Depósi o de In es igación de la Uni e sidad de Se illa
h ps://idus.us.es/
This is an Accep ed Manusc ip o an a icle published by Else ie in Compu e s
in Biology and Medicine, Vol. 99 on Augus 2018, a ailable a :
h ps://doi.o g/10.1016/j.compbiomed.2018.06.016
© 2018 Else ie . En idUS Licencia C ea i e Commons CC BY-NC-ND
P ojec i e geome ic model o au oma ic de e mina ion o X- ay-
emi ing sou ce o a s anda d adiog aphic sys em
Lau a Ga cía-Ruesgas*
Uni e si y o Se ille, Depa men o Enginee ing G aphics. Isla de la Ca uja, Camino de los
Descub imien os, s/n, Se illa 41092, Spain.
Ra ael Ál a ez-Cue o
Uni e si y o O iedo, Depa men o Cons uc ion and Manu ac u ing Enginee ing. Campus de
Gijón, Gijón 33203, Spain.
F ancisco Valde ama-Gual
Uni e si y o Se ille, Depa men o Enginee ing G aphics. Isla de la Ca uja, Camino de los
Descub imien os, s/n, Se illa 41092, Spain.
José Ignacio Rojas-Sola
Uni e si y o Jaen, Depa men o Enginee ing G aphics, Design and P ojec s. Campus de las
Lagunillas, s/n. Jaén 23071, Spain.
* Co esponding au ho
Uni e si y o Se ille. Isla de la Ca uja, Camino de los Descub imien os, s/n, Se illa
41092, Spain.
Telephone: 34 (954) 486161 E-mail: lau ag @us.es
This is he accep ed e sion o publica ion o he manusc ip published in Compu e s in
Biology and Medicine. Please, ci e he published e sion.
Ga cía-Ruesgas, L; Ál a ez-Cue o, R; Valde ama-Gual, F; Rojas-Sola, JI. P ojec i e
geome ic model o au oma ic de e mina ion o X- ay-emi ing sou ce o a s anda d
adiog aphic sys em. Compu . Biol. Med. 2018; 99: 209-220. DOI:
h ps://doi.o g/10.1016/j.compbiomed.2018.06.016
This accep ed e sion o he manusc ip is deposi ed unde a CC-BY-NC-ND license.
2
P ojec i e geome ic model o au oma ic de e mina ion o X- ay
emi ing sou ce o a s anda d adiog aphic sys em
ABSTRACT
Backg ound and objec i e: Cu en ly, many o hopedic ope a ions a e planned by
analyzing X- ays. The exac posi ion o he ocus is needed o calcula e he eal size o
an objec ha is ep esen ed in conical p ojec ion, al hough in p ac ice, his posi ion is
di icul o de e mine using cu en X- ay comme cial sys ems. In his pape , a new
geome ic model is p oposed in o de o de e mine accu a ely, p ac ically, and
economically he loca ion o he emi ing sou ce o comme cial imaging sys ems using
a single s anda d X- ay image.
Me hod: The me hod equi es a speci ic e e ence loca o objec o be posi ioned in
he isual ield o adiog aphic image. Because his objec canno implemen ideal
geome ic poin s, bu ins ead wo ks wi h small sphe es, i was necessa y o
expe imen ally alida e he p oposed me hodology. The implemen ed so wa e ha was
de eloped o alida e he model was used in ou se ies o es s. In hese es s, we
s udied he in luence on he inal esul o : 1. he selec ion o a speci ic se o ma ke s in
adiog aphy, 2. he ocus posi ion a ia ion in ela ion o adiog aph and 3. he possible
o a ed angle o loca o objec abou Z axis.
Resul s: The esul s o 164 es s ha we e pe o med wi h his so wa e showed
ha he expec ed e o o 99.5% o alues anges wi h maximum e o o [-0.35%,
+0.39%], which shows ha he model is independen o he design o loca o objec and
i s posi ion and o ien a ion in he adiog aphic ield. The so wa e used o alida e he
p oposed model has been ound use ul o e i y i s eliabili y, e ec i eness, ease o
implemen a ion, and accu acy.
3
Conclusions: This model is e ec i e o calcula e he p ecise posi ion o he X- ay ocus
o any s anda d adiog aphic sys em accu a ely.
Keywo ds: p ojec i e geome ic model, X- ay ocus emi e , s anda d adiog aph,
speci ic loca o e e ence objec , MATLAB.
