the sports camp. A significant increase in hyperglycemic incidents was diagnosed between 12.00 to 20.00 hours (Fig.3). This trend coincided with the distribution of physical activities carried out during the camp. In the morning we used low-intensity exercise of longer duration while the intensity of afternoon exercises was higher. This might suggest that intense exercise increased the rate of hyperglycemic episodes. A large number of episodes of hyperglycemia directly related to the high intensity exercise may suggest higher glucose levels as a defense mechanism against hypoglycemia.

The analysis of variance indicated a significant effect of the week day on the insulin dose (F=2.2; p<0.05) with significantly higher doses on Sunday compared to Saturday (p<0.05). The average daily glucose concentrations were similar in both groups with a tendency to higher differences in insulin doses in GrR compared to GrS. Sunday results showed an individualized decrease of daily steps, significant increase of insulin doses, and a tendency to hyperglycemia in all investigated diabetics.

**-60**

**0**

\*p<0.05 significant differences between GrS and GrR.

**Figure 2.** The number of hypoglycemic events at particular time of the day.

**1**

**2**

**incidents/day**

**3**

**4**

ces)

**-40**

**-20**

**0**

**steps/day [%]**

**M T W Th F S Sn**

**\*\* \***

The Effects of Energy Intake, Insulin Therapy and Physical Activity on Glucose Homeostasis in…

**\***

**\*\***

http://dx.doi.org/10.5772/57590

79

**\*\*\* \*\*\***

\*p<0.05; \*\*p<0.01; \*\*\*p<0.001 significant differences between GrS and GrR.

**\***

**the days of the week**

**Figure 1.** The number of steps compared to the standards in GrS and GrR. (values presented as percentages differen‐

**6-8 8-10 10-12 12-14 14-16 16-18 18-20 20-22 time of the day [hour]**

**Hypoglycemia GrR Hypoglycemia GrS**

GrR GrS

**20**

**40**

**60**

Analysis of variance revealed a significant effect of daily energy expenditure during school and rehabilitation programme activities on glycated hemoglobin (HbA1c) concentrations (F=5.3; p<0.05). A tendency to increased HbA1c levels was observed in GrS after the two weeks of study while GrR subjects had slightly lower levels after the summer camp (Fig. 4).

Participation in a particular study group had a significant effect on fat consumption (F=15.1; p<0.001) and protein content of the diet (F=6.9; p<0.01). Children with T1DM from GrR group showed higher fat intakes (p<0.05) and lower protein intakes compared to GrS group (p<0.05) (Table 3). Protein consumption was higher compared to standard dietary guidelines for children in both GrS and GrR groups (4.7 % vs 2.6% above, respectively). The average values of fat consumption exceeded standard recommendations for children being higher in GrR compared to GrS (9% vs 3.5% above). Carbohydrates consumption was lower than recom‐ mended in all investigated diabetics (12% for GrS and 15.3% for GrR below the normal ingestion). Significant correlation was observed between total energy intake and insulin dose (r=0.57; p<0.01). Lower physical activity was associated with an individualized increase of daily insulin doses in all investigated subjects.

\*\*p<0.01; \*\*\*p<0.001 significant differences between GrS and GrR.

**Table 2.** Mean energy expenditure, average number of steps, mean daily dose of insulin, and glucose concentrations on successive week days in the GrS and GrR.

The Effects of Energy Intake, Insulin Therapy and Physical Activity on Glucose Homeostasis in… http://dx.doi.org/10.5772/57590 79

\*p<0.05; \*\*p<0.01; \*\*\*p<0.001 significant differences between GrS and GrR.

number of hypoglycemic events between 10.00 to 12.00 hours compared to GrS (Fig. 2).The number of hyperglycemic events differed depending on the day of the study (F=442.0, p<0.001). Higher risk of hyperglycemia was noted in children with T1DM who participated in the sports camp. A significant increase in hyperglycemic incidents was diagnosed between 12.00 to 20.00 hours (Fig.3). This trend coincided with the distribution of physical activities carried out during the camp. In the morning we used low-intensity exercise of longer duration while the intensity of afternoon exercises was higher. This might suggest that intense exercise increased the rate of hyperglycemic episodes. A large number of episodes of hyperglycemia directly related to the high intensity exercise may suggest higher glucose levels as a defense mechanism

