蜂巢结构的应用与研究.doc

J I A N G S U U N I V E R S I T Y
蜂巢结构仿生研究与应用

学院名称： 京江学院

专业班级： J高分子1101
学生姓名： 胡文文
学 号： 41211260 16
指导老师： 吴平

2005年 12月

Estimation of human-hemoglobin using honeycomb structure:An application of photonic crystal
abstract
This paper proposes a method to estimate the hemoglobin concentration in human blood using 2D honeycomb photonic crystal structure. Though a few works deal with similar kind of investigation, presentresearch delivers an accurate estimation of hemoglobin as compared to previous works. The principleof investigation is based on linear variation of both photonic band gap and absorbance’s with respect to different concentration of hemoglobin in human blood. Aside these variations, energy transmittedthrough honeycomb photonic crystal structure is also varied linearly with respect to same concentration.In this work, photonic band gap of honeycomb structure is found using plane wave expansion method,whereas absorbance of same structure is computed by employing Maxwell Curl equation. Finally, simulation result revealed that transmitted energy through two dimensional honeycomb photonic crystalstructure containing blood is nicely fitted with linear trend line (

R2 = 1) which lead to an accurate investigation of hemoglobin in human blood. At last, this paper proposes an experimental set up to measurethe said concentrations with the help of an Arduino developmentboard(Uno)containingAtmega320microcontroller.
Keywords:Honeycomb photonic crystal structurePhotonic band gapTransmitted energ
1. Introduction
Photonics crystals are made, artificially created materials inwhich refractive index is periodically modulated in a scale comparable to the scale of the wavelength. Though the concept ofphotonic crystal has originated in the year 1857 by Lord Rayleigh,the research work in the field of photonic crystals is realized afteralmost 100 years, when Yablonovitch and John published twomilestone papers on photonic crystals in 1987 [1–3], since then,photonics have been progressing hastily and showing a remarkableresearch in the field of science and technology. As far as, application of photonic-devices are concerned, photonic crystal play animportant role to envisage various application in modern technology [4–6]. Though photonic crystal is used for different application,sensing application is one of the major relevance in photonics. As faras literature surveys on sensing application using photonic crystalstructure is concerned, recently few papers deal with similar typeof research [7

–13]. Considering a brief remark on above references,it is seen that reference [7] presents a novel method to find out theconcentration of sugar, salt, and alcohol in their aqueous solution.In this case, the author used 2D photonic crystal structure with11 × 11 air holes.Also using same technique, concentration of PAMhydrogel and strength of Cygel is investigated in Refs. [8,9], respectively. Also in Refs. [10,11], the concentration of potassium chloridein their aqueous and intrallipid in human blood is estimated usingphotonic crystal fiber. Apart from these, measurement of glycerolin B–H–G solution and concentration of hemoglobin in humanblood is investigated using 3D photonic crystal structure in Refs.[12,13], respectively. Though Ref. [13] measures the concentrationof hemoglobin in human blood using 3D photonic crystal structure,it is hard to fabricate 3D owing to photonic crystal structure. We inthis paper investigate the concentration of hemoglobin in humanblood using 2D honeycomb photonic crystal structure. The reasonfor choosing such structure is that it can be easily fabricated; secondly, these structures predict accurate result as compared to 3Dphotonic crystal structure, which is carried out in Ref. [13].
Hemoglobin is a main component of the blood, which isimportant for transportation of oxygen in blood, which leadsto circulation of blood in vein. This circulation of human bloodsystem has default functions, such as supply of oxygen to tissues, supply of nutrients such as glucose, amino acids, and fattyacids, removal of waste such as carbon dioxide, urea, lactic acid,immunological functions, including circulation of white cells, anddetection of foreign materials by antibodies, coagulation, messenger functions, regulation of body PH, regulation oh core bodytemperature hydraulic function etc. for normal human body. A

deficiency of hemoglobin in human blood creates serious problemsuch as downstream tissue dysfunction, Leukemia, iron deficiency,anemia, multiple myeloma, etc. [14–17]. Keeping the importanceof hemoglobin in human blood, this paper estimates the concentration of hemoglobin in both oxygenated and deoxygenatedblood.This paper is organized as follows: Section 2 presents the structure of the honeycomb photonic crystal structure including theprinciple of measurement. Simulation result and interpretation ismade in Section 3. Section 4 proposes an experimental set up andfinally conclusions are drawn in Section 5.

