\r\n\t \r\n\tComputer graphics are not entirely an original topic, because it defines and solves problems using some already established techniques such as geometry, algebra, optics, and psychology. The geometry provides a framework for describing 2D and 3D space, while the algebraic methods are used for defining and evaluating equality related to the specific space. The science of optics enables the application of the model for the description of the behavior of light, while psychology provides models for visualization and color perception. \r\n\t \r\n\t3D computer graphics (or 3D graphics, three-dimensional computer graphics, three-dimensional graphics) is a term describing the different methods of creating and displaying three-dimensional objects by using computer graphics. \r\n\tThe first types of graphic interpretations were put in the plane (two-dimensional 2D). Requirements for a universal interpretation led to a three-dimensional (3D) interpretation content. From these creations have arisen applied mathematics and information disciplines of graphic interpretation of content - computer graphics. It relies on the principles of Mathematics, Descriptive Geometry, Computer Science and Applied Electronics. \r\n\t \r\n\t3D computer graphics or three-dimensional computer graphics use a three-dimensional representation of geometric data (often in terms of the Cartesian coordinate system) that is stored on a computer for the purpose of doing the calculation and creating 2D images. The images that are made can be stored for later use (probably as animation) or can be displayed in real-time. \r\n\t \r\n\tObjects within the 3D computer graphics are often called 3D models. Unlike rendered (generated) images, data that are ""tied"" to the model are inside graphic files. The 3D model is a mathematical representation of a random three-dimensional object. The model can be displayed visually as a two-dimensional image through a process called 3D rendering or can be used in non-graphical computer simulations and calculations. With 3D printing, models can be presented in real physical form. \r\n\t \r\n\tComputer graphics have remained one of the most interesting areas of modern technology, and it is the area that progresses the fastest. It has become an integral part of both application software, and computer systems in general. Computer graphics is routinely applied in the design of many products, simulators for training, production of music videos and television commercials, in movies, in data analysis, in scientific studies, in medical procedures, and in many other fields.
",isbn:"978-1-78985-853-2",printIsbn:"978-1-78985-638-5",pdfIsbn:"978-1-78985-854-9",doi:null,price:0,priceEur:0,priceUsd:0,slug:null,numberOfPages:0,isOpenForSubmission:!0,hash:"de29c8802680e89528bdbecf055dffd1",bookSignature:"Dr. Dragan Mladen Cvetković",publishedDate:null,coverURL:"https://cdn.intechopen.com/books/images_new/8770.jpg",keywords:"Vector Graphics, Graphic design, 3D model, Computer-Aided Design (CAD), Computer-Aided Architectural Design (CAAD), 3D Rendering, Virtual engineering, 3D Mapping, 3D projection on 2D planes, Video games, 3D Printing, 3D Computer Graphics in Science",numberOfDownloads:null,numberOfWosCitations:0,numberOfCrossrefCitations:0,numberOfDimensionsCitations:null,numberOfTotalCitations:null,isAvailableForWebshopOrdering:!0,dateEndFirstStepPublish:"October 28th 2019",dateEndSecondStepPublish:"November 18th 2019",dateEndThirdStepPublish:"January 17th 2020",dateEndFourthStepPublish:"April 6th 2020",dateEndFifthStepPublish:"June 5th 2020",remainingDaysToSecondStep:"24 days",secondStepPassed:!0,currentStepOfPublishingProcess:3,editedByType:null,kuFlag:!1,editors:[{id:"101330",title:"Dr.",name:"Dragan",middleName:"Mladen",surname:"Cvetković",slug:"dragan-cvetkovic",fullName:"Dragan Cvetković",profilePictureURL:"https://mts.intechopen.com/storage/users/101330/images/system/101330.jpg",biography:"Dragan Cvetković graduated in Aeronautics from the Faculty of Mechanical Engineering, University of Belgrade, in 1988. In the Aeronautical Department he defended his doctoral dissertation in December 1997. So far, he has published 63 books, scripts, and practicums about computers and computer programs, aviation weapons, and flight mechanics. He has published a large number of scientific papers in the Republic of Serbia and abroad as well. Since March 20, 2007, he worked at the Singidunum University in Belgrade as an assistant professor. And from October 1, 2013, he has been working as the Dean of the Faculty of Informatics and Computing at the same university. 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From chapter submission and review, to approval and revision, copyediting and design, until final publication, I work closely with authors and editors to ensure a simple and easy publishing process. I maintain constant and effective communication with authors, editors and reviewers, which allows for a level of personal support that enables contributors to fully commit and concentrate on the chapters they are writing, editing, or reviewing. I assist authors in the preparation of their full chapter submissions and track important deadlines and ensure they are met. I help to coordinate internal processes such as linguistic review, and monitor the technical aspects of the process. As an ASM I am also involved in the acquisition of editors. 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1. Introduction
Comparative analyses of haplotype sequences allow many efficiencies. It is not surprising that there are many enthusiastic claims. Haplotypes, by any of many definitions, offer opportunities to understand the inheritance of polymorphic traits and their regulation. The most useful are markers of extensive complex polymorphic sequences of evolutionary significance even when the functional components, whether coding or noncoding, are yet to be elaborated.
Substantial advances became possible with the elucidation of genomic structure and function more than 20 years ago and long before recent advances in sequencing technology [1] and bioinformatics [2]. It became clear that haplotypes, not genes, can be regarded as the principal unit of inheritance.
This chapter evaluates some competing strategies and illustrates the power now available through NGS.
2. Haplotype terminology
A review of current literature reveals a staggering collection of terms synonymous with haplotypes, as listed in Table 1.
Even if it were possible to define the various neologisms, it seems certain that confusion will remain until there is recognition of the conceptual background.
We introduced the term ancestral haplotypes to emphasise the persistence of the founding pool [3, 4]. Such haplotypes are conserved over thousands of generations; they allow identification of remote ancestors and their contributions to the creation of individual members of the species with their diseases. Unfortunately, others use the same term in different ways and even in the opposite sense, that is, to refer to the single original haplotype which is presumed to have mutated to give rise to all the so-called variants now present. Indeed, as just one example of the problem, the reader has to be able to interpret the following: "we identified all nonredundant haplotypes with a frequency of ≥10% and consisting of at least 10 SNPs, which are likely to represent the nonrecombinant descendants from a single ancestor" [5].
To yet further confound matters, increasingly, the term haplotype is being used to describe any combination of alleles or markers, such as SNPs, without regard to their reproducibility, inheritance, polymorphism or biological significance. Currently, there are conflicting methods of detection. The problems appear to be increasing as ephemeral concepts diverge and as claims for better approaches focus on just one or another competing technology or bioinformatic package.
Several other aspects are clear.
Linkage groups relate to closely linked loci but do not define haplotypes.
Linkage disequilibrium is affected by relative frequencies and therefore fails to detect rare haplotypes.
Trios can be misleading since the coverage of the family is limited.
Haplobanks. The Tokunaga group has established some important principles with the intention of establishing haplotype-matched pluripotential stem cell banks [6]. Unfortunately, and amazingly, there is now uncertainty as to how to define the haplotypes. For example, a recent paper urges international collaboration to avoid fragmentation [7]. It would be wise to avoid neologisms and such redefinitions without clarity of meaning.
3. Definitions and concepts
In the presequencing era, there was a clear understanding of what was meant by the term haplotype: Combinations of alleles at different loci segregating together in multigenerational family studies [8]. Some seem unaware of this long history and have had to rediscover the concept [2].
The implications were apparent at least 50 years ago: a specific allele A1 at locus A is inherited together with a specific allele B1 at an adjacent, “closely linked” locus B [9]. The fact that these two alleles segregated together through multiple generations was unexpected and lead to controversy but, in retrospect, clearly implied that
The two alleles were encoded on the same chromosome, whether paternal or maternal.
The two loci were closely linked.
Recombination was rare.
The two loci arose by duplication.
Duplication is associated with polymorphism.
The repeated cosegregation of alleles came to be known as a haplotype: from άπλφούς = single [9].
It is worth emphasizing that it was the cosegregation as haplotypes through “phased” multigenerational families (rather than “unphased” populations) which foretold the later demonstration that there was a continuous haplospecific sequence. It is also pertinent, with the benefit of hindsight and in view of recent confusion, that the haplotypes, defined in one family, occurred in other families of similar remote ancestry raising the radical possibility of conservation beyond that expected from close linkage alone. In other words, recombination is patchy and does not necessarily disperse the components of duplications, even after thousands of meioses. The issue of linkage disequilibrium and the limits of LD mapping are considered below.
The implications of haplotypes, as listed above, became even clearer as the HLA A and HLA B locus alleles and then HLA DR alleles were defined during the 1970s. However, in this case, the loci were widely separated. Over time, it became clear that each of the A-B and B-DR haplotypes were some 800 kb in length. Patently, close linkage could not explain these haplotypes; either there was selection for cis interaction or there was suppression of recombination [3, 4].
Through their studies of diseases, the Alper–Yunis group discovered that the B-DR haplotypes contained specific alleles at duplicated loci which had no structural or functional relevance to HLA (i.e. complement and 21 hydroxylase loci) but which happen to be located within the major histocompatibility complex [10–16]. Thus, cis interaction alone could be rejected as the sole explanation.
The importance of discovery through disease was illustrated at a meeting held in 1982 [3, 4]. As shown in Table 2, it was disease associations which allowed the initial discovery of ancestral haplotypes; note, these three disease-associated haplotypes could have only been discovered through their associations. Two share DR3 and two share B18 but the frequencies differ. Thus, the three haplotypes cannot be detected by linkage disequilibrium.
Once the numerous other ancestral haplotypes were defined, multigenerational family studies identified cosegregating combinations of multiple alleles at separated loci, i.e. haplotypes stretching over nearly 2 Mb from HLA A to DR. A haplotype was defined by the alleles “inherited en bloc from one parent and implies the transmission of all of the chromosomal segment” from one generation to the next [4].
