**2. Diabetes mechanisms**

Defects in glucose metabolizing machinery (such as defective insulin secretion, insulin action due to de-expression of insulin receptors or insensitivity of expressed insulin receptors and glucose transporters, decreased peripheral glucose utilization and defective glucose metabolizing enzymes, *etc*.) and consistent efforts of the physiological system to correct the imbalance in glucose metabolism or maintain glucose homeostasis (such as increased insulin secretion, lipolysis, gluconeogenesis, glycogenolysis, *etc*.) place an over exertion on the endocrine system, resulting in hyperglycaemia. The persistent chronic exposure of pancreatic β-cells to the supraphysiological glucose concentrations (hyperglycaemia) results in non-physiological and potentially irreversible β-cell damage, a term known as glucose toxicity which is a gradual, time-related onset of irreversible lesion to pancreatic β-cellular components of insulin content and secretion.

Multiple biochemical pathways and cellular mechanisms for glucose toxicity have been identified and these include glucose autoxidation (resulting from oxidative stress in the presence of chronic hyperglycaemia), protein kinase C (PKC) activation, increased flux through the hexosamine biosynthesis pathway (HBP), formation of advanced glycation endproducts (AGEs), altered polyol pathway flux and altered gene expression. However, all these pathways share in common the formation of highly reactive oxygen intermediates (ROIs) or reactive oxygen species (ROS) which in excess amount and on prolonged exposure induce chronic oxidative stress on the pancreatic β-cell population, which in turn causes defective insulin gene expression and insulin secretion as well as increase pancreatic β-cell death.

Hyperglycaemia leads to the production of ROS which modulates various biological functions by stimulating transduction signals, some of which are involved in the pathogenesis of diabetes mellitus. Thus, redox-sensitive signalling pathways have been shown to play a pivotal role in the development, progression, and damaging effect on βcells population within the pancreatic islet of Langerhans. In the pancreatic tissues, as hyperglycaemia worsens, the redox-sensitive signalling pathways mediating insulin synthesis, storage and release from the pancreatic β-cells becomes compromised progressively. In addition, the oxidative stress induced by chronic hyperglycaemia promotes pancreatic β-cells apoptosis which ultimately resulting in an overt reduction in the insulin secreting pancreatic β-cells population. The hallmarks of these molecular events are pancreatic β-cells failure and hypoinsulinaemia, which constitute the major pathogenic factors in type 1 diabetes mellitus.

Similarly, chronic hyperglycaemia-induced oxidative stress (the presence of an excess amount of reactive oxygen intermediates, due to an imbalance between their formation and degradation as a result of chronic hyperglycaemia) has been considered a proximate cause and common pathogenic factor for tissue/systemic complications of diabetes such as endothelial cells (micro- and macro-angiopathies), nerve cells (neuropathy), proximal renal

resulting from disordered protein metabolism, and derangements in fatty acid and lipids metabolism. If the fasting blood glucose lies between 100 to 130 mg/dl, it is referred to as *Prediabetes* which is associated with an increased tendency or potential of developing *frank* diabetes. A fasting blood glucose of 140 mg/dl or higher is consistent with either type of diabetes mellitus, particularly, when accompanied by classic symptoms of diabetes

Defects in glucose metabolizing machinery (such as defective insulin secretion, insulin action due to de-expression of insulin receptors or insensitivity of expressed insulin receptors and glucose transporters, decreased peripheral glucose utilization and defective glucose metabolizing enzymes, *etc*.) and consistent efforts of the physiological system to correct the imbalance in glucose metabolism or maintain glucose homeostasis (such as increased insulin secretion, lipolysis, gluconeogenesis, glycogenolysis, *etc*.) place an over exertion on the endocrine system, resulting in hyperglycaemia. The persistent chronic exposure of pancreatic β-cells to the supraphysiological glucose concentrations (hyperglycaemia) results in non-physiological and potentially irreversible β-cell damage, a term known as glucose toxicity which is a gradual, time-related onset of irreversible lesion

Multiple biochemical pathways and cellular mechanisms for glucose toxicity have been identified and these include glucose autoxidation (resulting from oxidative stress in the presence of chronic hyperglycaemia), protein kinase C (PKC) activation, increased flux through the hexosamine biosynthesis pathway (HBP), formation of advanced glycation endproducts (AGEs), altered polyol pathway flux and altered gene expression. However, all these pathways share in common the formation of highly reactive oxygen intermediates (ROIs) or reactive oxygen species (ROS) which in excess amount and on prolonged exposure induce chronic oxidative stress on the pancreatic β-cell population, which in turn causes defective insulin gene expression and insulin secretion as well as increase pancreatic β-cell

Hyperglycaemia leads to the production of ROS which modulates various biological functions by stimulating transduction signals, some of which are involved in the pathogenesis of diabetes mellitus. Thus, redox-sensitive signalling pathways have been shown to play a pivotal role in the development, progression, and damaging effect on βcells population within the pancreatic islet of Langerhans. In the pancreatic tissues, as hyperglycaemia worsens, the redox-sensitive signalling pathways mediating insulin synthesis, storage and release from the pancreatic β-cells becomes compromised progressively. In addition, the oxidative stress induced by chronic hyperglycaemia promotes pancreatic β-cells apoptosis which ultimately resulting in an overt reduction in the insulin secreting pancreatic β-cells population. The hallmarks of these molecular events are pancreatic β-cells failure and hypoinsulinaemia, which constitute the major pathogenic

Similarly, chronic hyperglycaemia-induced oxidative stress (the presence of an excess amount of reactive oxygen intermediates, due to an imbalance between their formation and degradation as a result of chronic hyperglycaemia) has been considered a proximate cause and common pathogenic factor for tissue/systemic complications of diabetes such as endothelial cells (micro- and macro-angiopathies), nerve cells (neuropathy), proximal renal

[Diabetes Control and Complication Trial Research Group, 1997].

to pancreatic β-cellular components of insulin content and secretion.

