Report on the determination of the uncertainty budget for smart implants, the RF exposure system and gradient induced heating

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Deli e able Co e Shee
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o he Eu opean Union o EURAMET. Nei he he Eu opean Union no
he g an ing au ho i y can be held esponsible o hem.
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Me ology, co- inanced om he Eu opean Union’s Ho izon Eu ope
Resea ch and Inno a ion P og amme and by he Pa icipa ing S a es.
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21NRM05 STASIS
D6: Repo on he de e mina ion o he unce ain y budge o sma implan s,
he RF exposu e sys em and g adien induced hea ing
O ganisa ion name o he lead pa icipan o he deli e able:
Czech Ins i u e o Me ology (ČMI)
Due da e o he deli e able: 30 h o Sep embe 2025
Ac ual submission da e o he deli e able: 30 h o Sep embe 2025
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Glossa y
AIMD - Ac i e Implan able Medical De ice
RF - Radio equency
SAR – Speci ic Abso p ion Ra e
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TABLE OF CONTENTS
Table o con en s .............................................................................................................. 3
Summa y .......................................................................................................................... 4
Task A: Finding he co ela ion be ween he powe deposi ed in o he implan and he
ollowing empe a u e inc ease ......................................................................................... 5
The s anda diza ion backg ound ....................................................................................... 6
1. De ini ion o he ask ..................................................................................................... 7
2. Solu ion ......................................................................................................................... 8
2.1 De ini ion o he sol ed ask .................................................................................................... 8
2.2 Theo e ical backg ound ........................................................................................................... 8
3 Nume ical esul s ..........................................................................................................12
3.1 Ankle Pla e ............................................................................................................................ 12
3.2 Hip ......................................................................................................................................... 13
3.3 Knee ...................................................................................................................................... 15
3.4 Shoulde ................................................................................................................................ 17
3.5 All implan s oge he .............................................................................................................. 19
4 Summa y o he ask .....................................................................................................20
4.1 Summa i izing he esul s ...................................................................................................... 20
4.2 Wha we lea ned so a ? Ques ions and answe s ................................................................ 21
5 G aphical esul s ...........................................................................................................23
5.1 Ankle pla e ............................................................................................................................. 23
5.2 Hip ......................................................................................................................................... 27
5.3 Knee ...................................................................................................................................... 32
5.4 Shoulde ................................................................................................................................ 36
5.5 All ou implan s oge he ...................................................................................................... 39
Task B: Pe o ming a s a is ical analysis o he ag eemen be ween he expe imen al and
nume ical esul s. .............................................................................................................41
1. De ini ion o he ask ....................................................................................................41
2. Solu ion ........................................................................................................................43
2.1 Use o he s aigh -line unc ion ............................................................................................. 43
2.2 Calcula ion o he s aigh -line unc ion pa ame e s .............................................................. 44
2.3 Use o he de e mined s aigh -line unc ion pa ame e s ...................................................... 45
2.4 Summa y o he selec ed app oach ...................................................................................... 46
3 Calcula ions ..................................................................................................................47
Conclusion 48
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SUMMARY
De e mina ion o he unce ain y in any measu emen ha is ela ed o he MRI de ice pe o mance is
a complica ed ask ha is a ec ed by
a) a complexi y o he measu emen p oblem,
b) complica ed de ini ion o he ou pu quan i y,
c) p oblems wi h he de ini ion o he unc ional dependence among inpu quan i ies and he ou pu
quan i y,
d) de e mina ion o he in luence quan i ies,
e) quan i ica ion o he inpu quan i ies and in luence quan i ies.
Among o he s, he hea ing o he implan due o he elec ic and magne ic ield gene a ed du ing he MRI
de ice ope a ion is widely in es iga ed o enable sa e use o an MRI de ice also o pa ien s wi h implan s.
Wi hin p ojec STASIS se e al esea ch ac i i ies a e conduc ed by di e en esea ch g oups on he opic
e e ing o adio equency (RF) induced implan hea ing and g adien induced implan hea ing.
This documen ocusses on he unce ain y budge calcula ions o g adien induced implan hea ing as
mainly in es iga ed by INRIM (I aly), while ČMI and STU B a isla a p o ide hei suppo in s a is ical
analysis o he ob ained da a. The e o e his documen aims a he wo asks, being ca ied ou by ČMI and
STU B a isla a, ha we e asked o and de ined by INRIM. Those wo ask a e
a) inding he co ela ion be ween he powe deposi ed in o he implan unde di e en condi ions and
he ollowing empe a u e inc ease, oge he wi h he associa ed unce ain y,
b) Pe o ming he s a is ical analysis o he de ia ions be ween he expe imen al and nume ical esul s,
while accoun ing o he ele an unce ain ies.