When haplotypes defined in one family were compared with those identified in apparently unrelated families, sharing was immediately apparent. There were specific combinations of alleles at all the numerous unrelated loci as these were defined and typed. However, and increasingly relevant today, as summarized in refs. [3, 4, 17, 18]:
The combinations observed are not a simple function of allele frequencies; only some of the components inherited en bloc are in linkage disequilibrium.
Many haplotypes are rare combinations of frequent alleles at some loci but rare alleles at other loci.
Very few alleles are entirely haplospecific.
Haplotype frequencies are often less than 1%.
The same haplotypes are found in multiple, apparently unrelated, families.
Many of these nonrandom combinations are associated with a disease (such as systemic lupus erythematosus) or function (such as TNF production).
With a few dramatic exceptions (such as 21 hydroxylase and C2 deficiency carried by what we now call the 47.1 and 18.1 ancestral haplotypes), the individual alleles do not explain the haplospecific effects on disease and function.
Penetrance is low. That is to say, the haplotypes are sine qua non in that they permit particular diseases and functions but only in the presence of other genetic, infectious, environmental, hormonal and age-related factors.
Recombination is rare and difficult to demonstrate even within multigenerational families with the potential to confirm a meiotic recombinant. Nevertheless, over the life of an ancestral haplotype—say 10, 000 meioses—there have been recombinations which have resulted in shuffling between ancestral haplotypes [18, 19].
Figure 1.
Historic recombinations of AH 8.1. The HLA-B8 allele is carried by one ancestral haplotype marked by A1, Cw7, B8, BfS, C4AQ0, C4B1, DR3. All the haplotypes in data set 1 carrying HLA-B8 are represented. These haplotypes have been sorted so that haplotypes that carry all alleles of 8.1 from HLA-A to DR are shown at the top of the figure, followed by haplotypes that extend from HLA-B to DR. Telomeric recombinants are shown at the bottom. The boxed areas represent those portions of the 8.1 ancestral haplotype that are carried by unrelated B8-containing haplotypes. Vertical lines approximately indicate the region where historical recombination has occurred.
Some of these points are illustrated in Figure 1. It can be seen that subjects with B8 can be listed to show conservation but also historic recombinations between HLA A and B, between C4B and DR, and between HLA B and Bf.
By the mid-1990s, and long before the rediscoveries of the 2000s [2], such analyses led to the conclusion that there are polymorphic frozen blocks (PFB), as illustrated in Figure 2.
Figure 2.
Ancestral haplotypes and polymorphic frozen blocks within the human major histocompatibility complex. Each ancestral haplotype has its own unique DNA sequence which includes single nucleotide polymorphisms (SNPs), copy number variations, segmental duplications, insertion and deletion events (indels) including retroviral and retroviral-like elements (RLEs). The full length is approximately 4 Mb. Higher degrees of diversity indicated by shading define polymorphic frozen blocks (PFB). Recombination occurs far more frequently between, rather than within, these blocks. Mutations within blocks are effectively suppressed. Adapted from refs. [17, 20] and [21]. Reproduced with permission from ref. [22].
PFB throughout the genome are the latter-day equivalents of loci. Sequences which define ancestral haplotypes are the equivalent of alleles. The diversity is multifactorial with contributions from reiterative speciation as follows [17]:
Retroviral integration
Duplication
Indels
Polymorphism
These elements all contribute to the haplospecificity of the sequence of ancestral haplotypes as shown in Figure 3. Similar distribution of diversity has been found by many others [5, 17, 19, 20, 23, 24]. The same patterns are also found in primates [25].
Figure 3.
Sequence diversity is packaged as polymorphic frozen blocks (PFB). SNPs and indel occur in similar locations within PFB. (a) The SNP profile after removing indels. Peaks higher than 20 SNPs per 1000 nucleotides are truncated. (b) The location of indels. Peaks higher than six indels per 1000 nucleotides are truncated. (c) The position of indels greater than 100 nucleotides.
4. Use of ancestral haplotypes
Here, we illustrate the potential of sequence analysis, if designed to identify conserved, extended, ancestral haplotypes. The utility depends very largely on the concept behind the analysis. However, it also depends upon the genomic region actually sequenced and whether it is possible to interpret the patterns in the context of the heterogeneous architecture of the genome. Within PFB, there will be a multitude of alternative sequences to compare. In the genome between these blocks, there is much less diversity with long stretches of monomorphic sequence. Thus, the recent fashion for identifying homozygosity [27, 28], without regard to diversity, shifts the focus to less informative regions of the genome. Of course, by way of explanation for the fashion, homozygosity within PFB is much more difficult to find; the most common ancestral haplotypes with frequencies of 0.1 will be homozygous in only 1% of the general population. Until high-throughput NGS became available, it was necessary to examine disease panels or consanguineous families.
The conceptual background is summarised in the following figures which contrast two approaches. Population genetics teaches that free recombination effectively prevents the packaging of polymorphism. The reality, designated here as quantal genomics, emphasises clustering and conservation of polymorphism. Each haplotype is a specific sequence which regulates expressed genes by cis, trans or epistatic interaction. The whole sequence is conserved. Linkage disequilibrium, when it occurs, is simply a reflection of this conservation which includes haplotypes with alleles which are relatively common in one haplotype when compared with others. Each is ancestral, in the sense that they are shared by apparently unrelated families separated by hundreds or even thousands of generations. It follows that the polymorphisms are actively conserved and could not be a consequence of recent mutation.
Some of the implications are illustrated in Figures 4 and 5.
Figure 4.
Importance of clustering functional genes. Colours represent loci and numbers represent alleles at those loci. On the left is the basis of the infinitesimal model used in population genetics. Loci are biallelic and can be homozygous or heterozygous. Free recombination occurs between loci and alleles segregate independently. On the right, loci are within polymorphic frozen blocks (PFB), shown by alignment of loci. Alleles within PFB segregate en bloc, forming haplotypes, which are inherited intact through many generations. Important genes are carried within PFB, conserving their cis interactions. Loci within PFB have multiple alleles, allowing for a greater degree of polymorphism clustered within the block. There can be hundreds of ancestral haplotypes for each PFB. Trans interactions between haplotypes increase the diversity expressed in the population. The loci shown in green and yellow are outside the PFB and follow a pattern of inheritance similar to population genetics. De novo mutations are indicated by asterisk—on the right the mutations occur at loci outside of conserved PFB and will have little if any consequence because truly important differences are encoded within PFB. Monogenic diseases or traits are the partial exceptions. On the left, mutations can occur at any loci but are generally assumed to occur at loci that were monoallelic. They may or may not be important, depending upon frequency, context, repair and heritability. Adapted with permission from ref. [22].
Figure 5.
Modern haplotypes are derived from the deep past—they are ancestral haplotypes.
By 1987, it was clearly established that each ancestral haplotype has a specific content of genomic features such as duplications and indels. These too are actively conserved and can themselves be used as signatures for haplotypes of hundreds of kilobases and even megabases. These observations were very difficult to explain in terms of any form of neo-Darwinism, natural selection, random errors or population genetics as taught then and today. Rather, we realised, the genome is not actually homogeneous but partitioned into protected quanta or PFB [17, 22, 26, 29].
5. Sequencing of critical genomic regions
By 1992, there was sufficient sequencing to confirm the earlier prediction that each ancestral haplotype is actually a frozen sequence.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tHaplotype\n\t\t\t
\n\t\t\t
\n\t\t\t\tGeometric element at CL1\n\t\t\t
\n\t\t\t
\n\t\t\t\tLength\n\t\t\t
\n\t\t\t
\n\t\t\t\tGeometric element at CL2\n\t\t\t
\n\t\t\t
\n\t\t\t\tLength\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t57.1\n\t\t\t
\n\t\t\t
(TC)12(TG)6(TC)14(TG)3(TC)12\n\t\t\t
\n\t\t\t
94
\n\t\t\t
TA (TC)18 TT (TC) 9\n\t\t\t
\n\t\t\t
58
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t18.2\n\t\t\t
\n\t\t\t
(TC)14\n\t\t\t
\n\t\t\t
28
\n\t\t\t
Deleted
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t8.1\n\t\t\t
\n\t\t\t
(TC)28\n\t\t\t
\n\t\t\t
56
\n\t\t\t
(TC)15 TG (TC)6 TG (TC)8 TG (TC)5\n\t\t\t
\n\t\t\t
96
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t7.1\n\t\t\t
\n\t\t\t
(TC)12(TG)6(TC)14(TG)3(TC)12\n\t\t\t
\n\t\t\t
94
\n\t\t\t
(TC)14 TG (TC)6 TG (TC)8 TG (TC)5\n\t\t\t
\n\t\t\t
94
\n\t\t
\n\t
Table 3.
Haplospecific geometric elements. Ancestral haplotypes have specific sequence signatures at each of the duplicons. Note in 18.2, the duplication did not occur or has been deleted.
We now know that examples of the 8.1 ancestral haplotype are almost identical over megabases [31, 32].
We illustrate the differences between different haplotype sequences in Figure 6. It can be seen that there are certain sites where haplotypes differ. Importantly, haplospecificity is conferred by the whole sequence rather than single nucleotide polymorphisms. For example, reading from left to right, 8.1 and 18.2 differ in T/G but not A/G, etc. Note also that some of the differences are due to indels. Of critical importance is accurate, unmolested sequencing over kilobases, as is now possible through NGS. It is clear, however, that assembly is hazardous especially in areas of duplication and polymorphism. Note also, that there is no justification for regarding one particular sequence as the reference. Rather, it is necessary to compare each output with a library of known sequences within each PFB.