**2. Diabetes mechanisms** 

death.

factors in type 1 diabetes mellitus.

epithelial cell (nephropathy), pancreatic β-cells (pancreatic β-cell failure) through lipid peroxidation and glycation mechanisms in these organs. Hyperglycaemia has been shown to result in glycation (a non-enzymatic conjugation of glucose to proteins leading to the formation of advanced glycation (glycosylation) end-products (AGEs) and tissue damage. Increased glycation and build-up of tissue AGEs have been implicated in the aetiology of diabetes mellitus, its complications and progression because they alter glucose metabolizing enzyme activity, decrease ligand binding, modify protein half-life and alter immunogenicity.

One mechanism by which the effects of glucose toxicity result in chronic hyperglycaemia are thought to be mediated is oxidative stress [Baynes, 1991; Evans *et al*., 2002], and hyperglycaemia is known to be one of the main causes of oxidative stress in type 2 diabetes mellitus [Bonnefont-Rousselot, 2002; Robertson *et al*., 2003]. Oxidative stress is a state of imbalance between free radical generation and mopping up.

Oxidative stress is known to play a pivotal role in the pathogenesis of insulin resistance which is itself is thought to be mediated via its contribution to glucose toxicity, particularly, in insulin target tissues including the pancreatic β-cells [Gleason *et al*., 2000; Fantus, 2004]. Tissues such as the mesangial cells (in the kidneys), retinal cells and pancreatic islets are least endowed with intrinsic antioxidant enzyme expression, including *superoxidases-1* and *- 2*, *catalase* and *glutathione peroxidase* [Hayden & Tyagi, 2002; Robertson, 2004]. Prolonged exposure of pancreatic β-cell to hyperglycaemia, as in diabetes, results in decreased expression of the antioxidant gene *γ-glutamylcysteine ligase* (*γ-GCL*) and down-regulation of the rate-limiting enzyme for glutathione synthesis [Robertson, 2004]. The *γ-GCL* catalyses the rate-limiting step in the synthesis of γ-glutamyl cysteine from cysteine, which forms the substrate for the second enzyme regulating glutathione synthesis [Yoshida *et al*., 1995; Tanaka *et al*., 2002]. Reduced gluthathione plasma and tissue concentrations, as marked by elevated levels of ceruloplasmin, promote free radical generation, production of advanced glycation products (AGEs) and acute flunctuations in glucose concentrations.

In addition, oxidative stress promotes the onset and development of diabetes mellitus by directly decreasing insulin sensitivity and causing direct cytotoxicity to the pancreatic insulin-producing β-cells [Maiese *et al*., 2007]. The generated ROS penetrates through the cell membranes and reacts with the membrane phospholipids through the process of lipid peroxidation as well as reacts with the mitochondrial DNA to distrupt the mitochondrial respiratory machinery (mitochondrial electron transport) which is regulated by NADPH ubiquinone oxidoreductase and ubiquinone-cytochrome c reductase systems [Maiese *et al*., 2007].

Oxidative stress is known to depress the mitochondrial oxidoreductase and citrate synthase activities resulting in significant reductions in mitochondrial oxidative and phosphorylation activities as well as reduces the levels of mitochondrial proteins and mitochondrial DNA in adipocytes, particularly in type 2 diabetes mellitus (Petersen et al., 2003). Oxidative stress has been shown to trigger the opening of the mitochondrial membrane permeability transition pore which results in a significant depletion of mitochondrial NAD+ stores and subsequently apoptotic cell injury (Maiese et al., 2007). In the pancreatic tissues, these cellular events result in depletion of the β-cells population, insulin deficiency while in the skeletal muscle, it manifests as insulin resistance.

Oxidative stress is also known to modify a number of cellular signalling pathways that can results in insulin resistance. For example, a significant increase in muscle protein carbonyl content (often used as a reliable biological marker of oxidative stress) and elevated levels of malondialdehyde and 4-hydrononenal (as reliable indicators of lipid peroxidation) have been implicated in the aetiology of insulin resistance diabetes mellitus [Haber *et al*., 2003].

## **3. Glucose-insulin regulatory system modeling and simulation of OGTT blood glucose concentration dynamics to obtain indices for diabetes risk and detection**

This section deals with the bioengineering modelling of the glucose-insulin regulatory system and the OGTT blood glucose dynamics data, for more reliable detection of diabetes as well as designation of risk to diabetes.

The conventional way of diagnosing diabetes is based on designation of specific values of fasting plasma glucose equal or greater than 126 mg/dl (7.0 mmol/l), and (ii) 2-hour plasma glucose concentration equal or greater than 200 mg/dl (11.1 mmol/l) during OGTT. Instead of this rigid approach, we are proposing that for more reliable monitoring and diagnosis of diabetes, it is more relevant to mathematically characterise the trend of blood glucose concentration rise and decline after an oral intake of 75 g glucose load in OGTT. Hence, we provide the bioengineering analysis of the Glucose-insulin regulatory system and glucose response data, leading to the formulation of a novel nondimensional diabetes index for diagnosis of diabetic patients as well as of those who are at risk of becoming diabetic.

So, in this section, we present the Glucose-Insulin Regulatory System (GIRS) modeling in the form of governing differential equations, and converge to the equation representing blood glucose response to glucose infusion rate. This equation forms the basis of modeling of the Oral Glucose Tolerance Test (OGTT). We then demonstrate how this OGTT model equation's solutions can simulate the OGTT data, to evaluate the model parameters distinguishing diabetes subjects from normal subjects. The climax to this section is the formulation of the Non-dimensional Diabetes Index (DBI), involving combination of the model parameters into just "one number" by which we can reliably detect diabetes. In fact, by determining the range of values of DBI for a big patient population, we can even detect "patients at risk of being diabetic".