2. Honeycomb structure and principle of measurement
As far as measurement of hemoglobin in human blood is concerned, we use 2D honeycomb photonic crystal structure for thesame, which is shown in Fig. 1.Fig. 1 represents honeycomb photonic crystal structure having gallium Arsenide as background material containing air holes,where bloods with different percentage (g/L) of hemoglobin areinfiltrated. The proposed structure consists of 9 numbers of air holessuch that diameter of air holes is 420 nm and lattice spacing of thestructure is 1

m. The principle of measurement is based on linear variation of reflected energy and absorbance with respect toconcentration of hemoglobin in human blood. When light havingwavelength of 589 nm incident on honeycomb structure containingblood with different percentage of hemoglobin then, some amountof light will get reflect and some amount of light will be absorbed bythe structure. The rest amount of light will be transmitted throughthe structure. Since the principle is based on linear variation of
both reflected and absorbance, intensity transmitted through honeycomb structure also varies linearly with respect to hemoglobinconcentration in the blood which is a key factor (linear variation)to realize accurate investigation of hemoglobin in human blood.We use simple mathematical equation to find out the reflectedenergy, absorbance and transmitted energy for investigation ofhemoglobin. As far as, energy reflected from honeycomb structure is concerned, it is obtained from dispersion diagram, whichis carried out by employing plane wave expansion method [18]
In this case, we computed normalized frequency (a/) fromdispersion diagram, then the values of reflected energy (ER) is calculated using following simple equation:
ER=hc/R,where R is reflected wavelength, which is found from dispersion diagram.Since, wavelength 589 nm is used to investigate hemoglobinconcentration; the energy of incident light (EI) corresponding tothis wavelength is found using following expression.EI (2)where is the incident wavelength (589 nm)Using (1) and (2), the energy transmitted through the structureis written asET = E0 − ER (3)Eq. (3) represents as transmitted energy without considerationof absorption loss. However, from literature it is found that GaAsstructure and blood with different concentration of hemoglobinabsorb some light of wavelength, 589 nm. So, absorption loss shouldbe cogitated during this investigation. Using Ref. [19] and employing Maxwell curl equation, Eq. (3) is modified asE

T (4)From the above equation, it is seen that absorption loss takesplace due to two factors, such as absorption loss due to backgroundmaterialand absorption loss due to blood .Where is called the absorption coefficient of gallium arsenidematerial and ‘t’ is the thickness of background or substrate.ˇ is called the absorption coefficient of blood at wavelength589 nm, which is expressed where is called the extinction coefficient of blood at wavelength589 nm and ‘C’ is the concentration of hemoglobin in human bloodand ‘d’ is the diameter of air holes, where blood samples are infiltration.Using the above equation, output energy through 2D honeycomb photonic crystal structure is obtained corresponding to eachconcentration of hemoglobin in human blood sample.

3. Result and interpretation
From previous section, it is seen that output energy through thephotonic crystal structure corresponding to each concentration is a function of both reflected energy from the structure and energyabsorbed by the structure. As both reflection energy and absorption loss are important to obtain transmitted energy, we divide thissection into three sub-sections such that first sub-section discussesreflected energy, second sub-section analyses absorption loss and then transmitted energy is given in third subsection.
3.1. Reflected energy
We use dispersion diagram to compute the energy reflectedfrom honeycomb photonic crystal structure. Dispersion diagram isa graph between normalized frequency (a/) with wave vector (k),which gives an idea about the photonic band gap or reflected energyfrom same structure. So before going to compute reflected energy,we focus on dispersion diagram of 2D photonic honeycomb structure containing human blood sample with different percentageof hemoglobin. The dispersion relation (relation between normalized frequency and wave vector) depends on structure parameterssuch diameter of holes, lattice spacing, refractive indices of bothbackground and blood sample including the configuration of thestructure