The analysis of variance indicated a significant effect of the week day on the insulin dose (F=2.2; p<0.05) with significantly higher doses on Sunday compared to Saturday (p<0.05). The average daily glucose concentrations were similar in both groups with a tendency to higher differences in insulin doses in GrR compared to GrS. Sunday results showed an individualized decrease of daily steps, significant increase of insulin doses, and a tendency to hyperglycemia in all

Analysis of variance revealed a significant effect of daily energy expenditure during school and rehabilitation programme activities on glycated hemoglobin (HbA1c) concentrations (F=5.3; p<0.05). A tendency to increased HbA1c levels was observed in GrS after the two weeks

Participation in a particular study group had a significant effect on fat consumption (F=15.1; p<0.001) and protein content of the diet (F=6.9; p<0.01). Children with T1DM from GrR group showed higher fat intakes (p<0.05) and lower protein intakes compared to GrS group (p<0.05) (Table 3). Protein consumption was higher compared to standard dietary guidelines for children in both GrS and GrR groups (4.7 % vs 2.6% above, respectively). The average values of fat consumption exceeded standard recommendations for children being higher in GrR compared to GrS (9% vs 3.5% above). Carbohydrates consumption was lower than recom‐ mended in all investigated diabetics (12% for GrS and 15.3% for GrR below the normal ingestion). Significant correlation was observed between total energy intake and insulin dose (r=0.57; p<0.01). Lower physical activity was associated with an individualized increase of

> **GrS (n=25)**

**Table 2.** Mean energy expenditure, average number of steps, mean daily dose of insulin, and glucose concentrations

Energy expenditure [kcal/kg/day] 6.06 (0.86) 10.4 (0.85)\*\* Average number of steps [steps/day] 8904 (981) 14378 (1699)\*\*\* Dose of insulin [u/kg/day] 0.39 (0.03) 0.41 (0.03) Glucose concentration [ mg/dl] 125.1 (8.6) 129.8 (4.5)

**GrR (n=28)**

of study while GrR subjects had slightly lower levels after the summer camp (Fig. 4).

against hypoglycemia.

78 Glucose Homeostasis

investigated diabetics.

**Variables**

daily insulin doses in all investigated subjects.

\*\*p<0.01; \*\*\*p<0.001 significant differences between GrS and GrR.

on successive week days in the GrS and GrR.

**Figure 1.** The number of steps compared to the standards in GrS and GrR. (values presented as percentages differen‐ ces)

\*p<0.05 significant differences between GrS and GrR.

**Figure 2.** The number of hypoglycemic events at particular time of the day.

**Variables**

**GrS (n=25)**

The Effects of Energy Intake, Insulin Therapy and Physical Activity on Glucose Homeostasis in…

Energy supply with diet [kcal/kg/day] 38.8 (15.6) 35.6 (10.8)

Fat intake [g/kg/day] 1.4 (0.8) 1.7 (0.7)\*

Carbohydrate intake [g/kg/day] 3.5 (1.8) 3.2 (1.2)

Protein intake [g/kg/day] 2.1 (1.5) 1.9 (0.8)\*

protocols may increase the risk of hyperglycemic episodes [51, 57, 62, 89].

maintaining normoglycemia in children with type 1 diabetes.