### **3.1 Differential equation model of the glucose-insulin system**

With reference to the Blood Glucose-Insulin Control System (depicted in Fig. 1**)**, the corresponding first-order differential equations of the insulin and glucose regulatory subsystems are given by equations (1) and (2) [Dittakavi et al., 2001].

$$\mathbf{x}' = p \mathbf{ - a} \mathbf{x} \text{ - } \beta y \tag{1}$$

$$\mathbf{y}' = \mathbf{q} - \mathfrak{K} - \mathfrak{G}\mathbf{y} \tag{2}$$

where x' and y' denote the first time-derivatives of x and y, x: insulin output, y: glucose output, *p*: insulin input, *q*: glucose input, for unit blood-glucose compartment volume (*V*). In these equations, the glucose-insulin model system parameters (regulatory coefficients) are α *, β,* γ*, δ.*

These coefficients, when multiplied by the blood-glucose compartment volume *V* (which is proportional to the body mass) denote, respectively,

• the sensitivity of insulinase activity to elevated insulin concentration (α*V* ),

content (often used as a reliable biological marker of oxidative stress) and elevated levels of malondialdehyde and 4-hydrononenal (as reliable indicators of lipid peroxidation) have been implicated in the aetiology of insulin resistance diabetes mellitus [Haber *et al*., 2003].

**3. Glucose-insulin regulatory system modeling and simulation of OGTT blood** 

This section deals with the bioengineering modelling of the glucose-insulin regulatory system and the OGTT blood glucose dynamics data, for more reliable detection of diabetes

The conventional way of diagnosing diabetes is based on designation of specific values of fasting plasma glucose equal or greater than 126 mg/dl (7.0 mmol/l), and (ii) 2-hour plasma glucose concentration equal or greater than 200 mg/dl (11.1 mmol/l) during OGTT. Instead of this rigid approach, we are proposing that for more reliable monitoring and diagnosis of diabetes, it is more relevant to mathematically characterise the trend of blood glucose concentration rise and decline after an oral intake of 75 g glucose load in OGTT. Hence, we provide the bioengineering analysis of the Glucose-insulin regulatory system and glucose response data, leading to the formulation of a novel nondimensional diabetes index for diagnosis of diabetic patients as well as of those who are at risk of becoming diabetic. So, in this section, we present the Glucose-Insulin Regulatory System (GIRS) modeling in the form of governing differential equations, and converge to the equation representing blood glucose response to glucose infusion rate. This equation forms the basis of modeling of the Oral Glucose Tolerance Test (OGTT). We then demonstrate how this OGTT model equation's solutions can simulate the OGTT data, to evaluate the model parameters distinguishing diabetes subjects from normal subjects. The climax to this section is the formulation of the Non-dimensional Diabetes Index (DBI), involving combination of the model parameters into just "one number" by which we can reliably detect diabetes. In fact, by determining the range of values of DBI for a big patient population, we can even detect

With reference to the Blood Glucose-Insulin Control System (depicted in Fig. 1**)**, the corresponding first-order differential equations of the insulin and glucose regulatory sub-

> γ−−=

where x' and y' denote the first time-derivatives of x and y, x: insulin output, y: glucose output, *p*: insulin input, *q*: glucose input, for unit blood-glucose compartment volume (*V*). In these equations, the glucose-insulin model system parameters (regulatory coefficients) are

These coefficients, when multiplied by the blood-glucose compartment volume *V* (which is

δ

′

• the sensitivity of insulinase activity to elevated insulin concentration (

*x' = p - ax - βy* (1)

*yxqy* (2)

α*V* ),

**glucose concentration dynamics to obtain indices for diabetes risk and** 

**detection** 

as well as designation of risk to diabetes.

"patients at risk of being diabetic".

α *, β,* γ*, δ.*

**3.1 Differential equation model of the glucose-insulin system** 

systems are given by equations (1) and (2) [Dittakavi et al., 2001].

proportional to the body mass) denote, respectively,


Fig. 1. Physiological model of the Blood Glucose Control system (represented by equations 1 and 2).

From equations (1) and (2), the differential equation model in glucose concentration (y) for insulin infusion rate (*p* = 0) and glucose in flow rate (*q*), is obtained as

$$(\chi'' + \chi'(\alpha + \beta) + \chi(\alpha \delta + \beta \gamma) = q' + \alpha q \tag{3}$$

where *y'* and *y''* denote first and second time derivatives of y.

The transfer-function corresponding to Eqn. (3) is obtained by taking the Laplace transforms on both sides (assuming the initial conditions to be zero). Thereby, we obtain (for glucose response)

$$Y(s) \, / \, Q(s) = \frac{(s + \alpha)}{s^2 + s(\alpha + \delta) + (\alpha \delta + \beta \gamma)} = G(s) \tag{4}$$

### **3.2 Model analysis to simulate Oral Glucose Tolerance Test (OGTT)**

The OGTT model-simulation response curve is considered to be the result of giving an impulse glucose dose (of 4 gm of glucose/liter of blood-pool volume) to the combined system consisting of GI tract and blood glucose concentration (BGCS). Now, we can put down the transfer-function (TF) of the gastro-intestinal (GI) tract to be 1/ (s + α), because the intestinal glucose-concentration variation is an exponential decay, and the exponential parameter value is close to that of the parameter α. When we multiply this GI tract TF [1/(s + α)] by the TF of the blood-pool glucose-metabolism given by Eqn. (4), and put Q(S) = 'G' gm of glucose per litre of blood-pool volume per hour, we get

$$\mathbf{Y}(\mathbf{s}) = \mathbf{G} \left/ \left\{ \mathbf{s}^2 + \mathbf{s} (\alpha + \delta) + (\alpha \delta + \beta \gamma) \right\} \right. \tag{5}$$

