Accuracy of Localization System inside HumanBody using a Fast FDTD Simulation Technique

Pranay Swar, Kaveh Pahlavan and Umair KhanCenter for Wireless Information Network Studies, Worcester Polytechnic Institute, USA

Email: {pranay.swar, kaveh, uikhan}@wpi.edu

Abstract—In this paper we analyze the accuracy ofnarrowband and wideband localization techniques inside thehomogeneous human tissues using a fast finite difference timedomain (FDTD) technique. In the narrowband localization,the phase of the received carrier signal is used for rangingmeasurements, whereas for the wideband transmission, thetime of arrival (TOA) of the received signal is used. Forfast computations, we introduce a new perspective to FDTDsimulations of radio propagation by considering each simulationset for a given location of antennas as a Linear Time Invariant(LTI) discrete-time system. This way a set of simulations for avariety of transmitted waveforms can be reduced to only onesimulation to determine the impulse response of the simulatedchannel between the two antennas and the convolution of the setof waveforms with this impulse response. A typical simulationusing FDTD takes several minutes to a few hours and eachconvolution takes only a few seconds, resulting in a hugereduction in computational time.

I. INTRODUCTION

A Body Area Network (BAN) is a conceptual term for anetwork technology targeted for use in or around the humanbody. Two competing applications driving this developmentare medical applications (e.g. implants) and entertainment.The BAN system used for medical applications is generallyreferred to as implanted Body area networks, which consistsof a number of nano-size wireless communication devicesusing sophisticated semiconductor technology capable ofcommunicating with each other forming sensor networkinside the human body for health monitoring purposes.Implantable devices have a wide range of promising novelbiomedical applications that play vital and important rolesin building comprehensive tele-medical networks [1], [2]. In[3], a global overview of implanted microsystems, and theirclinical application is presented, and it is shown that at thecurrent stage, implanted devices can be almost everywhereinside the human body. To ensure wireless connectivity ofsuch implanted systems with external base stations, accurateunderstanding of the radio propagation channel, including theeffect of the antenna is necessary [3] [4]. The electrically smallsize of the commonly deployed implanted antennas, togetherwith the body losses, makes the electromagnetic analysis of thewireless communication extremely complicated and difficult.The aim of this paper is to characterize the accuracy withwhich localization of the implanted devices can be achievedusing the TOA information.

The finite-difference time-domain (FDTD) method [5]has been proven to be an effective simulation methodthat provides accurate predictions of field behaviors forvarieties of electromagnetic interaction problems. In the FDTD

To whom correspondence should be addressed.

method, Maxwell’s curl equations are discretized by utilizingcentral-difference equations with second-order accuracy, withthe electric and magnetic field components located at thesuitable position on the Yee cell [6]. Traditionally, FDTDsimulations have been widely used as a computation techniquefor determining the wave propagation for indoor localization,geolocation and channel modeling. Measurements along withFDTD simulations have been the center of focus for severalresearch papers in the past for determining the accuracy ofindoor geo-localization using RSS or TOA, but when it comesto body area networks, the measurements becomes more andmore challenging due to the several specifics of the humanbody medium and its applications that are profoundly differentfrom the traditional indoor radio propagation challenges, alsoit is practically impossible to go inside the human body orhave a sensor placed inside the human body to determine thecharacteristics of the wireless waveform transmissions withinthe human body. Moreover, measurements are expensive, timeconsuming and hardly repeatable; hence FDTD computationaltechnique becomes the natural choice for simulations todetermine the wave propagation and to analyze the radiationcharacteristics of implanted devices inside the human body.

A major emphasis within the computationalelectromagnetics (CEM) community concerns the solution ofMaxwell’s differential equations using finite-differencetime-domain (FDTD) techniques, Because of thecomputational time and memory requirements associatedwith these time-stepping algorithms, their application tovery large problems has been somewhat limited. To alleviatethese computational obstacles, some efforts have been aimedat the implementation of space-parallelism and concurrentcomputation of unknowns at different points in the spatialmesh using multiple processors [7]. For these schemes,however, communication and synchronization requirementshave limited the amount of computational speed-up providedby the use of additional processors. In this paper we willdiscuss how these computational efficiency can be improvedusing a much simpler approach to this problem.