The number of differences depends on which haplotypes are compared (see Table 4). Two of the most common Caucasian haplotypes, 8.1 and 7.1, differ by a hundred positions, representing approximately 1% nucleotide diversity. The most different haplotypes are 18.2 and 7.1, having 2.5% nucleotide diversity. Interestingly, these haplotypes are different functionally; 18.2 permits insulin-dependent diabetes mellitus whereas 7.1 is protective.
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\tAH Haplotype\n\t\t\t
\n\t\t\t
\n\t\t\t\t44.2\n\t\t\t
\n\t\t\t
\n\t\t\t\t62.1\n\t\t\t
\n\t\t\t
\n\t\t\t\t7.1\n\t\t\t
\n\t\t\t
\n\t\t\t\t44.1*\n\t\t\t
\n\t\t\t
\n\t\t\t\t8.1\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t44.2\n\t\t\t
\n\t\t\t
0
\n\t\t\t
\n\t\t\t
\n\t\t\t
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t62.1\n\t\t\t
\n\t\t\t
187
\n\t\t\t
0
\n\t\t\t
\n\t\t\t
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t7.1\n\t\t\t
\n\t\t\t
249
\n\t\t\t
221
\n\t\t\t
0
\n\t\t\t
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t44.1*\n\t\t\t
\n\t\t\t
73
\n\t\t\t
154
\n\t\t\t
227
\n\t\t\t
0
\n\t\t\t
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t8.1\n\t\t\t
\n\t\t\t
224
\n\t\t\t
219
\n\t\t\t
101
\n\t\t\t
204
\n\t\t\t
0
\n\t\t
\n\t\t
\n\t\t\t
\n\t\t\t\t18.2*\n\t\t\t
\n\t\t\t
184
\n\t\t\t
130
\n\t\t\t
250
\n\t\t\t
137
\n\t\t\t
245
\n\t\t
\n\t
Table 4.
Pairwise differences between haplotypes. Total differences between each pair of haplotypes in the 9277 bp region at HLA-B.
Figure 6.
Alignment of 9 kb sequence at HLA-B. Sequences of 6 individuals with homozygous ancestral haplotypes were downloaded from UCSC browser [33] at HLA B and aligned using ClustalX2 [34]. For the purposes of illustration only, common sequences were removed and the interruption marked as //. The nucleotides of AH 44.2 are displayed in the first row. Nucleotides of AH 62.1, 7.1, 44.1*, 8.1 and 18.2* are given only where they differ from AH44.2 and otherwise marked with a dot. Missing nucleotides are marked with a dash and shaded grey. The sequences are described by Horton et al. [24], whereas AH haplotypes have been assigned from the HLA allele types given by Horton, according to Cattley [35].
The degree of conservation of each ancestral haplotype is truly remarkable. For example, Smith et al. [32] found variation at only 11 of 3, 600, 000 positions between HLA-A and DR. Similar findings have been reported by others, including Aly et al. [31], see Figure 7. Mutation and recombination must be suppressed.
Figure 7 illustrates the importance of interpreting nucleotide diversity according to the block structure of the genome. Thus, conservation in the intervening, essentially monomorphic regions, is of minor interest, whereas differences within PFB allow the discovery of evolution, function and disease susceptibility.
Figure 7.
Remarkable conservation within 8.1 haplotypes. A total of 656 SNPs spanning 4.8 Mb in the MHC region are depicted. The lower frequency allele (row) for each SNP along each haplotype column is highlighted in yellow. The top group depicts SNP results from 8.1 AH haplotypes (n = 31), the lower group are HLA-DR3, non-B8 haplotypes (n = 13). The 29.9 Mb range between HLA and DRB1 was >99.9% conserved, with only 9 variant alleles of the 10, 768 alleles identified for the 384 SNPs in the 31 8.1 AHs.
The inescapable conclusion is that some parts of the genome have not two or three but hundreds of alternative ancestral sequences.
6. Sequence analysis of ancestral haplotypes
The challenge in terms of sequence analysis is to compile a sufficient matrix to be able to recognize each haplotype and its extent. Assume access to multigenerational families with accurate, truly phased but unmolested raw sequences of at least 100, 000 bases:
Clustering of these by independent criteria relating to as many as hundreds of distinct ancestral haplotypes.
Alignments which take account of haplospecific duplicons, indels and retroviral-like elements (RLE).
Functional information to address biological and disease significance.
Given NGS, this approach is now feasible, even if daunting.
Importantly, those regions which are complex because of duplications and indels should be included rather than “corrected” based on the assumption that there is a single reference or “wild” sequence. Some examples are shown in Figure 6.
In designing better algorithms [36], the strategy for comparative analysis will be crucial. In many polymorphic regions, the density of differences can be as high as 1 per 10 bases when different haplotypes are compared but as low as 0 if the haplotypes are the same. It follows that analysis without haplotype assignment will be misleading.
7. Finding polymorphic frozen blocks and their ancestral haplotypes
The best clue to the location of these blocks is segmental duplication [17, 37].
Figure 8.
Segmental duplications in MHC alpha block. (a) Gene families and retroelements PERB 11, HLA, HCGIV, AD-3, HERV-16, PERB3 are duplicated to form an ordered pattern within the alpha block of the MHC, indicating that a segment containing multiple genes and retroelements has been duplicated to give 10 duplicons. Full-length duplicons consist of PERB11, HLA, HCGIV, 1AD3, HERV-16 (P5) and PERB3 genes. HLA-80, HLA-A, HIA-K, HLA-16, HLA-90 and HLA-F duplicons lack PERB11 gene. f = fragment, 1 = LTR only, d = discontinuous. ψ = pseudogene. A, B and C represent subgroups of duplicons with greater similarity. (b) A dot plot of the 319 kb genomic sequence encompassing the alpha block was compared against itself. The oblique lines in the plot represent duplications whereas the dots represent retroelements. Lines connect regions of the dotplot to the appropriate duplicons. The primers shown amplify products of different lengths in each duplication. Sequence from GenBank accession number AF055066. Adapted from ref. [17].
To characterize the PFB, it is helpful to amplify haplospecific geometric elements [30], see also Table 3. Essentially, this approach reveals duplications as seen in Figure 8. McLure developed the approach to find PFB throughout the genome [36]. Paralogous regions are also helpful as shown in Figure 9.
Figure 9.
Paralogous locations of MHC genes. MHC genes are found on four chromosomes: 1, 9, 19 as well as chromosome 6. The arrangements of genes in each of the paralogous groups can be largely explained by duplication with and without inversion events. The genes common to chromosomes 6 and 9 are shown.
Once identified, we recommend tracking the polymorphism through panels of multigenerational families as illustrated in Figure 10. Although the region is over 10 megabases, recombination was not found. The different haplotypes in the three breeds must have been conserved for at least hundreds of generations and mark differences in function such as the melting point of fat [37].
Figure 10.
Tracing segregation through three generation families. The alleles at MRIP, now known as myosin phosphatase Rho-interacting protein, are used to designate haplotypes within the 5.5 Mb region of bovine chromosome 19 from SREBF1 to TCAP. Within this region, there are many genes involved in muscle development, growth and fatty acid synthesis. For further details, see Williamson et al. [38].
8. Applications to NGS and the 1000 genomes project
8.1. Mapping PFB from 1000 genomes data
Since it is known that PFB can be mapped by plotting diversity measurements (see Figure 3), we asked whether it would be possible to use data from the 1000 Genomes Project [39] in the same way.
Earlier work was based on haplotypes defined in multigenerational families. Initially, sequences of haplotypes were determined from Sanger sequencing of homozygous cell lines. In contrast, variations in 1000 genomes are determined from NGS for heterozygous and unrelated individuals. The phasing is an estimate based on ideas inherent in population genetics. It is known that the approach is a risky approximation. For example, artefactual “switch-overs” between haplotypes are misleading [40]. Since the reads tend to be short, such as just hundreds of bases, assembly can be fraught. There is a risk of missing complex polymorphisms and underestimating the number of ancestral haplotypes. Given these problems, we plotted several indices related to the 1000 genomes. The intention was to identify any similarities with the distribution as shown in Figure 3.
Unexpectedly, Figure 11 shows a remarkable correspondence between the classical measurements and our extraction from the 1000 Genomes database. The exception around 31.4 Mb was missed by the NGS reanalysis presumably because it is a region which is rich in complex iterative sequences, as shown in Figure 12.
Figure 11.
Regions of high sequence diversity within 1000 genomes are similar to previously identified PFB. Imputed haplotypes in the 600 kb region surrounding HLA-B from 553 individuals were downloaded from the 1000 Genomes browser [41]. The population groups chosen were of African, European and Asian origin (ACB, ASW, BEB, CEU, CHB and YRI). The majority of variations recorded in the 1000 Genomes vcf files are SNPs, but some indels up to 174 bp are recorded. For each imputed haplotype, we counted the number of differences from the reference sequence in 10 kb sections. Indels were counted as one difference, irrespective of length. The black curve represents the maximum difference at each 10 kb. The red lines, taken from ref. [42], show the amount of nucleotide diversity between two individual haplotypes, counted in 100 bp sections. Haplotypes compared for this section were 44.1 to 62.1, 44.1 to 8.1 and 8.1 to 14.1. Squares show the number of LD_link [41] “haplotypes”, calculated from sets of adjacent variants in 500 bp intervals. LD link requires that variants be biallelic and only takes single nucleotide changes, not indels. Only variants with at least two examples in the CEU and YRI populations were included.
Figure 12.
Complex iterative element. Dotplot of a 10 kb region in the MHC between MICA and MICB showing a complex iterative element. Gaudieri [42] shows high nucleotide diversity for this region which was not recorded within 1000 Genomes data. Example sequences for AH 7.1 and AH 44.1 downloaded from UCSC genome browser. Dotplot generated with Gepard [43] using word length 10.