4
1. In oduc ion
Cu en ly, o al knee a h oplas y is an e icien and eliable app oach in o hopedic
su ge y [1,2]. Mos su ge y pa ien s epo sa is ac o y unc ional esul s and signi ican
pain educ ion, hus no ably imp o ing hei quali y o li e [3]. The e o e, he numbe o
p ima y and e ision p os heses in ecen yea s has inc eased ma kedly, especially in
younge pa ien s [4], and implan su i al is es ima ed a 92.3% a 15 yea s a e
su ge y [5].
A common p ocedu e used in p eope a i e planning [6] o knee eplacemen s consis s
o analyzing X- ays p e iously made o he pa ien . In iew o he daily na u e o hip
and knee a h oplas ies, i is becoming inc easingly impo an o make accu a e
measu emen s on s anda d adiog aphic images in o de o pe o m pos ope a i e
su eillance [7], o imp o e he design o p os he ic sys ems [8], o pe o m clinical
s udies conce ning implan s eliabili y which assess hei possible wea o de e io a ion
o e ime [9,10] o o de e mine he a ia ion o he ela i e posi ion o he p os he ic
elemen s o e long ime pe iods [11].
In daily wo k, many analyses o adiog aphs a e pe o med by measu ing on hem
di ec ly o by using wo o h ee-dimensional o e lapping empla es, in o de o
de e mine by isual compa ison, he op imal size o he implan o be inse ed [12].
Despi e being imp ecise, he measu emen s wi h empla es help su geons adap he knee
implan s and align he join p ope ly [13].
An inhe en p oblem in hese me hods is ha X- ays do no show he eal size o
adiog aphed objec s, because he image is gene a ed by conical p ojec ions. This
in ol es he loss o in o ma ion needed o pe o m ce ain s udies [14], leading o he
use o mo e cos ly echniques such as Compu ed Tomog aphy (CT) [15] o Roen gen

5
S e eopho og amme y Analysis echniques (RSA) [16], which also expose he pa ien
o highe doses o adia ion.
The pinpoin ing o he X- ay ocus posi ion will enable hese s udies o be unde aken
economically and wi h he necessa y p ecision.
In his pape , we p opose a new p ojec i e geome ic model o de e mine accu a ely he
posi ion in space o he emi ing sou ce o X- ays (X-RFE, X-Ray Focus Emi e ) o a
s anda d comme cial adiog aphic sys em, i.e. o speci y he ideal geome ic poin om
which adia ion o X- ay comme cial ube is emi ed. The comme cial adiog aphic
sys ems used in indus ial and medical applica ions do no pe mi o de e mine he
posi ion o he ocus wi h he accu acy equi ed o pe o m high p ecision
measu emen s on adiog aphed objec s. The p oblem is he X- ay emi ing ubes emi
adia ion om an inaccessible poin inside a glass lask. In addi ion, ubes a e placed
inside lead capsules in o de o a oid adia ion leaks and hei posi ion, in ela ion o X-
ay machines, p e en any a emp o measu e he posi ion o ocus di ec ly.
The p oposed model wo ks wi h adiog aphic images which we e made wi h s anda d
sys ems, (i.e. wi h a single ocus), unlike RSA analysis sys ems, which equi e special
adiog aphic machines wi h wo ocuses ha ac simul aneously. In p ac ice, mos
hospi als do no ha e RSA sys ems because o hei high p ice.
All de elopmen o he p oposed model is based on geome y ha is associa ed wi h
conical p ojec ion and classic concep s o homog aphy ha e been applied.
As i is known, i is essen ial o place a speci ic e e ence loca o objec in he isual
ield o adiog aphic image o es o e he ocus posi ion in ela ion o p ojec ion plane.
Because o he ac ha , in p ac ice, i is impossible o implemen ideal geome ic
poin s, i was necessa y o expe imen ally alida e he p oposed model and we used
6
small an alum sphe es o ha . Tan alum was used because i is a adio opaque and
physiologically ine ma e ial which is o en used in medicine ield.
So he e o e, he objec i es o his esea ch a e:
- Fi s o all, o de elop a geome ic model ha can be implemen ed as a p ac ical
compu e p og am, o he accu a e de e mina ion o Ca esian coo dina es o he
X- ay emi ing sou ce o any s anda d adiog aphic sys em.