The corresponding governing differential equation is now:

$$\begin{aligned} y'' + 2Ay' + ay^2y &= \mathcal{G}\mathcal{S}(t) \\ \text{or} \\ y'' + \mathcal{X}T\_d y' + \mathcal{X}y &= \mathcal{G}\mathcal{S}(t) \end{aligned} \tag{6}$$

wherein ωn (= λ1/2) is the natural frequency of the system, A is the attenuation or damping constant of the system, λ = 2 A /Td = ωn2, and ω = (ωn<sup>2</sup> - A2) 1/2 is the angular frequency of damped oscillation of the system.

The solution of Eq. (6), for an under-damped response (corresponding to that of normal subjects, represented by the lower curve in Fig. 2) is given by

$$y(t) = \text{ (G/}a)e^{-At} \sin \text{ at} \tag{7}$$

where in *ω* (or *<sup>ω</sup>d*) <sup>=</sup><sup>1</sup> 2 2 <sup>2</sup> <sup>n</sup> ( A) ω − .

The solution for over-damped response (corresponding to that of diabetic subjects, represented by the upper curve in Fig 2) is given by:

$$y(t) \equiv (\mathbf{G}/a)e^{\cdot \mathbf{A}t} \text{ sivh } a\mathbf{t} \tag{8}$$

where in *ω* (or *<sup>ω</sup>d*) <sup>=</sup>*<sup>1</sup> 2 2 <sup>2</sup> <sup>n</sup> (A - <sup>ω</sup> )*

The solution for a critically-damped response (in which *A =*ω n), which applies to subjects at risk of becoming diabetic (whose blood glucose response curve would lie between the two curves of normal and diabetic subjects), is given by:

$$y\left(t\right) = G \text{ t } e^{-At} \text{ : }\tag{9}$$

$$\gamma\_A \quad \gamma\_A$$

for *2 2 <sup>ω</sup><sup>n</sup> =A = <sup>λ</sup>,* and derivative-time period *<sup>d</sup> <sup>2</sup> n 2A 2A T= = <sup>λ</sup> <sup>ω</sup>*

These solutions are employed to simulate the clinical data, and to therefore evaluate the model-system parameters A and ω (or λ and *Td*), to not only differentially-diagnose diabetes subjects as well as sbut also to characterize resistance-to-insulin.

Now, we can employ equations (7) and (8) to simulate the OGTT data shown in Fig. 2 to obtain the value of parameters: (i) *λ* = 2*.*6hr*−*2, *Td* = 1*.*08 hr, for the normal subject, and (ii) *λ =*0*.*27hr*−*2 and *Td =* 6.08 hr, for the diabetic subject [Ghista, 2004].

We now formulate the Non-dimensional Diabetes Index (*DBI*), as

$$DBI = AT\_d = \frac{2A^2}{\lambda} = \frac{2A^2}{\omega\_n^2} \tag{10}$$

The value of *DBI* for the normal subject is 1.3, whereas for the diabetic subject it is 4.9. We have further found (in our initial clinical tests) that *DBI* for normal subjects is less than 1*.*6, while the *DBI* for diabetic patient is greater than 4*.*5. Hence a DBI value of 2-4 can suggest that the subject is at risk of becoming diabetic. This is a testimony of how well we have simulated the OGTT by our BME model and employed this DBI to diagnose diabetes.

ω

wherein ωn (= λ1/2) is the natural frequency of the system, A is the attenuation or damping constant of the system, λ = 2 A /Td = ωn2, and ω = (ωn<sup>2</sup> - A2) 1/2 is the angular frequency

The solution of Eq. (6), for an under-damped response (corresponding to that of normal

ω*)e-At sin* 

The solution for over-damped response (corresponding to that of diabetic subjects,

ω

risk of becoming diabetic (whose blood glucose response curve would lie between the two

These solutions are employed to simulate the clinical data, and to therefore evaluate the model-system parameters A and ω (or λ and *Td*), to not only differentially-diagnose diabetes

Now, we can employ equations (7) and (8) to simulate the OGTT data shown in Fig. 2 to obtain the value of parameters: (i) *λ* = 2*.*6hr*−*2, *Td* = 1*.*08 hr, for the normal subject, and (ii)

*2A 2A DBI = AT = =*

The value of *DBI* for the normal subject is 1.3, whereas for the diabetic subject it is 4.9. We have further found (in our initial clinical tests) that *DBI* for normal subjects is less than 1*.*6, while the *DBI* for diabetic patient is greater than 4*.*5. Hence a DBI value of 2-4 can suggest that the subject is at risk of becoming diabetic. This is a testimony of how well we have simulated the OGTT by our BME model and employed this DBI to diagnose

*)e-At sinh* 

*2A 2A T= = <sup>λ</sup> <sup>ω</sup>*

*y(t) = (G/*

*n2y = G*

δ*(t)* 

ω

ω

*n*

*2 2*

*n*

*d 2*

*λ ω*

ω

( ) *-At y t = G t e ;* (9)

*(t)* (6)

*t,* (7)

*t* (8)

n), which applies to subjects at

(10)

*y"+ 2Ay'+*

λ*Tdy'+* λ*y= G*δ

The corresponding governing differential equation is now:

subjects, represented by the lower curve in Fig. 2) is given by

 or *y" +* 

*y(t) = (G /*

represented by the upper curve in Fig 2) is given by:

curves of normal and diabetic subjects), is given by:

The solution for a critically-damped response (in which *A =*

for *2 2 <sup>ω</sup><sup>n</sup> =A = <sup>λ</sup>,* and derivative-time period *<sup>d</sup> <sup>2</sup>*

subjects as well as sbut also to characterize resistance-to-insulin.