These results are very encouraging in that the advantages of NGS can be coupled with identification of genomic architecture and therefore targeting of the most informative regions. The similarity, by simply counting the base differences per 10 kb, can be refined and applied to the whole genome. The plot of number of “haplotypes” is also promising, although clearly not indicative of the number of ancestral haplotypes.
8.2. Comparing polymorphic sequences of well-characterised PFB
Since there are numerous ancestral haplotypes within a PFB, it is essential to compare as many sequences as possible. An example is shown in Figure 6.
It can be seen that
Only a minority of sites are informative and these must be selected from the remainder.
Kilobases need to be examined and reduced 10- to 100-fold, retaining the informative sites.
Different haplotypes are defined by specific combinations of bases at those informative sites.
Very few single nucleotide polymorphisms are specific for a particular ancestral haplotype. On the contrary, specific combinations may be best defined by comparison with a library of reference sequences.
Indels are important: alignments can be misleading.
Thus, although the identification of each of the many haplotype remains challenging, the overall patterns of informative sites are helpful in screening for PFB and for localising haplospecific sequences.
9. Conclusion
In analysing NGS databases, we recommend:
Screening for PFB.
Alignment based on the ability to detect multiple, and even hundreds of ancestral haplotypes.
Analysis must recognise that haplospecificity is confirmed by many characteristics including RLE, indels, copy number and complex iterative sequences.
Analysis may be facilitated by examining paralogous regions which help to define interactions, including epistasis.
Validation of results by showing segregation in multigenerational family studies.
Confirming biological significance by demonstrating permissive or sine qua non associations.
\n',keywords:"Ancestral haplotypes, Polymorphic frozen blocks, Genomic evolution",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/49529.pdf",chapterXML:"https://mts.intechopen.com/source/xml/49529.xml",downloadPdfUrl:"/chapter/pdf-download/49529",previewPdfUrl:"/chapter/pdf-preview/49529",totalDownloads:1099,totalViews:641,totalCrossrefCites:4,totalDimensionsCites:5,hasAltmetrics:1,dateSubmitted:"April 21st 2015",dateReviewed:"October 19th 2015",datePrePublished:null,datePublished:"January 14th 2016",readingETA:"0",abstract:"In this era of whole-genome, next-generation sequencing, it is important to have a clear understanding of the concept of “haplotype”. We show here that most of the important regions of the genome can be described in terms of polymorphic frozen blocks (PFB). At each PFB, there are numerous, even hundreds, of alternative ancestral haplotypes. Haplotypes, not genes, can be regarded as the principal unit of inheritance. We illustrate how sequence data can be analysed to reveal and define these ancestral haplotypes.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/49529",risUrl:"/chapter/ris/49529",book:{slug:"next-generation-sequencing-advances-applications-and-challenges"},signatures:"Sally S. Lloyd, Edward J. Steele and Roger L. Dawkins",authors:[{id:"176478",title:"Prof.",name:"Roger",middleName:null,surname:"Dawkins",fullName:"Roger Dawkins",slug:"roger-dawkins",email:"rldawkins@cyo.edu.au",position:null,institution:{name:"Uganda Wildlife Authority",institutionURL:null,country:{name:"Uganda"}}},{id:"177337",title:"Dr.",name:"Ted",middleName:null,surname:"Steele",fullName:"Ted Steele",slug:"ted-steele",email:"ejsteele@cyo.edu.au",position:null,institution:null},{id:"177338",title:"Dr.",name:"Sally",middleName:null,surname:"Lloyd",fullName:"Sally Lloyd",slug:"sally-lloyd",email:"slloyd@cyo.edu.au",position:null,institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Haplotype terminology",level:"1"},{id:"sec_3",title:"3. Definitions and concepts",level:"1"},{id:"sec_4",title:"4. Use of ancestral haplotypes",level:"1"},{id:"sec_5",title:"5. Sequencing of critical genomic regions",level:"1"},{id:"sec_6",title:"6. Sequence analysis of ancestral haplotypes",level:"1"},{id:"sec_7",title:"7. Finding polymorphic frozen blocks and their ancestral haplotypes",level:"1"},{id:"sec_8",title:"8. Applications to NGS and the 1000 genomes project",level:"1"},{id:"sec_8_2",title:"8.1. Mapping PFB from 1000 genomes data",level:"2"},{id:"sec_9_2",title:"8.2. Comparing polymorphic sequences of well-characterised PFB",level:"2"},{id:"sec_11",title:"9. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Kulski J, Suzuki S, Ozaki Y, Mitsunaga S. In Phase HLA Genotyping by Next Generation Sequencing—A Comparison Between Two Massively Parallel Sequencing Bench-Top Systems, the Roche GS. In: Xi Y, editor. HLA Assoc. 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Nucleic Acids Res 2014;42:D903–9. doi:10.1093/nar/gkt1188.'},{id:"B42",body:'Gaudieri S, Kulski JK, Dawkins RL, Gojobori T. Extensive nucleotide variability within a 370 kb sequence from the central region of the Major Histocompatibility Complex. Gene 1999;238:157–61.'},{id:"B43",body:'Krumsiek J, Arnold R, Rattei T. Gepard: A rapid and sensitive tool for creating dotplots on genome scale. Bioinformatics 2007;23:1026–8. doi:10.1093/bioinformatics/btm039.'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Sally S. Lloyd",address:null,affiliation:'
CY O’Connor ERADE Village Foundation, 24 Genomics Rise, Piara Waters, Western Australia, Australia
'},{corresp:null,contributorFullName:"Edward J. Steele",address:null,affiliation:'
CY O’Connor ERADE Village Foundation, 24 Genomics Rise, Piara Waters, Western Australia, Australia
'},{corresp:"yes",contributorFullName:"Roger L. Dawkins",address:"rldawkins@cyo.edu.au",affiliation:'
CY O’Connor ERADE Village Foundation, 24 Genomics Rise, Piara Waters, Western Australia, Australia
School of Veterinary and Biomedical Sciences, Division of Health Sciences, Murdoch University, Murdoch, Western Australia, Australia
Faculty of Medicine and Dentistry, University of Western Australia, Nedlands, Western Australia, Australia
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\n
1. Introduction
\n
Diagnosis and treatment of human diseases using an implantable electronic device represent a new trend in modern medicine. While the developments of biosensors, bioelectric stimulators and drug release mechanisms are important in the designs of medical implants, these developments are application specific. Therefore, they cannot be studied in a unified fashion. On the other hand, essentially all implantable devices require a common component: a power supply, which is usually a battery. Recent advances in wireless power transfer (WPT) provide an alternative method to power implantable electronic devices [1, 2, 3]. The WPT technology not only eliminates the needs of repeated surgical replacements of a depleted battery within the human body, but also reduces the size of the implant, simplifies the implantation procedure, and enables the device to be placed in restricted anatomic locations prohibitive to large implants.
\n
Due to the importance of WPT in the next-generation medical implants, there have been extensive studies over recent years [4, 5, 6, 7]. One of the major limiting factors in battery-less implants is the low power output at the receiving end due to the weak coupling of the wireless power link. Many existing WPT components in biomedical implants operate in the low-MHz frequency range, e.g., those utilizing the widely accepted 13.56 MHz industrial, scientific, and medical (ISM) band. Although the WPT component in this frequency range is easy to design and robust, a relatively large receiver antenna is required, which limits its application to implantable devices in millimeter scales [8]. In recent years, it has been demonstrated that this challenge can be overcome by increasing the operating frequency and producing spatially focused regions within the biological tissue [9]. This approach effectively makes the WPT component smaller; however, the design of the power receiver coils that both operate in a high frequency and adapt to anatomical features of biological organs or tissues has not be well studied. In essentially all magnetic resonance based WPT systems reported, the power receiver within the implant utilizes a spiral coil in either a planar or a solenoidal form, as shown in Figure 1a and b, respectively [4, 5, 6]. In general, the planar spiral coil (PSC) [4, 5, 7] has been used in implants having a relatively larger surface, such as certain cardiac pacemaker [10]. In other cases, medical implants are often designed in a cylindrical or capsular shape such as the Bion® microstimulator [11]. For these cases, the use of a solenoidal coil is more common [12, 13, 14]. Despite successful designs exist, these two forms of coils cannot meet the requirements for all medical implants. For example, the human body has many tubular- shaped organs, such as nerves, lymphatic channels and blood vessels. An implant that wraps around such a biological structure to perform sensing and therapeutic functions is often desirable. In these cases, serious problems are encountered, with rare exceptions, because the structure is not allowed to be cut, and it is difficult to cut and rejoin a solenoidal coil during surgery. In addition, the optimal orientation of the implant may not comply with the orientation of the power transmitter coil outside the human body. In order to solve these problems, we will present a new form of coil, called double-helix (DH) coil (Figure 1c), to be applied to tubular organs within the human body.
\n
Figure 1.
Power receiver coils within the body: (a) planar spiral coil, (b) solenoidal coil, and (c) DH coil.
\n
Implantable devices are used not only for diagnosis and treatment of human diseases, but also for developments of new drugs and therapeutic mechanisms (e.g., electric stimulation). In the early stage of these developments, an animal model (e.g., the rodent model) is often utilized to study both treatment efficacies and side effects. In these studies, specially designed microsensors are often implanted within the body of a laboratory rodent to measure certain variables of interest [9]. Frequently, animal behaviors are also monitored by videotaping and other means [15]. This approach often encounters a significant problem of lacking a suitable power supply because the use of either a battery or a wire connection to the implant inside the body seriously interferes with animal’s mobility and behavior. In this case, the application of the WPT technology is essential because it allows much reduced weight and size of the system being carried by, or implanted within, the rodent [16]. In order to provide the animal with a sufficient space for free movements, a special WPT system with a large stationary transmitter (in which the coil is embedded under the floor of an animal cage) and a miniature receiver (implanted within or carried by the animal) is required. In order for the WPT system to perform properly regardless of the animal’s location within the cage, the transmitter must produce an even radio-frequency (RF) magnetic field throughout the floor of the animal cage. As a result, the wirelessly delivered energy is relatively even everywhere over the entire floor. This chapter studies this problem and presents a seven-coil design with several desirable properties, including the theoretical optimality and ease of implementation.