- To ensu e ha he a o emen ioned model can be applied in sys ems wi h a single X-
ay sou ce and in expe imen al si ua ions using a single adiog aphic image.
- To design a speci ic Loca o Objec o Re e ence Ma ke s composed o small
an alum sphe es sui able o calcula ing he posi ion o he ocus o a adia ion
sys em om a single s anda d adiog aphic image.
- The geome ic model should be independen o Loca o Objec o Re e ence
Ma ke s used [17], as well as i s posi ion and o ien a ion, conside ing he
limi a ions o geome ic a angemen o i s ma ke s and i s numbe .
2. Ma e ials and Me hods
2.1 Geome ic ounda ion
I is p oposed as a me hodology o s uc u e he de elopmen o he geome ic model
he ‘p ojec i e uni y’ [18]. This me hodology consis s o he necessa y minimum
elemen s o de ine he conical p ojec ion o a poin o he h ee-dimensional space: he
ocus o p ojec ion cen e , X-RFE, which is he e e ence poin om which he conical
p ojec ion is made, a ma ke –in heo y, he O poin o he space o he geome ic cen e
o said ma ke - and i s ф(O) p ojec ion on he p ojec ion plane ( he adiog aphic image).
The p oposed p oblem sa is ies he way homog aphy is se ou pa ially, so some o i s
equa ions a e applied in he de elopmen o he p ojec i e model.
7
The coo dina es (x,y) o he p ojec ed poin s a e known in ela ion o a speci ic poin o
he plane, in he p oposed case, he uppe le co ne o he adiog aph. A single
p ojec i e uni canno de e mine he h ee coo dina es o he p ojec ion cen e and hence
mo e han one will be needed. Speci ically, acco ding o he p inciples o he
homog aphy, in o de o es o e an objec , a leas ou p ojec i e uni s mus be
conside ed and he ela i e dis ances be ween ou poin s o he objec and hei
co esponding p ojec ions ha e o be known.
The ma hema ical de elopmen equi es a se ies o poin s dis ibu ed in space o which
he coo dina es a e known in ela ion o a gi en e e ence sys em o be de e mined.
Thus, he aim is o ind he ocus o a conical p ojec ion om he ela i e dis ances
be ween poin s in space and he ela i e dis ances be ween he p ojec ions o hese
poin s. Ini ially, he posi ion o poin s in space is a bi a y. To simpli y, he o igin o
coo dina es has been placed in he p ojec ion cen e .
Since only ela i e dis ances be ween poin s will be conside ed, any poin ha is
inco po a ed mus be de ined acco ding o he i s poin O. The e o e, he dis ance h is
o be de e mined in ela ion o he adiog aph plane, and he coo dina es o he poin O
(O1, O2, O3) in ela ion o ocus, which is he o igin o he coo dina es. This in o ma ion
will allow o posi ion he adiog aph in ela ion o ocus since coo dina es o i s uppe
le co ne (X_ d, Y_ d , h) will be known. Once he i s poin O has been selec ed, he
h ee needed es poin s P1, P2 and P3, whose coo dina es may be any one a i s mus
be selec ed ( igu e 1).
8
Figu e 1. Gene al ske ch o he p oposed p oblem
The ela i e dis ances be ween he las h ee selec ed poin s in ela ion o he i s one O
a e known:
(1)
Dis ances be ween poin s p ojec ions o he objec a e also known:
(2)
These dis ances will be ou only s a ing da a and hey will be measu ed in he
adiog aph.
The pa ame ic equa ion o he line h ough wo poin s will be used as a ma hema ical
model o each p ojec i e uni y. This equa ion is e y simpli ied because he o igin o
coo dina es was placed in he ocus:
(3)
As he plane is loca ed a a heigh h in ela ion o ocus, z = h and he e o e λ = h/x3:
(4)
15
Figu e 7. Flow cha o so wa e applica ion

16
Figu e 8. LEFERX in e ace displaying ocus coo dina es
A special ea u e o conside when calcula ion is done is ha wo di e en e e ence
sys ems a e used. The i s one, absolu e e e ence sys em, has i s o igin o coo dina es
in he ocus, while he second, ela i e e e ence sys em, has he o igin o coo dina es in
he uppe le co ne o he adiog aph. P ojec ions o selec ed ma ke s a e chosen in
his las sys em.