*λ =*0*.*27hr*−*2 and *Td =* 6.08 hr, for the diabetic subject [Ghista, 2004]. We now formulate the Non-dimensional Diabetes Index (*DBI*), as

of damped oscillation of the system.

where in *ω* (or *<sup>ω</sup>d*) <sup>=</sup><sup>1</sup> 2 2 <sup>2</sup> <sup>n</sup> ( A) ω − .

where in *ω* (or *<sup>ω</sup>d*) <sup>=</sup>*<sup>1</sup> 2 2 <sup>2</sup> <sup>n</sup> (A - <sup>ω</sup> )*

diabetes.

$$\begin{aligned} \mathbf{y}(t) &= \frac{G}{\alpha \nu} e^{-ck} \sinh \alpha t & \mathbf{y}(t) &= \frac{G}{\alpha \nu} e^{-ck} \sinh \alpha t \\ (\mathcal{A} T\_d &= 4.9) & (\mathcal{A} T\_d &= 1.3) \\ (\mathcal{A} &= 0.808 \ \hbar r^{-1}, \mathcal{A} = 0.26 S \mathcal{T} \ \hbar r^{-2} & (\mathcal{A} = 1.4 \ \hbar r^{-1}, \mathcal{A} = 2.6 \ \hbar r^{-2}) \\ T\_d &= 6.08 \ \hbar r, & T\_d &= 1.08 \ \hbar r, \\ G &= 2.9464 \ \text{g} L^{-1} \hbar r^{-1}) & G &= 1.04 \ \text{g} L^{-1} \hbar r^{-1} \end{aligned}$$

Fig. 2. OGTT Response Curve [Ghista, 2004], showing the glucose concentration responses of normal and diabetic subject.

### **4. Biomedical signal processing and image processing techniques for diabetes analysis**

This section presents different signal and image processing methods that are used to evaluate the effect of diabetes on different organs.

### **4.1 Analysis of the heart rate variability signal**

Heart rate variability (HRV) decreases in patients with diabetes [Acharya et al., 2006; Acharya et al., 2011b; Faust et al., 2011]. This variability can be analyzed in the time domain, frequency domain, and by using non-linear methods. Fig. 3 shows typical HRV signals of normal and diabetes subjects. Visually, it is difficult to notice the variability in these two signals. Hence, analysis in time domain and frequency domain with the use of non-linear methods is necessary. These methods are explained in this section.

Fig. 3. Typical heart rate signals; (a) normal (b) diabetes.

### **4.1.1 Time domain analysis**

The time-and frequency-domain measures of HRV were analyzed by the Task Force of the European Society of Cardiology [Task Force, 1996]. Several time domain parameters are calculated from the original R-R interval: mean R-R interval, standard deviation of the NN intervals (SDNN), standard deviation of differences between adjacent RR (NN) intervals (SDSD), Standard Error, or Standard Error of the Mean (SENN), which is an estimate of the standard deviation of the sampling distribution of means based on the data, number of successive difference of intervals which differ by more than 50 msec expressed as a percentage of the total number of ECG cycles analyzed (pNN50%).

The HRV triangular index (TINN) is the integral of the density distribution (i.e. the number of all NN intervals) divided by the maximum of the density distribution. Thus, six standard measures namely Mean RR, SDNN, SENN, SDSD, pNN50% and TINN were studied.

### **4.1.2 Frequency domain analysis**

Spectral analysis of HRV signal results in three main components: high frequency (HF) component, low frequency (LF) component, and very low frequency (VLF) component [Task Force, 1996]. The influence of the vagus nerve in modulating the sinoatrial node is indicated by the HF component (0.15Hz -40Hz) of the spectrum. The LF component (0.04Hz-.155 Hz) indicates the sympathetic effects on the heart. The VLF component (0.003Hz -.04 Hz) explains many details of the heart, chemoreceptors, thermareceptors, and renin-angiotensin system [Task Force, 1996; Kamath et al., 1987; Van der Akker et al., 1983].

Fig. 4 shows a typical power spectral density (PSD) distribution of the heart rate signals obtained from a normal subject (Fig. 4-a) and a diabetes patient (Fig. 4-b). The beat to beat variation is greater in the normal heart rate signal compared to the diabetes heart rate signal. Hence, the power spectral density is more predominant in HF in the normal subject[Faust et al., 2011].

0 100 200 300 400 500 600 700 800 900 1000

0 100 200 300 400 500 600 700 800 900 1000

sample

The time-and frequency-domain measures of HRV were analyzed by the Task Force of the European Society of Cardiology [Task Force, 1996]. Several time domain parameters are calculated from the original R-R interval: mean R-R interval, standard deviation of the NN intervals (SDNN), standard deviation of differences between adjacent RR (NN) intervals (SDSD), Standard Error, or Standard Error of the Mean (SENN), which is an estimate of the standard deviation of the sampling distribution of means based on the data, number of successive difference of intervals which differ by more than 50 msec expressed as a

The HRV triangular index (TINN) is the integral of the density distribution (i.e. the number of all NN intervals) divided by the maximum of the density distribution. Thus, six standard measures namely Mean RR, SDNN, SENN, SDSD, pNN50% and TINN were studied.