The remainder of the paper is organized as follows.Section II describes the motivation to find a faster FDTDcomputational method. In Section III, we discuss the methodthat we used for the faster analysis using FDTD for waveformtransmission. The numerical analysis and simulation results aredone in Section IV. Finally, Section V concludes the paper.

II. FDTD FOR WAVEFORM TRANSFORMATION

In this Section, we first describe the FDTD method in detail.We show how we use FDTD simulation to do waveformtransmission and find out how well its fits the empirical

measurements. Finally, we discuss the motivation behindfinding a faster method for simulation using FDTD forwaveform transmission.

A. Formulation of FDTDFDTD is used to solve Maxwell’s equations for arbitrary

model spaces. Indeed, FDTD allows us to solve models thatwould be difficult or impossible with analytical methods.FDTD is a direct time-domain solution to Maxwell’s curlequations, which are given here below.

∂E

∂t=

1

εO×H − 1

ε(Jsource + σE) (1)

∂H

∂t=

1

µO× E − 1

ε(Msource + σ∗H) (2)

In the FDTD scheme, Maxwell’s curl equations are firstscalarized into their x, y, and z field components. Then,centered finite difference expressions are used to approximatethe spatial and time derivatives. Below is the resultingx-directed H-field equation and z-directed E-field equation;the other 4 field components are similar.Hx

n+1/2i,j,k+1/2 −Hx

n+1/2i,j,k+1/2

∆t=

1

µ

[Eyni,j,k+1/2 − Eyni,j,k−1/2

∆z

]− 1

µ

[Eyni,j+1/2,k − Eyni,j−1/2,k

∆y

]− 1

µ

[(Msource + σ∗Hx

n−1/2i,j,k )

]Ezn+1

i,j,k+1/2 − Ezn+1i,j,k+1/2

∆t=

1

ε

[Hyni,j,k+1/2 −Hyni,j,k−1/2

∆x

]−1

ε

[Hxni,j+1/2,k −Hxni,j−1/2,k

∆y

]−1

ε

[(Jsource + σEz

n−1/2i,j,k )

]This method was first introduced in the original FDTDpaper by Kane Yee [6]. In particular, he introduced the nextimportant FDTD concept known as the Yee Space Grid.

The key features to the Yee Space Grid as shown in figure1 relate to the staggering of the E and H fields [6]. The Eand H field are staggered to one another with respect to timeby one half of the time step. E and H are centered in spacesuch that each E field component is surrounded by four H fieldcomponents and vice versa.

The problem space is stored in a three dimensional grid.Each cell in the grid is assigned a material type that hascorresponding dielectric properties, and stores the x, y, andz components for both the E and H field initialized to 0.

B. Comparison of Waveform Simulation with MeasurementsThe comparisons of simulation and empirical measurement

is made to find out the accuracy of the simulation and how wellit fits the real time empirical measurements. The measurementis done in a anechoic chamber using a vector network analyzerhaving a frequency range up to 40 GHz. The anechoic chamberto a good extent represents the FDTD simulation environmentwhich consists of a finite domain surrounded by absorptionboundaries.

First we match the measurements with the FDTD simulationresults obtained in free space transmission which match

Figure 1. Yee Grid

Figure 2. Simulation and Measurement Comparison

perfectly. Then, the simulation and measurement is carriedout in two more scenarios a) With antennas place on thefront side surface of the phantom b) With the antenna placedon the front and back side of the phantom. In both thescenarios we use the ISM band 2.4GHz to 2.484GHz (whichlies within the operational bandwidth of FDTD for a gridsize of 12.5mm) as in this frequency band the simulation andmeasurement matched perfectly in free space. As you couldsee in figure 2, there is a good match between the simulationand measurement. Thus we conclude that all the simulation wehave done using the FDTD simulation software are in goodagreement with the real time measurement if the bandwidthof the signal is well within the operational bandwidth of thesimulation.

C. Computational Complexity

Despite its simplicity and flexibility, the FDTD isa computationally intensive technique that requires large

Figure 3. Computational time against grid size

computation memory and time for electrically small structure.Such intensive memory and CPU time requirements are mainlydue to the following two modeling constraints [5]: 1) Thespatial increment step must be small enough in comparisonwith the smallest wavelength (usually 10-20 steps per smallestwavelength) in order to make numerical dispersion errorsnegligible.2) The time step must be small enough so that it satisfies thefollowing CFL stability condition:

umax∆t ≤ [1/∆x2 + 1/∆y2 + 1/∆z2]−1/2 (-2)Here umax, is the maximum wave phase velocity within

the model. If the time step is larger than the value specifiedabove, the FDTD scheme will become numerically unstable,leading to an unbounded numerical error as the FDTD solutionmarches.