I is aken in o accoun ha di ec ions o loca o objec con ou , ma ch up wi h
di ec ions o he absolu e e e ence sys em. Axes di ec ions o his sys em a e known on
adiog aph because hey a e aligned wi h he a ays o ma ke s loca ed a he op and
unde side o loca o objec . Axes di ec ions o ela i e e e ence sys em a e pa allel o
adiog aph´s con ou .
Bo h e e ence sys ems mus be mo ed o he i s chosen ma ke o sol e he model.
This allows o calcula e he exis ing o a ed angle be ween bo h sys ems which mus be
aken in o accoun o calcula e ocus coo dina es. To his end, i is necessa y o
ans o m he ela i e dis ances calcula ed in ela ion o ela i e e e ence sys em, in o
dis ances in ela ion o absolu e e e ence sys em (algo i hm). Radiog aph esolu ion is
17
also needed. Once ocus posi ion is calcula ed in space, i s o hogonal p ojec ion is
displayed on adiog aph ( igu e 9). I we deno ed he o a ed angle as α, hen he
coo dina es on he axes o he absolu e e e ence sys em (x and y) would be calcula ed
as ollows in ela ion o he coo dina es o he axes o he adiog aph (x' and y'):
(7)
Figu e 9. Rep esen a ion o ocus posi ion on adiog aph
Finally, i ´s enough o add he wo known ec o s ( igu e 10) o know he posi ion o he
o igin o ela i e sys em, wi h ega d o he X- ay emi ing ocus.
Figu e 10. Calcula ion me hod o coo dina es o he uppe le co ne o image in ela ion o he ocus
18
3. Resul s
The inabili y o use geome ic poin s as ma ke s in p ac ice [22], o ced us o alida e
model accu acy expe imen ally unde eal use condi ions wi h ma ke s ha a e made up
o small sphe es, in o de o de e mine he o de o magni ude o he mis akes ha his
could cause. Fo ha pu pose, ou se ies o es s we e designed, he i s h ee wi h
syn he ic adiog aphs, and he las se ies wi h eal adiog aphs. This analysis
me hodology, using images bo h om i ual models and adiog aphs has p e iously
been used o o he expe imen s o iden i ying medical images wi h o he echniques
[23]. Ob iously, in i ual es s, he exac posi ion o he X- ay ocus is known, so i s
posi ion e o can be calcula ed easily. On he o he hand, i is necessa y o men ion ha
he se o ob ained samples ollows a no mal dis ibu ion, so [µ-kσ, µ+kσ] in e al
co esponds o 99.5% o he alues o k=2.578.
3.1. Fi s se ies o es s
The in luence in inal esul o he selec ion o a se o ou ma ke s o o he in
adiog aph was s udied [24,25], and o his pu pose, ou syn he ic adiog aphs we e
gene a ed. Th ee mis ake-es ima e pa ame e s we e conside ed like in he es o es s:
he coo dina es o ocus de e mined, he coo dina es o he i s chosen ma ke ha
allowed o e i y ha mis akes show no cha ac e is ic pa e n, and he esolu ion o
adiog aphic image. Fu he mo e, ou een di e en combina ions o he ou ma ke s
needed we e selec ed in each syn he ic adiog aph o calcula e he spa ial posi ion o
ocus, hese combina ions being equals in he ou adiog aphs. A o al o 56 es s we e
pe o med.
One o he ou analyzed syn he ic adiog aphs was gene a ed wi h he ollowing
pa ame e s:
h = 764,8mm O = (-46, -61, 469´5)
Resolu ion = 4 pixels/mm
19
(X_ d, Y_ d) = ( -177´25, -214´875)
The esul s in he o he h ee adiog aphs, gene a ed wi h comple ely di e en
pa ame e s o he i s one, we e simila .
Figu e 11. E o in he calcula ion o ocus coo dina es depending on selec ed ma ke s
Resul s o he i s ele en combina ions o he se o ou ma ke s show 99, 5% o he
alues a e wi hin a ange o maximum e o o [-0,35%, +0,39%] which is conside ed
accep able. E o a ia ion in he heigh o he ocus om he adiog aph in ela ion o
he exac posi ion o ocus does no exceed 0.3% in he con idence in e al, lea ing he
maximum measu ed e o in jus o e 2 mm in his case.