In this case, we consider honeycomb structure whose latticespacing is 1 m and diameter of air holes is 420 nm. Using theabove parameters and employing plane wave expansion method,simulation is made to obtain the dispersion graph of 2D honeycomb photonic crystal structure. Though, we have made simulation

for all concentration of hemoglobin from 0 g/L to 120/g/L of oxygenated and deoxygenated, simulation result for 0 g/L and 120 g/Lof oxygenated blood is shown in Fig. 2(a) and (b), respectively.Fig. 2(a) and (b) represent the dispersion diagram of 2D honeycomb photonic crystal structure containing human blood withhemoglobin concentration of 0 g/L and 120 g/L respectively. In thesefigures, normalized frequency (a/) is taken along vertical axisand wave vector (k) in m−−1 is taken along horizontal axis. Fromthese graphs, it is realized that electromagnetic wave at certainwavelength range cannot be propagated through the said photonic crystal structure, which refers as forbidden gap. It is alsoseen that red color band is represented as complete forbidden gap.From this graph, normalized frequency corresponding to ‘0’ and‘120’ concentration of human blood is found, and then photonicbandgap corresponding to each normalized frequency is computed.Though simulation result for 0 g/L and 120 g/L concentrations areshown here, simulation for other concentration of oxygenated anddeoxygenated blood are done but are not shown here. The photonic band gap corresponding to each normalized frequency ofoxygenated and de-oxygenated blood is investigated. The photonic band gap of said photonic crystal structure is nothing but thereflected energy (ER) from 2D honeycomb photonic crystal structure containing both oxygenated and de-oxygenated solution withdifferent concentration of hemoglobin. After computing reflectedenergy corresponding to each concentration of hemoglobin, wemoved to calculate absorption loss by said structure which is discussed in the next subsection.
3.2. Absorption loss
From Section 2, it is clear that absorption depends on bothstructure (background) of photonic crystal structure and humanblood with different concentration of hemoglobin. Since, the background material is fixed for measurement of all concentration

of hemoglobin, absorption due to background material (e−˛t) issame for all concentration. However, absorbance due to blood isdiffered for different concentration of hemoglobin because theabsorbance coefficient (ˇ = εc) depends on the concentration (c),so that absorbance due to hemoglobin concentration will be eThen the resultant absorbance is e The value of and ˇis obtained from the literature [20]. By putting the value of and d in Eq. (5), we compute the resultant absorbance with respectto concentration of hemoglobin of oxygenated and de-oxygenatedhuman blood. After computing both reflectance and absorbance,we compute the transmitted energy through the photonic crystal structure, which is discussed in the next session.

3.3. Transmitted energy
Before going to discuss transmitted energy emerging from thephotonic crystal structure, we propose an experimental setup bywhich one can measure the energy emerging from honeycombphotonic crystal structure. The setup is shown in Fig. 3.
Fig. 3 represents a proposed experimental setup to estimatethe concentration of hemoglobin in both oxygenated and deoxygenated blood. From this figure, it is seen that light havingwavelength of 589 nm incidents on 2D honeycomb photonic crystal structure, then some amount of light will be reflected and somegets absorbed by it and rest mount of light reaches at photo detectorand finally potential corresponding to such output light is collected at an Arduino development board (UNO) with an LCD display.Here, Arduino UNO is a development board containing Atmega 320with an LCD interfaced which is used to display both potentialcoming from photo detector corresponding to the concentrationof hemoglobin in human blood. Since, reflected energy as well asabsorbance is different for different concentration of hemoglobin,transmitted energy as well as potential corresponding to transmitted energy is differed from different concentration. Since, thispaper emphasizes on simulation work, the transmitted energy iscomputed using Eq. (4). After calculating the transmitted energy,a graph is plotted between transmitted energy with respect to different percentages of hemoglobin which is shown in Fig. 4.

ent percentages of hemoglobin which is shown in Fig. 4.Fig. 4 provides the information regarding the variation of transmitting energy emerging from 2D honeycomb photonic crystalstructure with respect to concentration of hemoglobin in oxygenated and de-oxygenated blood. From Fig. 4, it is seen thatthe concentration of hemoglobin (g/L) is taken along primaryx-axis, where transmitting energy in eV for oxygenated and deoxygenated blood sample is taken along primary and secondary y-axisrespectively. From above graph, it is observed that the transmittedenergy decreases linearly with respect to hemoglobin concentration, which varies from 0 g/L to 120 g/L for both oxygenated andde-oxygenated blood. For example, transmitted energy