The de ails abou bo h asks a e p o ided di ec ly in he espec i e chap e . The analysis o he esul s and
hei physical in e p e a ion a e ca ied ou by INRIM. The e o e, hose analyses and in e p e a ions
should be sough in he deli e able D4 Repo on he echnical speci ica ions and guidelines o
comp ehensi e es ing o g adien -induced hea ing o passi e implan s.
RF induced implan hea ing and he co esponding unce ain y calcula ions a e ound in he ollowing
documen s:
• Deli e able D1: Repo on he de elopmen and calib a ion o an implan sa e y concep in MRI,
comp ised o senso -equipped sma medical implan s and pTx capable MRI scanne s ha enable
o assess and mi iga e in si u RF induced implan hea ing. Lead pa icipan : PTB (Ge many).
• Deli e able D3: Repo on he de elopmen o open-sou ce e e ence ha wa e (RF coil, exci e ,
modula o s, RF powe ampli ie s) and open-sou ce con ol so wa e, including aceable
measu emen p ocedu es ha allow es ing o implan unde pa allel ansmission (pTx) MR
condi ions. Lead pa icipan : DKFZ (Ge many).
• Deli e able D5: Repo on he anla ion o in i o sa e y es ing esul s o ealis ic exposu e
condi ions conside ing combined GC and RF induced hea ing. Lead pa icipan : IT‘IS
(Swi ze land).
In summa y, he aims o he STASIS p ojec deli e able ha e been success ully achie ed, ul illing
Objec i e 1-3 o he p ojec .
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Task A: Finding he co ela ion be ween he powe deposi ed in o
he implan and he ollowing empe a u e inc ease
Scope
De e mina ion o he ela ionship be ween he induced powe and he empe a u e inc ease o he
implan due o g adien induced implan hea ing in MRI. Fou implan s a e conside ed in his documen :
a. Hip
b. Knee
c. Shoulde
d. Ankle Pla e

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THE STANDARDIZATION BACKGROUND
Technical speci ica ion ISO/TS 10974
Technical speci ica ion ISO/TS 10974 Assessmen o he sa e y o magne ic esonance imaging o pa ien s
wi h an ac i e implan able medical de ice con ains wo chap e s ha deal wi h ha m o he pa ien by he
MRI gene a ed hea :
- Chap e 8 P o ec ion om ha m o he pa ien caused by RF-induced hea ing
- Chap e 9 P o ec ion om ha m o he pa ien caused by g adien -induced de ice hea ing
In he chap e 8, he poin 8.4.4.4 s a es ha he local empe a u e ise T o SAR a a poin loca ion in a
ho spo p oduced by he AIMD can be ela ed o he o al powe deposi ion using a calib a ed RF powe
injec ion me hod. Fo each AIMD ho spo , a con e sion ac o m be ween T o SAR a he ho spo and
injec ed powe is expe imen ally de e mined (i.e. T = mPinjec o SAR = mPinjec ).
In chap e 9, he s anda d s a es ha he imaging g adien ield dB/d induces eddy cu en s on
conduc i e AIMD enclosu es and o he conduc i e in e nal su aces ha esul in de ice hea ing. The
hea ing will be g ea es o implan s wi h a la ge su ace a ea and high elec ical conduc i i y. Typically,
he hea ing is g ea es when he de ice is o ien ed so ha he g adien ield ec o is o hogonal o he
AIMD su ace(s) wi h he la ges conduc i e a ea. De ice hea ing could also depend on he g adien
wa e o m cha ac e is ics.
Technical epo ISO/TR 21900
Technical epo ISO/TR 21900 Guidance o unce ain y analysis ega ding he applica ion o ISO/TS
10974 in i s pa 4 in oduces wo me hods o unce ain y e alua ion (in p ac ice, o e laps be ween
hose me hods exis ):
a) Me hod 1 (pa 4.2 o he TR) de e mines he unce ain y o he measu emen sys em by conside ing
he a iabili y o he sys em as a whole. In his me hod, mul iple elemen s o he sys em a e assembled
oge he , and hei combined unce ain y is assessed. This is he me hod ha we employed o
e alua ing he p elimina y esul s, as p esen ed in his epo .
b) Me hod 2 (pa 4.3 o he TR) dissec s he assembly in o i s pa s, de e mines he unce ain y o
indi idual elemen s, and hen de e mines he unce ain y o he g oup by combining he unce ain y o
he componen s.