The exac posi ion o he i s chosen ma ke is known in i ual es s, as i was said,
and we can s udy i s posi ion e o in o de o look o possible pa e ns. In all es s ha
we e pe o med, i was e i ied ha he e is no co ela ion be ween he e o a ia ion
cu es. As expec ed, i can be obse ed ha he e is a co ela ion be ween he posi ion
e o s o his ma ke and hose o he ocus. The e is no an app eciable e o pa e n in
X and Y coo dina es o he ocus posi ion ei he .
In he las h ee combina ions o se o ma ke s, he hi d and ou h selec ed ma ke s
we e placed in he same e ical line and his case has no solu ion as i was al eady said.
20
The implemen ed p og am p e en s his si ua ion be o ehand by wa ning wi h an e o
message.
3.2. Second se ies o es s
The in luence on he inal esul o he ocus posi ion a ia ion in ela ion o he
adiog aph in he di ec ions o he X, Y and Z axes was s udied. In speci ic, i een
a ia ions o posi ion we e conside ed o each axis o he coo dina es, which we e
aken in inc emen s o i e millime e s o e a ange o ± 30mm, oge he wi h wo o he
cases a dis ances o ± 50mm in o de o check he beha io in he mos emo e a eas. In
Z axis, wo mo e cases we e added a dis ances o ±100 millime e s in ela ion o ini ial
posi ion. A o al o 47 es s we e pe o med in his se ies. In all cases he same ma ke s
we e chosen in o de o no o in oduce any addi ional ac o ha could in luence in
esul .
As an example, he esul s when he ocus o X- ay machine is mo ed in Y axis
di ec ion a e shown. Resul s in he o he wo di ec ions we e simila . The adiog aph
was gene a ed wi h he ollowing pa ame e s:
h = 1200 mm O = (-50, -60, 900)
Resolu ion = 5 pixels/mm
(X_ d, Y_ d) = ( -166, -220)
Figu e 12. E o in he calcula ion o ocus coo dina es when he ocus is mo ed in he Y axis di ec ion

21
The esul s in he i een posi ions clea ly show ha expec ed e o o 99.5% o he
alues conside ed is in a ange o maximum e o o [ -0.03%, +0.02%], so ha , he
in luence on he esul o he a ia ion o he ocus posi ion in Y axis is p ac ically null.
The esul o he e o o h was, in all cases, lowe han in he i s se ies, as i in no
case exceeded 0.01%, which was expec ed because he e a e no es ic ions o
dependences in he model ega ding he ocus posi ion. As in he i s se ies, no
co ela ion was ound be ween he pe cen age o posi ion e o s o he e e ence ma ke
and he posi ion e o s in X and Y a e also less han 0.01% in all es cases.
3.3. Thi d se ies o es s
The in luence on he inal esul o he possible o a ed angle (α) abou Z axis ( he only
axis is possible o a u n o ake place in he no mal eal use o he loca o objec ,
which is se on a able o he x- ay machine) be ween he axes o he e e ence sys ems
used, was s udied. Angula a ia ions o 15° in a ange be ween 0° and 90° we e
conside ed i s . To ensu e he eliabili y o he model, ega dless o he angle a which
he loca o objec is o a ed, a second analysis was made by u ning he loca o objec an
angle o 360° in in e als o 30°. Finally, since in p ac ice i is no easible o u n he
loca o objec 360°, a hi d s udy was pe o med a angula in e als o 5° wi hin ± 15°.
I was necessa y o conside he possibili y o u ning he loca o objec 180°. As in he
p e ious case, he same ma ke s we e always chosen.
In his sec ion, he esul s by o a ing he loca o objec 360º a 30º in e als a e shown.
The esul s in he es o he es s we e simila . Ini ial adiog aph was gene a ed wi h he
ollowing pa ame e s:
h = 1200 mm O = (-50, -60, 900)
Resolu ion = 5 pixels/mm
(X_ d, Y_ d) = ( -166, -220)
22
Figu e 13. E o in he calcula ion o α and ocus coo dina es when he loca o objec is o a ed
The esul s in he wel e adiog aphs show ha he expec ed e o o 99.5% o he
alues is in a ange o maximum e o o ± 0.12%, which is conside ed accep able.
As expec ed, because o he igonome ic unc ions ha implemen p og amming
languages, esul s o he e o o h, show a ela i ely high e o . This is because we
mus add his e o o he signaling e o , which inc eases he mean measu e o a
maximum o 0.06%, g ea e han ha measu ed in he second se ies.