**Table 3.** Mean energy supply with diet, mean daily fat, carbohydrate, and protein intake on successive days of the

Children and adolescents engage in different types of exercise, most frequently in unplanned and spontaneous physical activities, which can, of course, be associated with immediate and long-term health benefits [36, 62, 85-86]. Children with T1DM gain similar health benefits from physical exercise as their healthy peers; however, due to several consequences of the disease, some specific characteristics of their adaptation to exercise should be considered. Diabetic children and adolescents differ from the healthy pediatric population in their physiological responses to exercise. They are characterized by impaired utilization of exogenous glucose as an energy source during exercise despite hyperinsulinemia and higher rates of perceived exertion, which persist after glucose ingestion [60, 87]. In patients with diabetes, exercise may increases insulin sensitivity and insulin absorption from the site of administration. Plasma glucose levels decrease during and after low-and moderate intensity exercise in response to enhanced glucose utilization in skeletal muscle [88]. In contrast, high-intensity exercise

In the present study we analyzed the level of physical activity of children and adolescents with type 1 diabetes and the effect of exercise intensity to compensate blood glucose level depending on the insulin treatment and the diet. Furthermore the aim of the study was to determine the energy expenditure associated with the programmed physical activity which is effective for

The major findings of our study are that: 1) physical activity in children with type 1 diabetes was lower than the standards for the population of healthy children and recommendations for health training, 2) programmed physical activity significantly increased daily energy expen‐ diture; however, may also increase the risk of hyperglycemia, 3) greater physical activity

\*p<0.05 significant differences between GrS and GrR.

week in the GrS and GrR.

**7. Discussion**

**GrR (n=28)**

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81

**Figure 3.** The number of hyperglycemic events at particular time of the day. \*\*p<0.01; \*\*\*p<0.001 significant differen‐ ces between GrS and GrR.

**Figure 4.** Glycated hemoglobin concentrations (HbA1c%) in GrS and GrR before and after two weeks of study.

**Table 3.** Mean energy supply with diet, mean daily fat, carbohydrate, and protein intake on successive days of the week in the GrS and GrR.


**Acknowledgements**

Financial assistance from Natural Sciences and Engineering Research Council (NSERC) of Canada is gratefully acknowledged. A special thank you to Dr. Harold Szu for the numerous discussions we have had (VK) on ANNs during several SPIE conferences.


**Hilbert transform system:**

The delay of (filter tap length)/2 is given to I-channel of IQ-signals. It and the Hilbert transform output of Q-signal are subtracted or added. The direction separated signals are calculates by formulas (9) and (10). Here a convolution is indicated . The tap number is set to 128 in the estimation of the calculation load shown in Table 3.

$$F1(n) = \operatorname{Re}\left(X(n - n \text{trap } / \, \mathcal{D})\right) + \operatorname{Im}\left(X(n) \otimes h1(n \text{trap})\right) \tag{9}$$

$$R1(n) = -\operatorname{Re}\left(X(n - n\text{trap }/\ \mathcal{D})\right) + \operatorname{Im}\left(X(n) \otimes h1(n\text{trap})\right) \tag{10}$$

The coefficient *h1* of Hilbert transform is given by a formula (11).

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 219

Z

IQ signal is modulated and frequency is shifted *+fs/4* and *–fs/4*. The positive-component (0 to *+fs/2*) and negative-component (*-fs/2* to *0*) are extracted by LPF. The *+fs/4* shift and the *–fs/4* shift are returned by demodulation. The direction separation outputs are calculated by formulas (20) and (21). The example of Table 3 is referred to the prior art. The 128-tap FIR

> 5( ) ( ) exp ( ) exp 2 2 *F n Xn j n CLPF ntap j n* § · § · § · S

> 5( ) ( ) exp ( ) exp 2 2 *R n Xn j n CLPF ntap j n* § · § · § · S

The direction separation outputs are calculated by formulas (22) and (23).

There are two sets of phase-shifter with the transfer characteristic that makes relative phase difference of IQ-signal 90 degree. The addition-and-subtraction of these outputs is used.