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This chapter is organized as follows. In Section 2, we describe the DH coil that can be applied to tubular organs within the human body. The coupling factor and power transfer efficiency (PTE) were analyzed. To further evaluate the performance of the DH coil, both simulations and experiments were conducted and presented. In Section 3, we present a power mat consisting of an array of planar transmitter coils. This mat produces a nearly even magnetic field distribution over the entire animal cage floor. For clarity, we present our evaluation, simulation and/or experimental results at the end of each methodological section. Finally, we conclude this chapter in Section 4.
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2. Double-helix coil for wrap-around implants
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The human body contains networks of tubular organs, such as nerves, lymphatic channels and blood vessels [17]. In order to monitor the functions or pathologic states of these organs (e.g., clogging of a certain major blood vessel) or provide therapeutic functions (e.g., stimulating a peripheral nerve), a wirelessly powered miniature implant wrapped around a tubular or rod-like biological structure is highly desirable. Although an ordinary solenoidal coil can support this wrap-around implant, an intact tubular organ usually cannot be cut and rejoined to allow a solenoidal coil to be threaded into the desired implanting position. Alternatively, one may wind the coil wire around the tubular organs manually during surgery. This method is practically unacceptable due to the restricted time of surgery and difficulties in quality control manual winding. Another method is to wrap the tubular organ by a coil that has been cut longitudinally. To reform an intact coil, a surgeon needs to reconnect the wires by soldering or using special connectors. This approach is also unrealistic due to the high risk of infection involved and the possible failure of the connectors.
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In addition to these practical difficulties, the usage of a solenoidal coil for wrap-around implants suffers from another implementational problem. In most cases, it is desirable to use a flexible PSC for the power transmitter because this planar coil can be easily integrated with a garment, a blanket or a bedding sheet, providing a high convenience for unobtrusive recharging of the implant. In order to achieve the maximum coupling between the transmission and reception coils, the solenoidal coil of the implant is expected to be oriented perpendicularly to the body surface (Figure 2a). This requirement is highly problematic because, as indicated by human anatomy [17], many tubular organs within the body are oriented parallel to the body surface, which provides the worst orientation to the PSC for power transmission because of the weakest magnetic coupling (Figure 2b).
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Figure 2.
The implanted solenoid coil (a) perpendicular and (b) parallel to a planar transmitter (shown in blue).
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To address these significant problems, we have developed an air-core DH coil for tubular implants [18, 19]. The new coil can be printed on a flat flexible printed circuit board (PCB) and installed on a tubular biostructure during surgery. As shown in Figure 3, when the DH coil is wrapped around a tubular organ parallel to the skin surface, the optimal coupling can be achieved with a PSC integrated with a garment or a bedding sheet.
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Figure 3.
A DH coil is wrapped around a biological structure (red curve) to serve as a power receiver.
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2.1 Structural design of DH coil
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Figure 4a shows a set of parallel sinusoidal wires printed on both sides of a flexible PCB. This PCB is made of polyimide film which is characterized by high strength, low RF energy loss, small thickness, and high flexibility. The wires on two sides are connected to each other in series via a column of through holes (one of them is shown), forming closed loops. The current paths are denoted by the black arrows in Figure 4a. In addition to the DH coil, sensors, actuators, microprocessor and electronic elements (not shown) can be installed on the same flexible PCB. During surgery, the hermetically sealed PCB (using a biocompatible polymer material) is wrapped around the tubular structure at the position of interest forming a double helix winding along with all electronic components, as shown in Figure 4b. It can be observed that, after the tubular structure is formed, the closed loops on the two sides of the PCB form opposite tilt angles but maintain the clockwise/counterclockwise current direction.
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Figure 4.
(a) Schematic representation of the DH coil and current directions indicated by arrows. Conductors are printed on both sides of the flexible PCB; (b) the PCB is wrapped to form a DH coil.
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The two-layer structure in Figure 4 can be extended to a multiple-layer structure using a PCB with more than two layers. Similarly, the 45° tilted angle in each layer can be modified to adapt to specific tubular organ orientation for optimal wireless power delivery.
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2.2 Inductance and mutual inductance of DH coil
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As shown in Figure 5, for simplicity, the DH coil is separated into several cells and each cell consists of an inner loop (Loop 1) and an outer loop (Loop 2).
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Figure 5.
(a) The DH coil can be separated into n cells, having mutual inductance with each other; (b) cell model.
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By superposition, the inductance of the DH coil is equal to the sum of the cell inductance and the mutual inductance between each cell (Figure 5a), namely:
where Mi,j denotes the mutual inductance between cell i and cell j, and Lcell denotes the inductance of a single cell.
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According to the cell model (Figure 5b), the inductance of a single cell is the sum of the inductances of Loops 1 and 2 and their mutual inductance. Since the loops are perpendicular to each other, the mutual inductance between the loops is zero so that the inductance of a single cell is given by
Therefore, the total inductance of the DH is derived based on the superpositions of the calculated inductances by Eq. (2).
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As shown in Figure 7a, the mutual inductance between the DH coil and the transmitter (Tx) can also be regarded as the sum of all individual mutual inductances between Tx and each loop in the DH coil, namely,
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Figure 7.
(a) The total mutual inductance between Tx and the DH coil is calculated by the superpositions of the mutual inductances between Tx and all cells; (b) Modeling of the mutual inductance between Tx and one cell.
where MTi-1 and MTi-2 are the mutual inductances between Tx and the ith inner and outer loops, respectively, MTi is the mutual inductance between Tx and the ith cell, and n denotes the cell number. For simplicity, Tx is modeled as a circular coil with only one turn as shown in Figure 7b.
where RTX is the radius of Tx, μ0 is the magnetic permeability of free space, and d is the vertical distance between the cell and Tx. Accordingly, we have
According to the magnetic resonant WPT theory, the coupling factor k largely influences system performance [20]. In order to evaluate the coupling factor in the system with the misalignment between the transmitter and receiver coils, the proposed DH coil was compared to a conventional double-layer solenoid by simulation. The transmitter was modeled as a PSC with the outer and inner radii being 30 and 15 mm, respectively. For the DH coil and conventional solenoid, R1 and R2 were 5 and 6 mm, respectively. The variation of k was investigated with respect to the lateral and angular misalignments.
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Figure 8 shows the simulation models with lateral or angular misalignments. X0 and Y0 in Figure 8a and b indicate the displacements along the x-direction and y-direction, respectively. α and β indicate the rotating angles around the x-axis and y-axis, respectively. The vertical distance d in Figure 8c and d is 20 mm in all cases. The simulation was used to calculate the coupling factor in different scenarios. The results are shown in Figure 9.
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Figure 8.
Simulation models of (a) DH coil and (b) solenoid coil for lateral misalignment, and for angular shifting around (c) the x-axis and (d) the y-axis, respectively.
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Figure 9.
The coupling factor as a function of the relative position between the receiver and transmitter coils in different cases: (a) DH coil with lateral misalignment, (b) traditional coil with lateral misalignment, (c) the angular shifting around the x-axis, and (d) the angular shifting around the y-axis.
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It is seen that offers the maximum coupling factor k of the conventional solenoid much smaller than that of the DH coil, comparing Figure 9a and b. Additionally, the coupling factor k of the DH coil is larger than that of the conventional solenoid in most of the measurement range. Figure 9c showed that k is essentially invariable as the conventional solenoid rotates around the x-axis. However, the DH coil has an optimal angle as which the largest k is achieved. With β decreases, the central axes of both the DH coil and conventional solenoid change from being perpendicular to being parallel with the plane of Tx as shown in Figure 9d. Within such a process, the coupling factor of the solenoid decreases, while the coupling factor increases for the DH coil. In addition, when β is 0, the coupling factor of the DH coil is much larger than that of the conventional solenoid. Accordingly, the orthogonal-coil structure enhances the mutual inductance. This phenomenon verifies the superiority of the DH coil over the traditional solenoid.
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2.4 Experimental results
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We constructed several prototypes of DH coils with variable turns, gaps and widths. Then, the coil with the largest quality factor was chosen and tuned to a resonant frequency of 5.2 MHz using capacitors. This DH coil is presented in Figure 10.
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Figure 10.
Experimental setups for efficiency measurement.
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To study WPT performances in different misalignment scenarios, the PTE was chosen as an evaluation index. The PTE was measured based on the scatter parameters measured by a network analyzer. PTE measurements were also performed for both lateral and angular misalignments. The results shown in Figure 11 indicate that the WPT system achieves the maximum PTE at the resonant frequency. However, the PTE decreases as the misalignment increases, similar to the variation of the coupling factor.
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Figure 11.
PTE measurements vs. frequency with variable misalignments: (a) lateral misalignment in the x-direction, (b) lateral misalignment in the y-direction, (c) angular misalignment around x-axis, and (d) angular misalignment around y-axis.
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It can be observed that the PTE is strongly dependent on the inductive coupling, which was discussed in the previous section. Therefore, the proposed DH coil offers more efficient power delivery than the traditional solenoid.