Spectral analysis of HRV signal results in three main components: high frequency (HF) component, low frequency (LF) component, and very low frequency (VLF) component [Task Force, 1996]. The influence of the vagus nerve in modulating the sinoatrial node is indicated by the HF component (0.15Hz -40Hz) of the spectrum. The LF component (0.04Hz-.155 Hz) indicates the sympathetic effects on the heart. The VLF component (0.003Hz -.04 Hz) explains many details of the heart, chemoreceptors, thermareceptors, and renin-angiotensin

Fig. 4 shows a typical power spectral density (PSD) distribution of the heart rate signals obtained from a normal subject (Fig. 4-a) and a diabetes patient (Fig. 4-b). The beat to beat variation is greater in the normal heart rate signal compared to the diabetes heart rate signal. Hence, the power spectral density is more predominant in HF in the normal subject[Faust et

sample

0.7 0.8 0.9 1

0.55

**4.1.1 Time domain analysis** 

**4.1.2 Frequency domain analysis** 

al., 2011].

0.6

0.65

R-R interval

0.7

(a)

(b)

Fig. 3. Typical heart rate signals; (a) normal (b) diabetes.

percentage of the total number of ECG cycles analyzed (pNN50%).

system [Task Force, 1996; Kamath et al., 1987; Van der Akker et al., 1983].

R-R interval

Fig. 4. Typical power spectral density of heart rate signal (a) normal (b) diabetes subject. The PSD of normal heart rate signal has LF, HF components. The diabetic heart rate signal, however, does not have HF components due to lower variability in the heart rate signal [Acharya et al., 2011b].

### **4.1.3 Non-linear parametric analysis of heart rate signals**

Various non-linear parameters can be used to analyze the diabetes heart rate signals. They are Approximate Entropy (ApEn), Correlation Dimension (CD), Largest Lyapunov Exponent (LLE), The Hurst exponent (H), Recurrence plot (RP), and Fractal Dimension (FD).

The Approximate Entropy *ApEn* measures regularity of the time series. The method proposed by Pincus et al can be used to evaluate the ApEn [Pincus, 1991]. For the data points *Nxxx* )(),...,2(),1( , with an embedding dimension *m*, the ApEn or *APEN* is given by:

$$APEN(m, r, N) = \frac{1}{N - m + 1} \Sigma \frac{N - m + 1}{i = 1} \log C\_i^m(r) - \frac{1}{N - m} \Sigma \frac{N - m}{i = 1} \log C\_i^{m + 1}(r) \tag{11}$$

 where ∑ ( ) +− = −−Θ +− <sup>=</sup> 1 1 <sup>1</sup> <sup>1</sup> )( *mN j ji m <sup>i</sup> r mN rC* **xx** is the correlation integral. For this study, *m* is

set to 2, and *r* is chosen as 0.15 times the standard deviation of the original data sequence, and N is the total number of data points.

The *Correlation dimension (CD)* is a quantitative measure of the informational complexity of the heart rate signal [Grassberger, 1983]. Some unique ranges of CD for different cardiac diseases have been proposed by Acharya et al. [2007]. The formula for CD involves the correlation function *C*(*r*), which is the probability that two arbitrary points on the orbit are closer together than *r*. This is done by calculating the separation between every pair of *N* data points and sorting them into bins of width d*r* proportionate to *r*. The correlation dimension can be calculated by using the distances between each pair of points in the set of N number of points, −= *XXjia ji* ),(

$$\mathcal{C}\{r\} = \frac{1}{N^2} \rtimes \left( \text{Number of pairs of (i, j) with } a\{i, j\} \lhd r \right) \tag{12}$$

Correlation dimension (CD) is given by:

$$CD = \lim\_{r \to 0} \frac{\log\left(\mathcal{C}\left(r\right)\right)}{\log\left(r\right)}\tag{13}$$

*The Largest Lyapunov Exponent (LLE)* measures the predictability of the system and determines sensitivity of the system to initial conditions [Rosenstien et al., 1993]. A positive LLE indicates chaos. The LLE is estimated by using a least squares fit to "average "line, and is given by:

$$y(n) = \frac{1}{\Delta t} \langle \ln \left( d\_i(n) \right) \rangle \tag{14}$$

where ( ) *ndi* is the distance between *th i* phase-space point and its nearest neighbor at *th n* time step, and . denotes the average overall phase space points.

*The Hurst Exponent (HE)* indicates the self-similarity and correlation properties of heart rate signal. The *HE* has been defined and proposed by Dangel et al [Dangel et al., 1999]. Unique range of H values has been proposed by Acharya et al, for various cardiac states [Acharya et al., 2007].

$$\mathbf{H} = \log(\mathbf{R}/\mathbf{S}) / \log(\mathbf{T}) \tag{15}$$

where T is the duration of the sample of data and R/S is the corresponding value of rescaled range. An *HE* value of 0.5 indicates the presence of a random walk, *HE* < 0.5 depicts anti persistence, and *HE* > 0.5 indicates the persistence in the signal.

The *Recurrence plot (RP)* can be used to unearth the non-stationarity in the heart rate signals [Acharya et al., 2006], and was originally introduced by Eckmann et al. [Eckmann et al., 1987].

*A Fractal* is a set of points which, when looked at smaller scales, looks similar to the whole group [Madelbrot, 1983]. The Fractal Dimension (FD) determines the complexity of the time series. FD has been used in heart rate analysis to recognise and differentiate specific states of physiologic functions [Acharya et al., 2007].

The heart rate signal is a non-linear and non-stationary signal. The hidden intricacies of the signal can be easily extracted using non-linear analysis methods. The heart rate variation is more random in normal subjects as compared to the diabetes subjects. Hence, most of these non-linear parameters may show distinct values for normal and diabetes subjects. These clinically significant non-linear parameters can be fed into the classifiers as features for automatic classification. Moreover, these non-linear parameters can be combined in the form of an integrated index [Ghista, 2004; 2009a; 2009b]. Such an index may have unique range of values for normal and diabetes classes. Hence, one can diagnose normal and diabetes subjects by just using one index value without the need for automatic classifiers.