*F z X z Phase z X z Phase z* 6( ) Re ( ) 1( ) Im ( ) 2( )   (22)

The two sets of phase-shifter are the cascade connection of second-order all-pass filter arrays. They are denoted by formulas (24) and (25) as a *Phase1 (z)* and a *Phase2 (z).* In the estimation of Table 3, the cascade connections of four steps of all-pass filters are used. Moreover, in order to improve the performance near the Nyquist frequency, an interpolator and a decimator are added before and after phase-shifter. Table 3 is calculated in *N*= 4, and

 (19)

 S

 S

§ · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹ © ¹ (20)

§ · ¨ ¸ ¨ ¸ ¨ ¸ ¨ ¸ © ¹ © ¹ © ¹ © ¹ (21)

*R z X z Phase z X z Phase z* 6( ) Re ( ) 1( ) Im ( ) 2( )   (23)

1

1

*n k k k*

*a z*

*b z*

*n k k k*

1 1( ) 1

1 2( ) 1

*z a Phase z*

*z b Phase z*

Above six kinds of signal-processing algorithms are confirmed by the simulation. The chirpwaveform that frequency and a direction are changed is used as an input. The result of a simulation is shown in Fig. 7. Fig. 7(a) is an input signal and the sign of frequency has inverted near 200ck (equivalent to the time shown in the Fig. 7 broken line). A solid line is Isignal and a dotted line is Q-signal. Figures 7(b) to (g) are output waveforms of each signalprocessing system. A solid line is a positive-output (forward) of the Doppler audio, and a dotted line is a negative-output (reverse) of the Doppler audio. Amplitude of positiveoutput becomes large on the right-hand side of a broken line, and it becomes small on the

1

1

(24)

(25)

*R n IFFT WR FFT X n h n* 4( ) Re ( ) ( ) 4( )

**Modulation/demodulation system:**

**Phase-shift system:**

low-pass filter, which has 63/128 cut-off, is used.

the FIR filter of *2N* tap is used as an interpolator.

$$\begin{aligned} h1(n) &= \frac{2}{\pi} \cdot \frac{\sin^2(\pi \cdot n / 2)}{n} \quad &\text{( $n \neq 0$ )}\\ &= 0 \quad &\text{( $n = 0$ )} \end{aligned} \tag{11}$$

#### **Complex FIR system:**

There is a report of the Doppler audio separation processing using a complex FIR filter. However, since there is no description about a filter coefficient, we designed in a frequency domain and transformed into FIR coefficient in time domain using inverse Fourier transform. The output of complex FIR system is denoted by formulas (12) and (13). In the estimation of Table 3, the 128-tap coefficient sequence with the pass band of r *fs* /128 to r 63 /128 *fs* is used.

$$F2(n) = X(n) \otimes HF2(n \text{top}) \tag{12}$$

$$R\mathfrak{D}(n) = X(n) \otimes HR\mathfrak{D}(n \text{top}) \tag{13}$$

#### **Complex IIR system:**

Based on the shift theory of Fourier transform, frequency shift is applied to *z* operators. A real-LPF transfer function is changed into the positive-BPF and the negative-BPF. The complex IIR transfer functions become a formulas (14) and (15).

$$F\mathfrak{Z}(z) = HF\mathfrak{Z}(z) \cdot X(z) \tag{14}$$

$$R\mathfrak{B}(z) = HR\mathfrak{B}(z) \cdot X(z) \tag{15}$$

When the transfer function of real LPF is set to *RLPF (z),* transfer functions of *HF3 (z')* and *FR3 (z'')* are calculated by transformed operators. In the estimation of Table 3, the filter with the 8th order Butterworth type is used.

$$HF3(z) = RLPFS(z') \qquad \text{where} \qquad z' = -j \cdot z \tag{16}$$

$$\text{RHS}(z) = \text{RLPF3}(z'') \quad \text{where} \quad z'' = \mathbf{j} \cdot \mathbf{z} \tag{17}$$

#### **FFT/IFFT system:**

The IQ-signal is separated by the positive-filter and negative-filter in a frequency domain. Next, the separated spectra are returned to waveforms in time domain by inverse-FFT. There is a report of this system aiming at the Doppler noise rejection. For the continuous output after inverse-FFT, a shift addition of the time waveform is carried out in time domain. The outputs of this system can be denoted by formulas (18) and (19). In estimation of Table 3, FFT/IFFT point number is set to 128, and used the frequency filter of r *fs* /128 to r 63 /128 *fs* for separation. Moreover, Hamming window (*h4*) is applied, and 32 timeseries are shift-added.