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1. DEFINITION OF THE TASK
Inpu da a
Each implan is associa ed wi h an ac i i y1_.ma ile con aining he ollowing a iables:
• powe _map : Nθ × Nϕ ma ix o he o al powe exp essed in wa s deposi ed in o he implan o a
speci ic o ien a ion o he uni a y ha monic magne ic ield exp essed in pola coo dina es. θ : [0, π/2]
is he pola angle ( he angle be ween he magne ic ield ec o and he z-axis), and ϕ : [−π, π] is he
azimu h angle ( he angle be ween he magne ic ield ec o and he 1 x-axis). Nθ and Nϕ a e he
numbe s o θ and ϕ in e als a which he powe has been compu ed;
• powe _wo s _H : 3-elemen ec o ep esen ing he uni a y magne ic ield ha esul s in he maximum
powe deposi ed in o he implan ;
• emp_map_min : Nθ × Nϕ ma ix o he maximum empe a u e inc ease exp essed in kel in, a e
minu es o exposu e, o a speci ic o ien a ion o he uni a y ha monic magne ic ield exp essed in
pola coo dina es wi h he same c i e ia used in he powe _map ma ix;
• emp_wo s _H_min : 3-elemen ec o ep esen ing he uni a y magne ic ield ha esul s in he
maximum empe a u e inc ease a e minu es o exposu e;
• ex e nal_su ace : ex e nal su ace o he implan exp essed in squa e me e s (i.e., he in e ace
be ween he implan and he backg ound).
Each o he pa icula da a iles powe _map, emp_map_min con ains 40,000 da a poin s ( o any he a and
i combina ion i is one da a poin ). The h ee iles emp_map_min we e ecei ed, o 5 minu es, 15
minu es, and 30 minu es.
The ask
I is expec ed ha he ollowing poin s a e in es iga ed in he amewo k o he ac i i y:
1. Fo each implan , he co ela ion be ween he magne ic ield di ec ion ha maximises he powe
deposi ion in o he implan and ha maximises he empe a u e inc ease a e 5 minu es, 15 minu es,
and 30 minu es o exposu e;
2. Fo each implan , he co ela ion be ween he powe deposi ed in o he implan and he ollowing
empe a u e inc ease as a unc ion o he magne ic ield di ec ion. The co ela ion should be e alua ed
by accoun ing o a empe a u e inc ease a e 5 minu es, 15 minu es, and 30 minu es o exposu e;
3. Fo each implan , a coe icien , wi h associa ed unce ain y/con idence le el, ha allows es ima ing he
empe a u e inc ease a e a speci ied ime ins an gi en he powe deposi ed in o he implan .
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2. SOLUTION
The ollowing ex o his documen deals wi h poin 3 o he o mula ed ask, i.e. inding he dependence
be ween he deposi ed powe and a empe a u e ise, including he espec i e unce ain y.
2.1 De ini ion o he sol ed ask
The e o e, he ask is de e mining he ela ionship be ween he deposi ed powe (deno ed as X), and he
empe a u e di e ence a e a gi en ime o 5, 15, and 30 minu es (deno ed as Y). I is assumed ha his
ela ionship can be app oxima ed by linea eg ession, i.e. a heo e ical model is
𝑌=𝛽 𝑋
o 𝑌=𝛼+ 𝛽 𝑋
The ask is o de e mine:
1. o 𝑌=𝛽 𝑋
a. es ima e b he unknown coe icien 𝛽 o he line,
b. he unce ain y ub;
2. o 𝑌=𝛼+ 𝛽 𝑋
a. es ima es a and b he unknown coe icien s
𝛼 and 𝛽 o he line,
b. hei unce ain ies ua, ub, and co a iance among hem uab.
I we de e mine hose pa ame e s, o any gi en x ( he alue o powe ) we can calcula e he alue o y ( he
empe a u e di e ence) and i s co esponding unce ain y uy.
Mo eo e , an addi ional calcula ion was ca ied ou , whe e he deposi ed powe was ans e ed o
ene gy, and he ela ion be ween ene gy and he empe a u e inc ease was in es iga ed.