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3. Mat-based wireless power transfer to moving targets
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Neural stimulation and recording provide emerging prosthetic and treatment options for spinal cord injury, stroke, sensory dysfunction, and other neurological diseases and disorders. Neural recording from awake animals with observable behavior has greatly enhanced our understanding of central and peripheral nervous systems. Although there has been substantial studies on miniaturized, implantable electronic circuits that record neural data and stimulate neuronal networks in freely moving laboratory animals, the mobility of the animal subject is often limited, and the experimental results obtained under restricted conditions may not reflect the full repertoire of brain activity corresponding to their natural behaviors [16]. There are similar problems in the study of new drugs which often requires monitoring a number of variables from the inside of the animal body and observation of their mobility and behaviors.
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Traditionally, magnetic induction was used for WPT using a similar form to a transformer [21]. This form of the magnetic induction method is highly efficient (>90%) in the near-field range, but much less efficient as the transmission distance increases. In 2007, an efficient mid-range WPT via strongly coupled magnetic resonance was reported [22]. This system consists of four coils (Figure 12), namely, driver, primary (or transmitter), secondary (or receiver), and load coils. Inductive coupling is used between the driver and primary coils as well as between the secondary and load coils. The primary and secondary coils with the same resonant frequencies tend to exchange energy efficiently. This mechanism is valuable in the application to medical implants because biological tissues are generally non-resonant at the operating frequency in the RF range.
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Figure 12.
A resonance based WPT system including four coils, namely driver, primary, secondary, and load coils.
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Because our special WPT system involves moving targets (animals, e.g., rodents), the vertical component of the magnetic field generated by the transmitter is required to be distributed as even as possible over the entire area of interest (e.g., floor of the rodent cage). When this condition is satisfied, the device carried by or implanted within each rodent can receive steady power at any location of the floor. Previously, we designed a WPT system in which multiple circular spiral coils were printed on hexagonal PCBs [23]. These PCBs were then tiled hexagonally forming a “power mat” shown in Figure 13. Note that the use of hexagons in the pack of coils is not an arbitrary choice, rather it has been proven that this design will leave the smallest gap between circular resonator coils [24]. The power mat is able to deliver wireless power to the implants and “carry-on” devices to multiple rodents which move freely on the floor above the mat.
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Figure 13.
WPT system in which the floor of the animal cage is located over a hexagonally packed power mat.
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It has been found from computer simulation that the packing of a circle by identical disks demonstrates interesting patterns [25]. Denser packings consist of specific numbers of disks. The first several numbers are: 1, 7, 19, 37, 61, and 91. Although the packing density increases as more disks are packed within the enclosing circle, the density is upper-bounded by \n\n\nπ\n2\n\n/\n12\n≈\n0.822\n\n. Although, in general, using more disks produces a higher density, the implementation complexity increases as the number of disks increases. Additionally, it is difficult to connect the RF signal to numerous transmitter (Tx) coils, and the cost involved is high. On the other hand, we have previously reported that the RF signal can be easily connected to a pair of open concentric rings to power seven Tx coils simultaneously [23]. Therefore, if more than one coil is used in the Tx, the seven-coil design is often the best choice for most practical applications to power free-position devices although its packing density is not the highest.
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3.1 Theoretical analysis of mat-based WPT system
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As shown in Figure 14, the mat-based WPT system enables magnetically coupled resonance between an array of transmitter coils and a single receiver coil. An adjustable RF oscillator produces a sinusoidal signal, which is amplified by a power amplifier. The output of the amplifier is connected to an array of driver coils which are inductively coupled with primary coils [23]. At the power receiving site (a laboratory animal), the receiver coil is inductively coupled with a load coil to supply the power to the electronic components within the implant.
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Figure 14.
Mat-based WPT system design.
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In the coupled mode theory (CMT), the first eigen-mode is used to analyze a resonant system. The approximation by the first eigen-mode is quite accurate under the condition of a strong coupling in the WPT system. In practical applications, it is not possible or necessary to directly work on an arbitrary large number of resonators. Rather, for a large hexagonally packed transmitter (HPT) mat (Figure 15), every one of the resonators can be treated as in the middle of the mat, except for those ones at the edge, and fortunately the edge effect can be solved simply by making the mat larger than the animal cage floor. For this reason, we may simplify analysis by examining the seven-resonator case.
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Figure 15.
A large hexagonally packed power mat.
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Let us index the seven transmitters from 1 to 7 and the single receiver have an index of 8. In order to describe the strongly coupled system, a set of differential equations based on CMT is given by [22].
where \n\n\na\ni\n\n\nt\n\n\n, \n\ni\n=\n1\n,\n2\n,\n⋯\n,\n7\n\n, and \n\n\na\n8\n\n\nt\n\n\n are, respectively, the first eigenmodes of the transmitter and receiver resonators corresponding to the natural frequency \n\n\nω\n0\n\n\n, \n\n\nΓ\ni\n\n\ns are the intrinsic loss rates of resonators due to absorption and radiation, \n\n\nΓ\nL\n\n\n represents the rate of energy going into the load, \n\nκ\n\ns are pairwise coupling coefficients between resonators, and \n\n\nf\ni\n\n\ns are the inputs to the transmitter resonators. In our case, all \n\n\nf\ni\n\n\ns are the same, i.e., \n\n\nf\n1\n\n=\nf\n\n=\n\n2\n\n\n⋯\n=\n\nf\n7\n\n=\nf\n\n. Note that \n\n\na\ni\n\n\ns are also known as positive frequency components in terms of CMT. Although \n\n\na\ni\n\n\n (generally complex-valued) does not represent a voltage or current directly, the energy contained in each resonator can be represented as \n\n\n\n\na\ni\n\n\n2\n\n\n, and the power output of the system is \n\n2\nΓ\n\n\n\n\na\n8\n\n\n\nL\n\n\n2\n\n\n. Using the CMT concept, the goal of obtaining a uniform power output becomes finding a constant\n\n\n\na\n8\n\n\n\n within the WPT space.
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To make Eq. (12) more concise, we write it into the following form:
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\n\n\na\ṅ\n\n=\nAa\n+\nf\n\nE13
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where the vectors and matrices are in correspondence with Eq. (12).
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If the WPT system is driven by a sinusoidal input, e.g., \n\nf\n\nt\n\n=\n\nFe\n\njω\n\nt\n\n0\n\n\n\n\n\n\n1\n1\n\n⋯\n1\n\n0\n\nT\n\n\n, the positive frequency components have the form of\n\na\n\nt\n\n=\na\n\ne\n\nj\n\nω\n0\n\nt\n\n\n\n at the steady state. Substituting this into Eq. (13), we can solve for \n\na\n\nt\n\n\n
In case where B is not invertible, its pseudo inverse can be used instead. Thus, given \n\n\nΓ\ni\n\n\n, \n\n\nκ\nij\n\n\n, and \n\n\nf\ni\n\n\n, we can compute \n\n\na\ni\n\n\nt\n\n\n analytically by Eq. (14). The CMT approach provides a powerful analytical tool for the multi-resonator WPT system. For example, it has been utilized to maximize the efficiency of power transfer and investigate the relay effect by inserting one or more resonators between the transmitter and receiver [26]. Using CMT, we have studied the dynamics of the system involving an array of resonators [27]. Although the previous studies have shown that CMT well characterizes the temporal behavior of the WPT system, it has clear limitations when the system parameter changes. For example, when the receiving resonator moves over the HPT mat, the coupling coefficients \n\n\nκ\n\n8\ni\n\n\n\n\ni\n=\n1\n\n2\n⋯\n7\n\n\n change, and the variations of the system behavior are difficult to determine analytically. In order to study the motion effect of the receiving resonator and answer the critical question whether the receiver resonator can harvest sufficient amount of power at different locations over the HPT mat, we performed numerical simulation and conducted an experimental test.
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3.2 Simulation of mat-based WPT system
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For a clear illustration of the design principle of the mat-based WPT system, we simulated a single HPT cell consisting of seven PSCs, as limited by the computational complexity. This simulation does not cause a loss of generality because the results of multiple cells can be obtained simply by superposition of single cell results. In most cases, changes in the position of a device lead to a variation in mutual inductance which results from a change in the magnetic field distribution. Although some unevenness in the distribution is unavoidable, we expect this distribution to be nearly uniform with enhanced misalignment tolerability for WPT applications involving moving targets.
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We utilize the concentric model to approximate the coil where the total magnetic field is a superposition of the fields of individual loops in the coil. Assuming that a loop with a radius of a is centered at the origin carrying a current I. Based on the Biot-Savart law, the x-, y- and z-components of the magnetic field at point r (x, y, z) are given by [28].
where \n\n\nρ\n2\n\n=\n\nx\n2\n\n+\n\ny\n2\n\n\n, \n\n\nr\n2\n\n=\n\nx\n2\n\n+\n\ny\n2\n\n+\n\nz\n2\n\n\n, \n\n\nα\n2\n\n=\n\na\n2\n\n+\n\nr\n2\n\n−\n2\naρ\n\n, \n\n\nβ\n2\n\n=\n\na\n2\n\n+\n\nr\n2\n\n+\n2\naρ\n\n, \n\n\nk\n2\n\n=\n1\n−\n\nα\n2\n\n/\n\nβ\n2\n\n\n, \n\nC\n=\n\nu\n0\n\nI\n/\nπ\n\n, and K(.) and E(.) are the complete elliptic integrals of the first and second kinds, respectively. For easier calculation, without loss of generality, the current is chosen so that \n\nC\n=\n1\n\n. With the magnetic field of a single loop, we can apply the superposition rule to get the magnetic field generated by a multi-loop circular coil. Since the receiver coil is always in parallel with the transmitter coil (which is installed below the animal cage floor), the fluxes in the receiver coil are contributed by the z-component of the magnetic field. Therefore, we will focus on the z-component of the magnetic field in our analysis.