$$F4(n) = \operatorname{Re}\left\{IFFT\left(VNF(o) \cdot FFT\left(X(n)\right)\right)\right\} \cdot h4(n) \tag{18}$$

$$R4(n) = \operatorname{Re}\left(IFFT\left(VRR(a) \cdot FFT\left(X(n)\right)\right)\right) \cdot h4(n) \tag{19}$$

#### **Modulation/demodulation system:**

IQ signal is modulated and frequency is shifted *+fs/4* and *–fs/4*. The positive-component (0 to *+fs/2*) and negative-component (*-fs/2* to *0*) are extracted by LPF. The *+fs/4* shift and the *–fs/4* shift are returned by demodulation. The direction separation outputs are calculated by formulas (20) and (21). The example of Table 3 is referred to the prior art. The 128-tap FIR low-pass filter, which has 63/128 cut-off, is used.

$$F5(n) = \left( \left( X(n) \cdot \exp\left(-\frac{\pi}{2} \cdot j \cdot n\right) \right) \otimes \text{CLPF}(n \text{tap}) \right) \cdot \exp\left(+\frac{\pi}{2} \cdot j \cdot n\right) \tag{20}$$

$$R\mathbf{5}(n) = \left( \left( X(n) \cdot \exp\left( + \frac{\pi}{2} \cdot j \cdot n \right) \right) \otimes \text{CLPF}(n \text{atap}) \right) \cdot \exp\left( -\frac{\pi}{2} \cdot j \cdot n \right) \tag{21}$$

#### **Phase-shift system:**

218 Applications of Digital Signal Processing

*n h n n n*

There is a report of the Doppler audio separation processing using a complex FIR filter. However, since there is no description about a filter coefficient, we designed in a frequency domain and transformed into FIR coefficient in time domain using inverse Fourier transform. The output of complex FIR system is denoted by formulas (12) and (13). In the estimation of Table 3, the 128-tap coefficient sequence with the pass band of r *fs* /128 to

Based on the shift theory of Fourier transform, frequency shift is applied to *z* operators. A real-LPF transfer function is changed into the positive-BPF and the negative-BPF. The

When the transfer function of real LPF is set to *RLPF (z),* transfer functions of *HF3 (z')* and *FR3 (z'')* are calculated by transformed operators. In the estimation of Table 3, the filter with

*HF z RLPF z* 3( ) 3( ') where *z jz* ' (16)

The IQ-signal is separated by the positive-filter and negative-filter in a frequency domain. Next, the separated spectra are returned to waveforms in time domain by inverse-FFT. There is a report of this system aiming at the Doppler noise rejection. For the continuous output after inverse-FFT, a shift addition of the time waveform is carried out in time domain. The outputs of this system can be denoted by formulas (18) and (19). In estimation of Table 3, FFT/IFFT point number is set to 128, and used the frequency filter of r *fs* /128 to r 63 /128 *fs* for separation. Moreover, Hamming window (*h4*) is applied, and 32 time-

> *F n IFFT WF FFT X n h n* 4( ) Re ( ) ( ) 4( )  Z

complex IIR transfer functions become a formulas (14) and (15).

S

**Complex FIR system:**

r 63 /128 *fs* is used.

**Complex IIR system:**

**FFT/IFFT system:**

series are shift-added.

the 8th order Butterworth type is used.