### **4.2 Image processing of digital fundus images in diabetic retinopathy**

Diabetic retinopathy is an important complication of diabetes. As the diabetes retinopathy progresses, the number of blood vessels varies, and the exudates appear in the advanced DR stages [Yun et al., 2008; Acharya et al., 2011a]. Different image processing techniques have been used to extract blood vessels and exudates in DR subjects, and these techniques are explained in this section. Moreover, techniques for plantar pressure images analysis, which have proved to be useful in detecting diabetic neuropathy conditions, are also been presented in this section.

### **4.2.1 Retinal blood vessels detection**

The detailed steps involved in the blood vessel detection are shown in Fig. 5 [Nayak et al., 2008; Acharya et al., 2011a; Acharya et al. 2009; Acharya et al., 2011b]. The green

*The Largest Lyapunov Exponent (LLE)* measures the predictability of the system and determines sensitivity of the system to initial conditions [Rosenstien et al., 1993]. A positive LLE indicates chaos. The LLE is estimated by using a least squares fit to "average "line, and

*The Hurst Exponent (HE)* indicates the self-similarity and correlation properties of heart rate signal. The *HE* has been defined and proposed by Dangel et al [Dangel et al., 1999]. Unique range of H values has been proposed by Acharya et al, for various cardiac states [Acharya et

where T is the duration of the sample of data and R/S is the corresponding value of rescaled range. An *HE* value of 0.5 indicates the presence of a random walk, *HE* < 0.5 depicts anti

The *Recurrence plot (RP)* can be used to unearth the non-stationarity in the heart rate signals [Acharya et al., 2006], and was originally introduced by Eckmann et al. [Eckmann et al., 1987]. *A Fractal* is a set of points which, when looked at smaller scales, looks similar to the whole group [Madelbrot, 1983]. The Fractal Dimension (FD) determines the complexity of the time series. FD has been used in heart rate analysis to recognise and differentiate specific states of

The heart rate signal is a non-linear and non-stationary signal. The hidden intricacies of the signal can be easily extracted using non-linear analysis methods. The heart rate variation is more random in normal subjects as compared to the diabetes subjects. Hence, most of these non-linear parameters may show distinct values for normal and diabetes subjects. These clinically significant non-linear parameters can be fed into the classifiers as features for automatic classification. Moreover, these non-linear parameters can be combined in the form of an integrated index [Ghista, 2004; 2009a; 2009b]. Such an index may have unique range of values for normal and diabetes classes. Hence, one can diagnose normal and diabetes

Diabetic retinopathy is an important complication of diabetes. As the diabetes retinopathy progresses, the number of blood vessels varies, and the exudates appear in the advanced DR stages [Yun et al., 2008; Acharya et al., 2011a]. Different image processing techniques have been used to extract blood vessels and exudates in DR subjects, and these techniques are explained in this section. Moreover, techniques for plantar pressure images analysis, which have proved to be useful in detecting diabetic neuropathy conditions, are also been

The detailed steps involved in the blood vessel detection are shown in Fig. 5 [Nayak et al., 2008; Acharya et al., 2011a; Acharya et al. 2009; Acharya et al., 2011b]. The green

subjects by just using one index value without the need for automatic classifiers.

**4.2 Image processing of digital fundus images in diabetic retinopathy** 

( ) ( ) <sup>1</sup> <sup>=</sup> 〈 〉 ln *<sup>i</sup> y(n) d n <sup>Δ</sup><sup>t</sup>* (14)

*i* phase-space point and its nearest neighbor at *th n* time

H log R /S /log T = ( ) () (15)

is given by:

al., 2007].

where ( ) *ndi* is the distance between *th*

physiologic functions [Acharya et al., 2007].

presented in this section.

**4.2.1 Retinal blood vessels detection** 

step, and . denotes the average overall phase space points.

persistence, and *HE* > 0.5 indicates the persistence in the signal.

component of the RGB (Red, Green Blue) blood vessel image is considered for this study. The border of the image is obtained by applying an edge detection algorithm on the inverted green component of the image. Morphological operation is performed by using a disk shaped structuring element (SE) for blood vessels detection. Adaptive histogram equalization is then performed on these images to enhance the image, and subsequently, morphological opening operation is performed using a ball structuring element. Thresholding is carried out on the resulting image followed by the median filtering to obtain the boundary of the image. The small holes are then filled and the boundary is removed. Finally, the image with only blood vessels is obtained (Fig. 7) [Acharya et al., 2011b]. It can be seen from Fig. 7(a) that the number of blood vessels is different in the normal and the proliferative diabetes retinopathy (PDR) classes.

Fig. 5. The block diagram for detecting retinal blood vessels.

## **4.2.2 Exudates detection in digital fundus images**

Fig. 6 shows the block diagram of the exudates extraction in digital fundus images [Acharya et al., 2008; Nayak et al., 2008; Acharya et al., 2011a; Acharya et al., 2011b]. The green component of the original image is extracted and subjected to the morphological closing operation by using octagonal shaped structuring element. Then, the resulting image is subjected to thresholding, and morphological closing operation is carried out by using disk shaped SE.

The edges are detected by using the Canny method. Subsequently, an 80x80 region of interest (ROI) is considered to remove the optic disc, and then the border of the image is also removed. Finally, by performing morphological erosion operation with disk shaped SE of size 3, the final image with only exudates is obtained (Fig. 7) [Acharya et al., 2011b]**.** It can be seen from the Fig. 7(b) that there are no exudates in the normal image, while the PDR image has exudates.