Like he posi ion e o s o he e e ence ma ke , he e is no hing di e en o no e in his
se ies o es s, no e o s o X and Y. Resul s o α e o we e illus a ed in igu e 13, as
α is a alue which in luences on calculus o adiog aph posi ion in ela ion o ocus.
3.4. Fou h se ies o es s
P e ious se ies o es s con i med he e ec i eness and accu acy o he p oposed model
using sphe ical ma ke s [26]. Howe e , a las se ies o es s was pe o med wi h eal
adiog aphs using a s anda d equipmen o clinical use. Real adiog aphs we e made
only wi h he loca o objec , wi hou he p esence o he pa ien , because any mo emen
o he la e could alsi y he esul s. As i is no possible o use he eal ocus posi ion in
ela ion o he adiog aph, in o de o es ima e he e o , a i s posi ion was accep ed as
ac ual ocus posi ion, which was calcula ed by LEFERX so wa e. A e wa ds, he
23
ocus o he X- ay machine was mo ed p ecise known dis ances in he h ee space
coo dina es and i was p o en ha di e ences be ween calcula ed solu ions ma ched up
wi h displacemen s ha we e done. Se ies o en adiog aphs we e made in each space
coo dina e a in e als o 10 millime e s each, so he ange o a ia ion be ween he i s
and he las one was 90 millime e s.
Figu e 14. E o in he calcula ion o ocus coo dina es when he ocus is mo ed in he Z axis di ec ion
Resul s show 99.5% o he alues a e wi hin a ange o maximum e o o [ -0.23%,
+0.17%] which is conside ed accep able.
Resul s in all es s ha we e pe o med in he i s expe imen al se ies, sugges he
alidi y, in p ac ice, o he p oposed model and allow o a i m ha small a ia ions in
he signaling o he cen e s o eal ma ke s gene a es minimal al e a ions in he esul ,
and also ha , he selec ion o he ou ma ke s is independen o he me hod accu acy.
Based on esul s o second se ies o es s, i can be s a ed ha he in luence on he esul
o he a ia ion o he ocus posi ion in he h ee coo dina e axes is p ac ically null and
he independence o he geome ic model is gua an eed in ela ion o he ocus posi ion.
Resul s o he hi d se ies o es s p o ed he independence o he geome ical model in
ela ion o he ocus o ien a ion on adiog aphs. On he o he hand, he esul s o es s on
24
eal adiog aphs ha dly di e ed om hose made on i ual adiog aphs, in ela ion o
he e o ange o he coo dina es. The e o e, i can be concluded ha i an alum
ma ke s which diame e is 0.5 mm a e used, hen i will be possible o ensu e ha he
maximum e o in each coo dina e o he ocus posi ion on he adiog aph will no
exceed 0.8%. Accu acy is high enough o s a e ha he geome ic model ha was
p oposed is eliable and accu a e. Also, i can be said ha he loca o objec p o o ype
ha was manu ac u ed pe o ms he objec i es ha we e se ini ially, p o iding he
necessa y in o ma ion o calcula e he posi ion o he ocus in space.
4. Discussion
Taking measu emen s on s anda d adiog aphs is a common me hod used in
p eope a i e planning and pos ope a i e su eillance in biomechanics ield.
Biomechanical s udies made om adiological images a e sa e, e sa ile and
economical bu oday, hey su e om poo p ecision [14,27], al hough an au oma ed
measu emen me hod is used [28], which limi s hei ield o applica ion.
In his pape , we p esen a no el geome ic model based on p ojec ions in o de o
calcula e accu a ely, p ac ically and economically, he exac posi ion o he ocus
equi ed o pe o m accu a e measu emen s o e adiog aphs. The model was
implemen ed as a p ac ical compu e p og am by a mul idisciplina y g oup o enginee s,
p o iding a use ul and iendly ool which can be used wi h any s anda d adiog aphic
sys em, ha is, a sys em a ailable in any hospi al. I is impo an o highligh ha his
model can be applied in sys ems wi h a single ocus and a single adiog aphic image. A
no el e e ence loca o objec was also designed and manu ac u ed, which a oids
in oducing ma ke s inside he human body. Model e ec i eness was demons a ed by
pe o ming i ual simula ions wi h syn he ic adiog aphs p io o pe o ming es s wi h
31
Design, analysis and e i ica ion o a knee join oncological p os hesis ini e
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