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With these simplifications, we can calculate the magnetic field of the seven-transmitter powering platform. Figure 16 shows a magnetic field with different distances between the transmitter and the surface (evaluating plane) where the field was evaluated. It can be seen that the separation between the evaluating plane and the transmitter enables the variation of the z-component of magnetic field. When the distance is increasing, the flatness of the magnetic field also improves at first. However, when the height is too large, the magnetic field distribution becomes similar to that of a larger spiral coil, which affects both the flatness and magnitude of the magnetic field. On the other hand, when the height is too small, although the peak magnitude is larger, the z-component is inversed at the gap between resonators, which implies a large fluctuation of the magnetic field.
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Figure 16.
Z-component of the magnetic field distribution with different separations between the evaluation plane and the transmitter consisting of seven coils. (a) 3.25 cm, (b) 7.25 cm, (c) 10.25 cm, and (d) 20.05 cm.
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In order to investigate the effect of mutual inductance between turns in the spiral coil, we also performed a simulation study on the 7-coil mat using a commercial finite element (FE) software HFSS (Ansys Corp., Pittsburgh, PA). Figure 17 shows the 3D model of the HPT mat used in the simulation, where each PSC was 20 cm in outer diameter, 1 cm in conductive trace width, and 1 cm in trace spacing. The input power was set at 1 W. As stated previously, the goal of the power mat design was to obtain a nearly uniform magnetic field within an extended region to support WPT for moving targets, rather than optimizing PTE (the animal cage is powered from a regular AC socket).
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Figure 17.
HFSS simulation. (a) 3D model of the transmitter mat; (b) Dimensions of each PSC.
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We excited the seven PSCs simultaneously using a common RF power source. Energy was injected into the driver coil array to maintain resonance in the presence of losses and energy drawn from the magnetic field by the receiver coil. Figure 18 shows the z-component distribution of the magnetic field at 8 and 20 cm distances, respectively, above the power mat (i.e., the X-Y plane). Color indicates the magnitude of the magnetic field in the z-direction. It can be seen that, at z = 8 cm (Figure 18a), the magnitude of the magnetic field was the highest (peak) at the center of each coil, and the lowest (valley) at the junction of three coils. When the distance to the HPT mat increased to 20 cm, a smoother magnetic field distribution was observed, but approaching to the field generated by a large spiral coil (Figure 18b). In order to evaluate the evenness of distribution quantitatively, the coefficient of variation (COV) was utilized which was defined as the standard deviation of the field values divided by the mean. Thus, a smaller value of the COV indicates a more uniform distribution. Figure 19 shows the COVs of the magnetic field in the z-direction above the HPT mat at distances from 5 to 40 cm. It can be observed that the COV achieves a value <10% when the distance is larger than the size of the transmitter coil.
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Figure 18.
Distribution of the z-component of the magnetic field in a plane at (a) 8 cm and (b) 20 cm above the HPT mat at the resonant frequency of 85.2 MHz.
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Figure 19.
Variation in coefficient of variation (COV) of vertical field distribution as a function of distance above the HPT mat at the resonant frequency of 85.2 MHz.
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3.3 Receiver coil design
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In practical applications, it is almost always beneficial to reduce the size of an implantable device, whereas the WPT system requires a match of the resonant frequencies of the primary and secondary coils. We have designed a new structure of the implantable coil with a miniaturized size while having enough turns to match the resonant frequency of the primary coil. Figure 20 illustrates our design in which coils serve as both implant exterior housing and power receiving elements. It consists of two planar sub-coils and one helical sub-coil. The sub-coils are combined into a single coil within a shallow box assembly. By choosing different geometric designs for the sub-coils, different shaped boxes can be obtained. In practical implementation, the exterior of the box must be covered by a biocompatible material for biological safety.
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Figure 20.
(a) Three sub-coils winded in proper directions are combined and connected to form a single coil shown in (b).
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3.4 Experiment tests
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In order to study the performance of the mat-based WPT system experimentally, we constructed a prototype mat-based system shown in Figure 21, where a transmitter consists of seven circular spiral coils arranged in a hexagonal form. Each PSC was 13.2 cm in diameter, 2.9 mm in trace width, and 1.6 mm in trace spacing. On the reverse side of each PSC, several conductor strips were utilized to form distributed capacitances with respect to the coil on the front side. By changing the numbers of these strips, the resonant frequencies of the PSCs became adjustable. The frequencies were adjusted to 29.453 ± 0.072 MHz with a Q-factor of approximately 100. The prototype of a receiver coil includes three coils and is 25 mm in diameter, 7 mm in height, and 3.39 g in weight. The resonant frequency and Q factor were measured to be 29.075 MHz and 61, respectively.
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Figure 21.
Experimental platform for measuring magnetic field distribution.
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By measuring the induced voltage in the small receiver coil, the variation of the vertical magnetic field is given by
When the measuring coil is sufficiently small and the system is driven by sinusoidal input, the induced voltage V in the measuring coil is proportional to the local Bz. As our objective function cancels out the constants relating these two values, we can directly evaluate the cost function using V instead of Bz and compare with the calculation results. As shown in Figure 22, these measurement locations were chosen because the magnetic field distribution at any interior PSC in a regular mat can be approximated by the central PSC in each single seven-coil cell (Figure 15).
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Figure 22.
Sketch of a seven-resonator mat and the test points.
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In order to compare the measured voltage with the calculated Bz, we need to normalize both to the same scale, as they are proportional to each other. Figure 23 shows that the measured data matches the calculated ones very well, except for that the measured data tends to be larger than the calculated ones, which is because the receiver can capture a small portion of horizontal field in additional to the field in the vertical direction. When the measured data are normalized to the center value where the horizontal component is almost zero, the other positions will have larger field than the expected one.
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Figure 23.
Comparison of measured and calculated vertical magnetic field over the prototype mat.
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In our WPT system design (Figure 13), the separation between the primary and secondary coils includes a distance between the mat and the floor. This distance can be adjusted to achieve both a high WPT performance and an acceptably uniform magnetic field distribution. At different separations, we measured the peak-to-peak values of induced RF voltages in the load coil when the system was powered by a sinusoidal wave at the resonant frequency (approximately 26.6 MHz). Our experiments show that, for our particular system design, the separations of approximately 10 cm and 8 cm between the primary and secondary coils provide a good compromise between performance and magnetic field distribution. In order to visualize this distribution, we interpolated the 21 measured values and plotted the results in Figure 24. At a separation of 10 cm, the measured 21 voltage values were in the range between 1.12 and 1.64 V, whereas the mean and standard deviation were 1.23 and 0.11 V, respectively. The relatively small standard deviation indicates a nearly uniform magnetic field distribution, as observed in Figure 24. The results indicate that a flat magnetic field can be achieved by our power mat design and that this design is effective for WPT to biomedical implants in freely moving animals.
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Figure 24.
Voltage distribution computed by interpolating the 21 measured voltage values across the load coil at a constant primary and secondary coil separation of (a) 8 cm and (b) 10 cm.
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4. Conclusion
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We have presented a DH coil as the WPT receiver in implantable medical devices. This new coil has several attractive properties that it can be made conveniently at high precision on a flexible PCB along with other electronic components, forming a complete flexible sheet. This sheet, after being hermetically sealed, can be wrapped around a tubular biological structure, such as a blood vessel or a nerve bundle, to perform diagnostic, monitoring and therapeutic functions. The DH coil has been mathematically analyzed, and expressions for both mutual inductance and self-inductance have been derived. We have found that the DH coil provides a higher coupling factor than the conventional solenoid coil when a lateral or angular misalignment exists. In addition, the DH coil achieves the largest coupling factor and energy transfer efficiency when the axis of the DH coil is in parallel with the plane of the planar spiral transmitter coil. Our computer simulation and experiments under lateral and angular misalignments have been conducted and their results have verified our analytical results.
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In order to support biomedical studies using the animal model, we have designed a new power mat, enabling wireless power delivery to miniaturized moving targets. The power mat contains a single or multiple transmitter cells and each cell consists of seven hexagonally packed PSCs. We have conducted theoretical, computational and experimental studies on the special WPT system to meet the challenge of distributing the electromagnetic field evenly over the power mat. We have analyzed the HPT cell using the CMT. Formulas have been derived relating the received power to the inputs and system parameters. Then, we utilize computer simulation to study the evenness of the magnetic field distribution over the power mat at different distances between the power mat and the floor of the animal cage. Finally, we constructed a prototype system, measured its magnetic field distribution and verified that our design has met the challenge. We have also presented a new design of the receiver coil consisting of three serially connected sub-coils. This new design of the receiver coil allows it to capture the most magnetic flux produced by the transmitter, facilitates a match of resonant frequencies of the transmitter and receiver, and reduces the volume of the implant.