Fig. 6. The block diagram for detecting exudates in digital fundus images.

Fig. 7. Results of blood vessel detection and exudate detection from normal and PDR images. (a) Original normal and PDR images (b) Results of blood vessel detection (c) Results of exudate detection. The number of blood vessels are different for normal and PDR images, and exudates are absent in the normal fundus image.

### **4.3 Plantar pressure distribution image analysis**

430 Biomedical Science, Engineering and Technology

Morphological closing using octagon

Edge detection (Canny)

operation using disk

using SE

Normal (a) PDR

Column wise neighborhood operation

Region of interest

Final Image with only exudates

(ROI)

shaped SE

Original Image Extract Green

Thresholding Morphological

Component

closing using disk SE

Fig. 6. The block diagram for detecting exudates in digital fundus images.

Remove optic disc Remove border Morphological

(b)

(c)

images, and exudates are absent in the normal fundus image.

Fig. 7. Results of blood vessel detection and exudate detection from normal and PDR images. (a) Original normal and PDR images (b) Results of blood vessel detection (c) Results of exudate detection. The number of blood vessels are different for normal and PDR Fig. 8 shows the plantar pressure distribution images of normal subjects, and subjects with diabetes type II without and with neuropathy. It can be seen from the figure that the pressure distribution is different for normal, diabetes without and with neuropathy subjects [Acharya et al., 2008; Acharya et al., 2011b]. This difference can be further analyzed using Fourier transform and discrete wavelet transform (DWT).

Fig. 8. Static pedobarograph images of (a) the normal foot, (b) a diabetic foot with neuropathy, and (c) a diabetic foot without neuropathy.

The important feature used to diagnose the normal, diabetes type II with and without neuropathy classes is the power ratio (PR) that is obtained using the Fourier transform [Rahman et al., 2006]. This method is clearly explained below.

**Fourier domain analysis:** The Fourier spectrum *F(u,v)* of each region of the image can be obtained by using the below equation (16) [Cavanagh et al., 1991]. In this equation, *M* and *N* represent the numbers of rows and columns of the image. The power ratio (*PR*) is the ratio of the high frequency power (*HFP*) to the total power (*TP*). The Fourier spectrum is given by

$$F(\mu, \nu) = \frac{1}{\text{MN}} \sum\_{x=0}^{M-1} \sum\_{y=0}^{N-1} f(x, y) e^{-j2\Pi \left(\frac{\mu x}{M} + \frac{\nu y}{N}\right)} \tag{16}$$

where *x*, *y*,*u and v* are the variables.

*F*(0,0) is the DC component of the image in the frequency domain and is the sum of all the pixels of an image in spatial domain [Cavanagh et al., 1991]. The *total power (TP)* of the image is given by

$$TP = \left[\sum\sum \left| F(\mu, \nu) \right|^2 \right] - \left| F(0, 0) \right|^2 \tag{17}$$

Fig. 9. Typical power spectra after deleting the DC component from region 6 of the left foot for (a) normal subject (b) diabetes subject without neuropathy (c) diabetes subject with neuropathy[Acharya et al., 2011b].

0

0

0

(c) Fig. 9. Typical power spectra after deleting the DC component from region 6 of the left foot for (a) normal subject (b) diabetes subject without neuropathy (c) diabetes subject with

Frequency v cycles/sec Frequency u cycles/sec

0

20

40

neuropathy[Acharya et al., 2011b].

Power spectrum

10

20

30

40

(b)

Frequency v cycles/sec Frequency u cycles/sec

0

20

40

60 -0.5 0 0.5 1 1.5 2 2.5 x 105

Power spectrum

10

20

30

40

(a)

Frequency v cycles/sec Frequency u cycles/sec

0

20

40

60 -1

Power spectrum

10

20

30

40

The low frequency and high frequency components are separated by *So* , which is given by

$$S\_o = \begin{cases} \frac{M}{4} & \text{if } M \le N\\ \frac{N}{4} & \text{if } M \le N \end{cases} \tag{18}$$

$$LFP = \left\{ \sum\_{S(\mu,\nu)=0}^{S\_a} \left| F(\mu,\nu) \right|^2 \right\} - \left| F(0,0) \right|^2 \tag{19}$$

$$HFP = TP - LFP\tag{20}$$

$$PR = \left(\frac{HFP}{TP}\right) \text{x100} \tag{21}$$

where *LFP, HFP*, and *PR,* denote the low frequency power, high frequency power, and the power ratio, respectively.

Fig. 9 shows the typical power spectra obtained for a normal subject, having diabetes without neuropathy, and subject having diabetes with neuropathy. It is a 3D figure, with *u* and *v* frequencies corresponding to row and column. The Y-axis indicates the power. The power spectrum of normal class has a peak in the centre and very small peaks around it. In the case of diabetes without neuropathy, the adjacent peaks are slightly larger; in the case of diabetes with neuropathy, there are dominating peaks on four sides. These plots are unique and depict variation of power spectrum. The PR values extracted from various regions of the plantar image are shown in Table 1[Acharya et al., 2011b]**.** 


Table 1. Power ratio values for the various regions of the plantar pressure images obtained from the three classes.

The PR is the ratio of HF power to the total power. This value is higher for diabetes subjects with neuropathy when compared to the normal and diabetes without neuropathy subjects for regions 1, 2, 5, 6, and 7 (Table 1). These ranges are unique and clinically significant (p<0.0001). These PR features can be used to diagnose the three classes automatically using classifiers.

Likewise, DWT coefficients have also been used to identify the normal, diabetes type II with and without neuropathy classes [Acharya et al., 2008; Acharya et al., 2011b].