In order to examine how much is the computationalcomplexity and the time required to run the entire simulation,we performed an experiment using our 3D FDTD equationimplemented in MATLAB. Here we examine the performanceas a function of the grid size. We perform a simulation infree space with point source antennas located at 20cm awayfrom each other with the sine wave given as an input to thetransmitter antenna at frequency of 100MHz. The grid sizesconsidered here are 25mm, 12.5mm, 6.25mm. For the purposeof simplicity we have considered the grid size along all threeaxis to be same i.e x = y = z = δ ,where δ is the grid size.Figure 3 shows the computational time required as a functionof the grid size. It is very clear that as the grid size decreases,the increase in the computational time is not linear, instead thetime required increase as a cubic power of the grid size. TableI shows the statistical information related to the this simulation

Table ICOMPUTATIONAL COMPLEXITY AND RELATIVE RATIO

Domain Dimension Grid Size Time in s Relative ratio192X192X192 6.25 1200 197X97X97 12.5 146 849X49X49 25 36 64

Figure 4. A Linear Time Invariant system

Figure 5. FDTD as Linear Time Invariant system

which shows the relation between the grid size and the timerequired.

III. FAST SOLUTION TO FDTD USING LTI ANALYSIS

From a signal processing point of view, the FDTD algorithmcan be considered a LTI (Linear Time-Invariant) system whichcan be fully characterized by its transfer function. It isobserved that, the output obtained at the receiving antennaafter simulation is same as the convolution of the input signalwith the impulse response of the system obtained with thesame simulation settings. If we denote the impulse responseby h(n) then the simulation result of FDTD for any given inputwaveform x(n) will be represented by the following

y(n) =

N∑k=1

h(k)x(n− k)

The frequency Response of the output is given byY (ω) = H(ω)X(ω) where, H(ω) and X(ω) are given below

H(ω) =∑

h(n)e−jωn;X(ω) =∑

x(n)e−jωn

The advantage of LTI considerations are a) If we simulatethe impulse response between two points, we can obtainany other waveform transmission between those two pointsusing convolution integral and save the computational timetremendously. b) We can use the Fourier Transform of theimpulse response to determine the bandwidth limitations of thesimulations. In particular, this method can be used determinethe effect of bandwidth on the accuracy of TOA basedlocalization, without running the FDTD simulation for hours.Figure 5 gives you a basic overview of how this mechanismworks in case of FDTD. The input to the FDTD software

is the waveform shown in the lower left part of the figurewhich has a bandwidth of 84 MHz (ISM band) and the outputof the simulation is the waveform shown in the upper rightside of the figure. We then convolve the impulse responseshown in the center bottom of the figure obtained keeping thesame FDTD simulation setup with the input waveform, weget the waveform shown in the lower right part of the figure.The outputs obtained from the two methods are identicalconcluding that the simulation can be interpreted as a LTIsystem. Using this approach for two locations in the body,for example, first we determine the impulse response withone simulation. After that the response to any other waveformwith different bandwidths can be obtained without doing timeconsuming simulation and by simply convolving the inputwaveform with the impulse response of the system.

Wireless Body area networks (WBAN) is an area whosestandardization activity is underway, in such situations,highlighting the significance of bandwidth on the accuracyof localization inside human body becomes very important.Looking at FDTD as an LTI system simplifies this task bywhich the accuracy of time of arrival can be found by simplyconvolving the input wideband/narrowband signal with theimpulse response.

IV. EFFICIENT TOA BASED LOCALIZATION WITH BANS

Simulations are performed with transmitter and receiverplaced at different points inside the body as shown the thefigure 6. The 3D human body model used for the simulationhas a spatial resolution of 2mm is extracted form the threedimensional full wave electromagnetic field simulation systemnamed HFSS (High Frequency Structure Simulator). Forsimplicity we have considered a uniformly homogeneoushuman body with a constant dielectric constant of ε = 50.