2.2 Theo e ical backg ound
The wo o ms o linea eg ession will be in es iga ed:
a. he linea eg ession (line) which c osses he ze o poin (in e sec ion o x and y axes),
b. he linea eg ession (line) which is shi ed om he ze o poin (in e sec ion o x and y axes)
2.2.1 Fo he linea eg ession in he o m o 𝒀=𝜷 𝑿
1. Employing he leas squa es me hod, he unknown coe icien b can be de e mined as ollows:
𝑏= 1
∑𝑥𝑖2∑𝑥𝑖𝑦𝑖
whe e
xi is he measu ed powe inpu alue ( om he supplied da a),
yi is he measu ed empe a u e ise ( om he supplied da a).
2. The unce ain y ub o he coe icien b can be de e mined as ollows:
21NRM05 STASIS
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𝑢𝑏=1
√∑𝑥𝑖2𝑠,
whe e s can be es ima ed by a o mula o sample esidual a iance
𝑠=√1
𝑛−1∑[𝑦𝑖−(𝑏𝑥𝑖)]2
𝑛
𝑖=1
3. The unce ain y uy o he calcula ed alue y = bx can be de e mined as ollows:
𝑢𝑦=𝑥 𝑢𝑏=𝑥 1
√∑𝑥𝑖2𝑠
4. Coe icien o de e mina ion R2 is a s a is ical measu e o how well he eg ession p edic ions
app oxima e he eal da a poin s
𝑅2=1−∑ (𝑦𝑖−𝑏𝑥𝑖)2
𝑛𝑖=1
∑ (𝑦𝑖−𝑦)2
𝑛𝑖=1
5. Con idence in e als (UCL, LCL)
𝑦±𝑡𝑛−1,1−𝛼/2 𝑢𝑦
𝑦±𝑡𝑛−1,1−𝛼/2 𝑠√x
∑𝑥𝑖2
6. P edic ion in e als (UPL, LPL)
𝑦±𝑡𝑛−1,1−𝛼/2 𝑠√1 + x
∑𝑥𝑖2
7. Tole ance in e als (UTL, LTL)
𝑦±𝑘2,1−𝛼/2,𝑝,𝑛 𝑠
8. Unce ain y o con e sion is de e mined as ollows. The expanded unce ain y Uy,con o he
empe a u e inc ease ∆T ob ained by con e sion om deposi ed powe is de ined as hal he in e al
be ween he uppe and lowe ole ance limi s (UTL esp. LTL), he in e al ha ep esen s (1-α)∙100 =
95% ce ain y ha he e is a p∙100 = 90% chance, ha he co ec p edic ion o ∆T lies be ween he
uppe and lowe limi s o he ole ance in e al, i.e.
𝑈𝑦,con =𝑘2,1−𝛼/2,𝑝,𝑛 𝑠
whe e
𝑘2,1−𝛼/2,𝑝,𝑛=𝑘2,0,975,0,9,𝑛
2.2.2 Fo he linea eg ession in he o m o 𝒀=𝜶 + 𝜷 𝑿
1. Employing he leas squa es me hod, he unknown coe icien s a, and b can be de e mined as ollows:
21NRM05 STASIS
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4. Linea eg ession 𝑌=𝛽 𝑋 o empe a u e inc ease depending on he ene gy (in J) (n – numbe o
poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=12∙104)
bknee_ene gy_b =
0.00146018 K/J
ubknee_ene gy_b =
1.1829946310-6 K/J
Rknee_ene gy_b2 =
0.68011614
sknee_ene gy_b =
1,4954181610-9 K
𝑘2,0,975,0,9,120 000=1,6449
Uy,con knee_ene gy_b =
2,4598110-9 K
Rema k: Please no e ha he co ela ion coe icien indica es a weak linea ela ionship, compa ed o he
dependence o empe a u e inc ease on he deposi ed powe a e 5, 15, and 30 minu es. Please
compa e wi h he co ela ion coe icien o 𝑌=𝛽 𝑋.