2 2 sin ( / 2) 1( ) ( 0)

z

S

0 ( 0)

*n*

*F n X n HF ntap* 2( ) ( ) 2( ) (12)

*R n X n HR ntap* 2( ) ( ) 2( ) (13)

*F z HF z X z* 3( ) 3( ) ( ) (14)

*R z HR z X z* 3( ) 3( ) ( ) (15)

  (18)

*HR z RLPF z* 3( ) 3( '') where *z jz* '' (17)

(11)

There are two sets of phase-shifter with the transfer characteristic that makes relative phase difference of IQ-signal 90 degree. The addition-and-subtraction of these outputs is used. The direction separation outputs are calculated by formulas (22) and (23).

$$F\mathfrak{G}(z) = \operatorname{Re}\left(X(z)\right) \cdot \operatorname{Phase1}(z) + \operatorname{Im}\left(X(z)\right) \cdot \operatorname{Phase2}(z) \tag{22}$$

$$R\Theta(z) = -\operatorname{Re}\left(X(z)\right) \cdot \operatorname{Phase1}(z) + \operatorname{Im}\left(X(z)\right) \cdot \operatorname{Phase2}(z) \tag{23}$$

The two sets of phase-shifter are the cascade connection of second-order all-pass filter arrays. They are denoted by formulas (24) and (25) as a *Phase1 (z)* and a *Phase2 (z).* In the estimation of Table 3, the cascade connections of four steps of all-pass filters are used. Moreover, in order to improve the performance near the Nyquist frequency, an interpolator and a decimator are added before and after phase-shifter. Table 3 is calculated in *N*= 4, and the FIR filter of *2N* tap is used as an interpolator.

$$Phase1(z) = \prod\_{k=1}^{n} \frac{z^{-1} - a\_k}{1 - a\_k \cdot z^{-1}} \tag{24}$$

$$Phase2(z) = \prod\_{k=1}^{n} \frac{z^{-1} - b\_k}{1 - b\_k \cdot z^{-1}} \tag{25}$$

Above six kinds of signal-processing algorithms are confirmed by the simulation. The chirpwaveform that frequency and a direction are changed is used as an input. The result of a simulation is shown in Fig. 7. Fig. 7(a) is an input signal and the sign of frequency has inverted near 200ck (equivalent to the time shown in the Fig. 7 broken line). A solid line is Isignal and a dotted line is Q-signal. Figures 7(b) to (g) are output waveforms of each signalprocessing system. A solid line is a positive-output (forward) of the Doppler audio, and a dotted line is a negative-output (reverse) of the Doppler audio. Amplitude of positiveoutput becomes large on the right-hand side of a broken line, and it becomes small on the

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 221

The comparison of time-delay is shown in Table 2. Frequency resolution is adjusted by parameter of each system in accordance with the target performance of Table 1. Since the signal-processing inputs are sampled by *fs*, time-delay will become large if *fs* becomes low. Table 2 is calculated by *fs*=4kHz condition. Incidentally by *fs*=1kHz, time-delay increases 4 times. The time-delay caused by operation is assumed zero, and estimated only the delay caused by sampling simply. Moreover, the influence of the transient response of the complex IIR system and the phase-shift system is not taking into

(a) input signal

forward

reverse

Fig. 8. Comparison of response between complex FIR method and complex IIR method

method estimation time-delay (ms) Hilbert transform *tap/fs* 32 (*tap*=128) Complex FIR *tap/fs* 32 (*tap*=128) Complex IIR *order/fs* (\*1) 2 (*order*=8) FFT/IFFT *1.5\*N/fs* (\*2) 48 (*N*=128) Moduration/Demoduration *tap/fs* 32 (*tap*=128) Phase shift *max(2,order/N)/fs* (\*1) 1 (*order*=4, *N*=1) Estimated at *fs*=4kHz, (\*1) not including transient response, (\*2) IFFT shift addition pitch is *N/4*

I-channel Q-channel

(c) output signal of the complex IIR system

As calculation load depends on the hardware architecture, the multiplication and addition times per 1 second (floating point single precision) is used for this estimation. Moreover, the complex-multiplication is considered as 4 times, and complex-addition is considered as twice. The overhead of the processing which requires a lot of memory buffers is assumed to be 20%. The other overhead is assumed to be 10%. The calculation elements, estimation formula and calculation load for each signal-processing systems are shown in Table 3. Incidentally, at *fs*=52 kHz (maximum PRF in actual system), calculation load increases 13 times. The result of Table 2 and Table 3 shows that the complex IIR system and the phase-

(b) output signal of the complex FIR system

reverse

Time (ck)

Time (ck)

Time (ck)

consideration here.