A. Simulation Scenario

The simulation points located inside the body takes intoaccount the major part of the torso which is the most stablepart as compare to other parts of the body which are mostof the time moving with respect to whole body. Since oursimulation is static and does not consider the movement ofthe whole body, in general, understanding the behavior of thewaveform transmission inside the torso is the most obviousoption. The simulations were performed with the transmitterand receiver located at these points using a point sourceantenna. A Point source antenna is a isotropic antenna whichradiates equally in all directions. In section III, we discusshow a single impulse response can be used to characterizethe transmission between any two of these points in the torso.Here we will apply this method to do some analysis and showsome results.

B. Simulation Bandwidth as a Function of Distance

The FDTD method discussed has bandwidth limitations. Fora given grid size, there a maximum limit on the bandwidthfor which the simulation gives acceptable results. If weconsider the FDTD simulation as a LTI system representedby the channel impulse response, the Fourier Transform ofthe impulse response represents the transfer function of thesystem illustrating the bandwidth of the simulation system.In this section we discuss how the distance between the two

Figure 6. Simulation Scenario

points inside human body affects the operational bandwidth.Since the impulse response changes as the distance betweentwo simulated locations is increased, the bandwidth of thefrequency response would be sensitive to the distance betweentwo simulated points. To further elaborate on this point weconsidered the simulation scenario shown Figure 6. In thisscenario, the transmitter antenna is fixed on the top point andthe receiver is located at different points shown in the scenario.The top and bottom plots in Fig 7 shows the transfer functionof the channel with receiver at second and third point from thetop most point in the figure. Figure 8 shows how the bandwidthdecreases as the distance between the two points increases.These results indicate that if we want to simulate using FDTD,we always have bandwidth limitations that is a function ofthe distance. Figure 8 indicates that if the bandwidth of thetransmitted signal for a grid size of 12.5mm is more than850MHz, we can not get accurate results using FDTD for adistance of 10cm between transmitter and the receiver. Thisis a very powerful conclusion useful for practical aspects of

Figure 7. Simulation Bandwidth for distance of 8cm (up) and 16 cm (down)inside human body

Figure 8. Operational Bandwidth v/s distance

Figure 9. TOA accuracy for Narrow Band

simulations inside human body using the FDTD techniques.

C. TOA Accuracy as a Function of Bandwidth

The human body channel suffers form severe multipathpropagation and heavy shadow fading conditions someasurement for localization are far form accurate for manyinstances. Here we try to find the TOA localization accuracyand not RSS as pointed out in [8], TOA measurement aremore accurate than that by RSS. To examine the applicationof waveform transmission inside human body using FDTDsimulations, we determined the statistics of the distancemeasurement errors using TOA of the received waveformin the scenario shown in Figure 6. The TOA of the signalbetween the different points in the simulation scenario werecalculated for different waveforms using the impulse responseof the channel. We use two different waveforms for differentlocalization techniques. First we use a sinusoidal signal,representing narrow band transmission of signal, and use thephase information of the received sinusoidal signal to measurethe distance and compared that with the actual physicaldistance to determine the distance measurement error for TOA

Figure 10. TOA accuracy for Wide Band

estimation using the phase of a carrier. Then we repeat theexperience for the wideband pulse transmission by detectionof the peak of the received signal for TOA estimation. Thestatistics of the distance measurement errors obtained from thetwo experiences for TOA estimation using the narrowband andwideband signals are shown in Figure 9-10. The error of thenarrowband measurements is 4.18 cm with a variance of 0.453cm compared with the error of the wideband measurementsthat is 1.419 cm with variance of 0.0614 cm. This simpleexperiment reveals the usefulness of the approach describedin this paper. All the results obtained are using the LTIinterpretation of the FDTD simulations and the calculationtime was negligible with respect to hours of computationsneeded for the direct simulation of the waveforms.

V. CONCLUDING REMARKS

In this paper, we looked at the potential drawbacks of FDTDmethod in general and looked at how they can be eliminatedfor the analysis of the TOA localization accuracy by lookingat FDTD as a LTI system. We demonstrated to what degreethe TOA accuracy improves as a function of bandwidth. Wealso investigated that FDTD has bandwidth limitations and toget accurate results the simulation should be operated withinthe operational bandwidth for a given grid size. The futurework in this area would be to have a heterogeneous humanbody model instead of homogeneous human body model usedhere to find the effect of tissues of different material on theTOA accuracy.

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