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\n\n',keywords:"implantable device, wireless power transfer, animal experiment, power transmitter, power receiver, antenna, double-helix coil, blood vessel, nervous system, resonance, even magnetic field, miniaturization",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/69348.pdf",chapterXML:"https://mts.intechopen.com/source/xml/69348.xml",downloadPdfUrl:"/chapter/pdf-download/69348",previewPdfUrl:"/chapter/pdf-preview/69348",totalDownloads:65,totalViews:0,totalCrossrefCites:0,dateSubmitted:"April 8th 2019",dateReviewed:"August 11th 2019",datePrePublished:"October 3rd 2019",datePublished:null,readingETA:"0",abstract:"Miniature implantable electronic devices play increasing roles in modern medicine. In order to implement these devices successfully, the wireless power transfer (WPT) technology is often utilized because it provides an alternative to the battery as the energy source; reduces the size of implant substantially; allows the implant to be placed in a restricted space within the body; reduces both medical cost and chances of complications; and eliminates repeated surgeries for battery replacements. In this work, we present our recent studies on WPT for miniature implants. First, a new implantable coil with a double helix winding is developed which adapts to tubularly shaped organs within the human body, such as blood vessels and nerves. This coil can be made in the planar form and then wrapped around the tubular organ, greatly simplifying the surgical procedure for device implantation. Second, in order to support a variety of experiments (e.g., drug evaluation) using a rodent animal model, we present a special WPT transceiver system with a relatively large power transmitter and a miniature implantable power receiver. We present a multi-coil design that allows steady power transfer from the floor of an animal cage to the bodies of a group of free-moving laboratory rodents.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/69348",risUrl:"/chapter/ris/69348",signatures:"Qi Xu, Tianfeng Wang, Shitong Mao, Wenyan Jia, Zhi-Hong Mao and Mingui Sun",book:{id:"9289",title:"Wireless Energy Transfer Technology",subtitle:null,fullTitle:"Wireless Energy Transfer Technology",slug:null,publishedDate:null,bookSignature:"Dr. Pedro Pinho",coverURL:"https://cdn.intechopen.com/books/images_new/9289.jpg",licenceType:"CC BY 3.0",editedByType:null,editors:[{id:"122497",title:"Dr.",name:"Pedro",middleName:null,surname:"Pinho",slug:"pedro-pinho",fullName:"Pedro Pinho"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:null,sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Double-helix coil for wrap-around implants",level:"1"},{id:"sec_2_2",title:"2.1 Structural design of DH coil",level:"2"},{id:"sec_3_2",title:"2.2 Inductance and mutual inductance of DH coil",level:"2"},{id:"sec_4_2",title:"2.3 Coupling factor simulations",level:"2"},{id:"sec_5_2",title:"2.4 Experimental results",level:"2"},{id:"sec_7",title:"3. Mat-based wireless power transfer to moving targets",level:"1"},{id:"sec_7_2",title:"3.1 Theoretical analysis of mat-based WPT system",level:"2"},{id:"sec_8_2",title:"3.2 Simulation of mat-based WPT system",level:"2"},{id:"sec_9_2",title:"3.3 Receiver coil design",level:"2"},{id:"sec_10_2",title:"3.4 Experiment tests",level:"2"},{id:"sec_12",title:"4. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'Ma A, Poon ASY. Midfield wireless power transfer for bioelectronics. IEEE Circuits and Systems Magazine. 2015;15(2):54-60. DOI: 10.1109/MCAS.2015.2418999\n'},{id:"B2",body:'Jow U, Ghovanloo M. Design and optimization of printed spiral coils for efficient transcutaneous inductive power transmission. IEEE Transactions on Biomedical Circuits and Systems. 2007;1(3):193-202. DOI: 10.1109/TBCAS.2007.913130\n'},{id:"B3",body:'RamRakhyani AK, Mirabbasi S, Mu C. Design and optimization of resonance-based efficient wireless power delivery systems for biomedical implants. IEEE Transactions on Biomedical Circuits and Systems. 2011;5(1):48-63. DOI: 10.1109/TBCAS.2010.2072782\n'},{id:"B4",body:'Zhong WX, Zhang C, Xun L, Hui SYR. A methodology for making a three-coil wireless power transfer system more energy efficient than a two-coil counterpart for extended transfer distance. IEEE Transactions on Power Electronics. 2015;30(2):933-942. DOI: 10.1109/TPEL.2014.2312020\n'},{id:"B5",body:'Zarifi T, Maunder A, Moez K, Mousavi P. Tunable open ended planar spiral coil for wireless power transmission. In: 2015 IEEE International Symposium on Antennas and Propagation & USNC/URSI National Radio Science Meeting, Canada; 19-24 July 2015\n'},{id:"B6",body:'Seung Hee J, Zhigang W. Stretchable wireless power transfer with a liquid alloy coil. In: 28th IEEE International Conference on Micro Electro Mechanical Systems (MEMS); 18-22 January 2015; Portugal; 2015\n'},{id:"B7",body:'Hasan N, Yilmaz T, Zane R, Pantic Z. Multi-objective particle swarm optimization applied to the design of wireless power transfer systems. In: Wireless Power Transfer Conference (WPTC); USA: IEEE; 2015. 13-15 May 2015\n'},{id:"B8",body:'Yakovlev A, Kim S, Poon A. Implantable biomedical devices: Wireless powering and communication. IEEE Communications Magazine. 2012;50(4):152-159. DOI: 10.1109/MCOM.2012.6178849\n'},{id:"B9",body:'Ho JS, Yeh AJ, Neofytou E, Kim S, Tanabe Y, Patlolla B, et al. Wireless power transfer to deep-tissue microimplants. Proceedings of the National Academy of Sciences. 2014;111(22):7974-7979. DOI: 10.1073/pnas.1403002111\n'},{id:"B10",body:'Available from: http://www.implantable-device.com/category/technologies/wireless-power-transmission/\n\n'},{id:"B11",body:'Available from: http://news.bostonscientific.com/news-releases?item=58598\n\n'},{id:"B12",body:'Ahn D, Ghovanloo M. Optimal design of wireless power transmission links for millimeter-sized biomedical implants. IEEE Transactions on Biomedical Circuits and Systems. 2016;10(1):125-137. DOI: 10.1109/TBCAS.2014.2370794\n'},{id:"B13",body:'Kyungmin N, Heedon J, Hyunggun M, Bien F. Tracking optimal efficiency of magnetic resonance wireless power transfer system for biomedical capsule endoscopy. IEEE Transactions on Microwave Theory and Techniques. 2015;63(1):295-304. DOI: 10.1109/TMTT.2014.2365475\n'},{id:"B14",body:'Loeb GE, Richmond FJ, Baker LL. The BION devices: Injectable interfaces with peripheral nerves and muscles. Neurosurgical Focus. 2006;20(5):1-9. DOI: 10.3171/foc.2006.20.5.3\n'},{id:"B15",body:'Kimchi T, Xu J, Dulac C. A functional circuit underlying male sexual behaviour in the female mouse brain. Nature. 2007;448:1009-1014\n'},{id:"B16",body:'Xu Q, Hu D, Duan B, He J. A fully implantable stimulator with wireless power and data transmission for experimental investigation of epidural spinal cord stimulation. IEEE Transactions on Neural Systems and Rehabilitation Engineering. 2015;23(4):683-692. DOI: 10.1109/TNSRE.2015.2396574\n'},{id:"B17",body:'OpenStax College. Anatomy and Physiology. Rice University, Houston: OpenStax College; 2013\n'},{id:"B18",body:'Mao S, Wang H, Mao ZH, Sun M. A miniature implantable coil that can be wrapped around a tubular organ within the human body. AIP Advances. 2018;8(5):056629. DOI: 10.1063/1.5007258\n'},{id:"B19",body:'Mao S, Wang H, Mao ZH, Sun M. A double-helix and cross-patterned solenoid used as a wirelessly powered receiver for medical implants. AIP Advances. 2018;8(5):056603. DOI: 10.1063/1.5007236\n'},{id:"B20",body:'Yin N, Xu G, Yang Q, Zhao J, Yang X, Jin J, et al. Analysis of wireless energy transmission for implantable device based on coupled magnetic resonance. IEEE Transactions on Magnetics. 2012;48(2):723-726. DOI: 10.1109/TMAG.2011.2174341\n'},{id:"B21",body:'Mayordomo I, Dräger T, Spies P, Bernhard J, Pflaum A. An overview of technical challenges and advances of inductive wireless power transmission. Proceedings of the IEEE. 2013;101(6):1302-1311. DOI: 10.1109/JPROC.2013.2243691\n'},{id:"B22",body:'Kurs A, Karalis A, Moffatt R, Joannopoulos JD, Fisher P, Soljacic M. Wireless power transfer via strongly coupled magnetic resonances. Science. 2007;317(5834):83-86. DOI: 10.1126/science.1143254\n'},{id:"B23",body:'Xu Q, Wang H, Gao Z, Mao Z, He J, Sun M. A novel mat-based system for position-varying wireless power transfer to biomedical implants. IEEE Transactions on Magnetics. 2013;49(8):4774-4779. DOI: 10.1109/TMAG.2013.2245335\n'},{id:"B24",body:'Xu Q, Gao Z, Wang H, He J, Mao Z, Sun M. Batteries not included: A mat-based wireless power transfer system for implantable medical devices as a moving target. IEEE Microwave Magazine. 2013;14(2):63-72. DOI: 10.1109/MMM.2012.2234640\n'},{id:"B25",body:'Graham RL, Lubachevsky BD, Nurmela KJ, Östergård PRJ. Dense packings of congruent circles in a circle. Discrete Mathematics. 1998;181(1-3):139-154. DOI: 10.1016/S0012-365X(97)00050-2\n'},{id:"B26",body:'Zhang F, Hackworth SA, Fu W, Li C, Mao Z, Sun M. Relay effect of wireless power transfer using strongly coupled magnetic resonances. IEEE Transactions on Magnetics. 2011;47(5):1478-1481. DOI: 10.1109/TMAG.2010.2087010\n'},{id:"B27",body:'Zhang F, Liu J, Mao Z, Sun M. Mid-range wireless power transfer and its application to body sensor networks. Open Journal of Applied Sciences. 2012;2(1):35-46. DOI: 10.4236/ojapps.2012.21004\n'},{id:"B28",body:'Simpson J, Lane J, Immer J, Youngquist R. Simple analytic expressions for the magnetic field of a circular current loop. NASA Technical Document Collection. Document ID: 20010038494; 2001\n'}],footnotes:[],contributors:[{corresp:null,contributorFullName:"Qi Xu",address:null,affiliation:'
School of Artificial Intelligence and Automation, Huazhong University of Science and Technology, China
Department of Neurosurgery, University of Pittsburgh, USA
Department of Electrical and Computer Engineering, University of Pittsburgh, USA
Department of Neurosurgery, University of Pittsburgh, USA
Department of Bioengineering, University of Pittsburgh, USA
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