Amplitude

Amplitude

Amplitude

Table 2. Comparison of time-delay

forward

left-hand side of the broken line. Amplitude of negative-output becomes small on the righthand side of a broken line, and it becomes large on the left-hand side of the broken line. This result shows that each system works correctly. Moreover, it shows that the waveform and response time at the turning point of sign (near the DC) have a difference among the systems. As these causes, performance differences, such as the response characteristic and delay time, can be considered.

Fig. 7. Chirp wave responses

### **3.3 Comparison of time-delay and calculation load**

The response is important for blood vessel detection, and the time-delay estimates it. The simulation result of the time-delay is shown in Fig. 8. They are response waveforms of the sinusoidal-waveform that changes discontinuously. Solid line and dotted line are I-signal and Q-signal in Fig. 8(a). Amplitude and frequency are changing near the 50ck. The solid lines of Fig. 8(b) and Fig. 8(c) are positive-output waveforms, and dotted lines are negativeoutput waveforms. The output waveform of the complex FIR system of Fig. 8 (b) changed from a turning point of the input shown with the dashed line after 64ck (time shown with the chain line among Fig. 8(b)), and is stable gradually. The output waveform of the complex IIR system of Fig. 8(c) is stable from the turning point after 8ck (time shown with the chain line among Fig. 8(c)).

220 Applications of Digital Signal Processing

left-hand side of the broken line. Amplitude of negative-output becomes small on the righthand side of a broken line, and it becomes large on the left-hand side of the broken line. This result shows that each system works correctly. Moreover, it shows that the waveform and response time at the turning point of sign (near the DC) have a difference among the systems. As these causes, performance differences, such as the response characteristic and

I-channel

Q-channel

(b) output signal of the Hilbert transform system

reverse

forward

reverse

forward

(c) output signal of the complex FIR system

forward

reverse

(d) output signal of the complex IIR system

(e) output signal of the FFT/IFFT system

forward

reverse

(g) output signal of the phase-shift system

The response is important for blood vessel detection, and the time-delay estimates it. The simulation result of the time-delay is shown in Fig. 8. They are response waveforms of the sinusoidal-waveform that changes discontinuously. Solid line and dotted line are I-signal and Q-signal in Fig. 8(a). Amplitude and frequency are changing near the 50ck. The solid lines of Fig. 8(b) and Fig. 8(c) are positive-output waveforms, and dotted lines are negativeoutput waveforms. The output waveform of the complex FIR system of Fig. 8 (b) changed from a turning point of the input shown with the dashed line after 64ck (time shown with the chain line among Fig. 8(b)), and is stable gradually. The output waveform of the complex IIR system of Fig. 8(c) is stable from the turning point after 8ck (time shown with

(f) output signal of the modulation/demodulation system

reverse

forward

forward

reverse

Time (ck)

(a) input signal

delay time, can be considered.

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

Amplitude

**3.3 Comparison of time-delay and calculation load**

Fig. 7. Chirp wave responses

the chain line among Fig. 8(c)).

The comparison of time-delay is shown in Table 2. Frequency resolution is adjusted by parameter of each system in accordance with the target performance of Table 1. Since the signal-processing inputs are sampled by *fs*, time-delay will become large if *fs* becomes low. Table 2 is calculated by *fs*=4kHz condition. Incidentally by *fs*=1kHz, time-delay increases 4 times. The time-delay caused by operation is assumed zero, and estimated only the delay caused by sampling simply. Moreover, the influence of the transient response of the complex IIR system and the phase-shift system is not taking into consideration here.

Fig. 8. Comparison of response between complex FIR method and complex IIR method

Estimated at *fs*=4kHz, (\*1) not including transient response, (\*2) IFFT shift addition pitch is *N/4*

### Table 2. Comparison of time-delay

As calculation load depends on the hardware architecture, the multiplication and addition times per 1 second (floating point single precision) is used for this estimation. Moreover, the complex-multiplication is considered as 4 times, and complex-addition is considered as twice. The overhead of the processing which requires a lot of memory buffers is assumed to be 20%. The other overhead is assumed to be 10%. The calculation elements, estimation formula and calculation load for each signal-processing systems are shown in Table 3. Incidentally, at *fs*=52 kHz (maximum PRF in actual system), calculation load increases 13 times. The result of Table 2 and Table 3 shows that the complex IIR system and the phase-

Complex Digital Filter Designs for Audio Processing in Doppler Ultrasound System 223

separation performance. The separation performance is deteriorated especially near the

*tap* =128 *tap* =32 *tap* =8

Power (dB)

forward forward

Power (dB)

forward forward

Power (dB)

forward forward

Fig. 9. Example of frequency response: the Hilbert transform system

(a) the Hilbert transform system

Frequency (*fs*) (c) the complex IIR system

(e) the modulation/demodulation

Frequency (*fs*)

reverse reverse

reverse reverse

Frequency (*fs*)

We made the target performances of the direction separating process of digital Doppler audio, and evaluated six kinds of digital-signal-processing ideas that were pre-existing or were newly devised. The performances of each processing were evaluated by comparing

1. The complex IIR system and the phase-shift system are filling the target performance of

2. The target performance of direction separation is filled except for the phase-shift

Fig. 10. Frequency characterization and direction separation performance

many responses such as chirp or step and so on. The results are following.

reverse reverse

Frequency (*fs*)

(b) the complex FIR system

(d) the FFT/IFFT system

(f) the phase-shift system

Frequency (*fs*)

Frequency (*fs*)

Frequency (*fs*)

Nyquist frequency.

Power (dB)

Power (dB)

Power (dB)

**3.5 Conclusion**

response time.

system.

Power (dB)

shift system are filling the target performance of time-delay. It turns out that calculation load is light in order of the phase-shift system, the complex IIR system, and the Hilbert transform system.

R-add: real addition, R-mul: real multiplication, Ovh: over head, C-add: complex addition, C-mul: complex multiplication, Calculation load is estimated at *fs*=4kHz

Table 3. Comparison of calculation load


**3. New demand for treating municipal tertiary wastewater**

In the past decades, there have been numerous attempts to employ phycoremediation technologies for the treatment of primary or secondary effluents, while less attention has been given to tertiary treated effluents. Although the advanced physical, chemical, and/or biological techniques used in modern WWTPs can remove the most nutrients, the tertiary effluents still contain considerable loads of N and P contributing to eutrophication. With more concerns of environmental eutrophication and rapid loss of nonrenewable resource of P, how to effectively eliminate the residual nutrients in the final discharge becomes an emerging request for most WWTPs. In Norway, for example, it was reported that more than 900 tons of phosphorus and about 15,000 tons of nitrogen were discharged into the ecosystem via WWTPs per annum [12]. These nutrients are equivalent to approx. 5% and 15% of agriculture P and N fertilizer consumptions as reported at a national level in 2017 [13]. Instead of releasing them to the aquatic environment as pollutants, it is apparently beneficial to recover these nutrients from the released wastewater.

Compared to primary and secondary wastewaters, tertiary treated wastewater has relatively stable pH and less turbidity, and these are acceptable conditions for algae to grow. Furthermore, along with the biological oxidation and denitrification process, tertiary wastewater contains much less organic macronutrients and the major dissolved nutrients are inorganic forms and less bioavailable organic compounds. In fact, they are the preferable medium conditions for algae proliferation. With the potential benefits of biomass valorisation and carbon sequestration, it is conceived that the application of filamentous algae to purify tertiary wastewater could represent a new win-win strategy for WWTPs. However, there is a suspicion on the algae productivity when the filamentous algae are exposed to the treated municipal wastewater. After all, the low concentration of those nutrient residuals (normally in a level of mg L1 ) seems not optimal for the algae growth. In order to address this concern, the case study introduced in this book chapter will provide more details to demonstrate the possibility of employing filamentous phycoremediation for a Norwegian WWTP.