3.3.2 Fo he linea eg ession in he o m o 𝒀=𝜶 + 𝜷 𝑿
1. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 5 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
aknee5m_ab =
3.365910-11 K
uaknee5m_ab =
3.636210-12 K
bknee5m_ab =
1.135547694 K/W
ubknee5m_ab =
0.001170572 K/W
ua,bknee5m_ab =
-3.8910410-15 K2/W
Rknee5m_ab2 =
0.9592295
sknee5m_ab =
2.9479510-10 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con knee5m_ab =
4,8490810-10 K
2. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 15 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
aknee15m_ab =
-9.1403910-12 K
uaknee15m_ab =
4.8616110-12 K
bknee15m_ab =
1.780577858 K/W
ubknee15m_ab =
0.001565058 K/W
ua,bknee15m_ab =
-6.9555410-15 K2/W
Rknee15m_ab2 =
0.970024943
sknee15m_ab =
3.9414210-10 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con knee15m_ab =
6,4832410-10 K
3. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
aknee30m_ab =
-3.2243210-11 K
uaknee30m_ab =
5.4247210-12 K
bknee30m_ab =
2.288048166 K/W
ubknee30m_ab =
0.001746334 K/W
ua,bknee30m_ab =
-8.6601410-15 K2/W
Rknee30m_ab2 =
0.977230186
sknee30m_ab =
4.3979410-10 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con knee30m_ab =
7,2341810-10 K
4. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he ene gy (in J) (n – numbe o
poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=12∙104)
aknee_ene gy_ab =
1.9700352010-9 K
uaknee_ene gy_ab =
5.2594130310-12 K

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bknee_ene gy_ab =
0.00104006 K/J
ubknee_ene gy_ab =
1.4412788710-6 K/J
ua,bknee_ene gy_ab =
-5.8988354910-18 K2/J
Rknee_ene gy_ab2 =
0,81272095
sknee_ene gy_ab =
1.1442336110-9 K
𝑘2,0,975,0,9,120 000=1,6449
Uy,con knee_ene gy_ab =
1,8821510-9 K
3.4 Shoulde
3.4.1 Fo he linea eg ession in he o m o 𝒀=𝜷 𝑿
1. Linea eg ession
𝑌=𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e o 5
minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
bshould5m_b =
2.28773545 K/W
ubshould5m_b =
0.00040099 K/W
Rshould5m_b2 =
0.988382321011267
sshould5m_b =
3.6729410-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should5m_b =
6,0416310-11 K
2. Linea eg ession 𝑌=𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e o 15
minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
bshould15m_b =
3.56581087 K/W
ubshould15m_b =
0.0005406969 K/W
Rshould15m_b2 =
0.99128182
sshould15m_b =
4.9526210-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should15m_b =
8,1465610-11 K
3. Linea eg ession 𝑌=𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e o
30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
bshould30m_b =
4.45101618 K/W
ubshould30m_b =
0.00061052 K/W
Rshould30m_b2 =
0.99280986
sshould30m_b =
5.59223810-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should30m_b =
9,1986710-11 K
4. Linea eg ession 𝑌=𝛽 𝑋 o empe a u e inc ease depending on he ene gy (in J) (n – numbe o
poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=12∙104)
bshould_ene gy_b =
0.00287617 K/J
ubshould_ene gy_b =
2.3593049210-6 K/J
Rshould_ene gy_b2 =
0.54590741
sshould_ene gy_b =
4.3970863210-10 K
𝑘2,0,975,0,9,120 000=1,6449
Uy,con should_ene gy_b =
7, 3277210-10 K
Rema k: Please no e ha he co ela ion coe icien indica es a weak linea ela ionship, compa ed o he
dependence o empe a u e inc ease on he deposi ed powe a e 5, 15, and 30 minu es. Please
compa e wi h he co ela ion coe icien o 𝑌=𝛽 𝑋.
21NRM05 STASIS
18 o 51
3.4.2 Fo he linea eg ession in he o m o 𝒀=𝜶 + 𝜷 𝑿
1. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 5 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
ashould5m_ab =
-7.3825577710-11 K
uashould5m_ab =
4.9214646310-13 K
bshould5m_ab =
2.44132357 K/W
ubshould5m_ab =
0.00107459 K/W
ua,bshould5m_ab =
-5.0389435510-16 K2/W
Rshould5m_ab2 =
0.99231007
sshould5m_ab =
2.9883168010-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should5m_ab =
4,9154810-11 K
2. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 15 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
ashould15m_ab =
-1.1529653510-10 K
uashould15m_ab =
6.0297758610-13 K
bshould15m_ab =
3.80567595 K/W
ubshould15m_ab =
0.00131658 K/W
ua,bshould15m_ab =
-7.5640273910-16 K2/W
Rshould15m_ab2 =
0.99523567
sshould15m_ab =
3.6612841610-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should15m_ab =
6,0224510-11 K
3. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=4∙104)
ashould30m_ab =
-1.3627949110-10 K
uashould30m_ab =
6.5323085910-13 K
bshould30m_ab =
4.73453459 K/W
ubshould30m_ab =
0.00142631 K/W
ua,bshould30m_ab =
-8,8773663210-16 K2/W
Rshould30m_ab2 =
0.99638305
sshould30m_ab =
3,9664223910-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con should30m_ab =
6,5243710-11 K
4. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he ene gy (in J) (n – numbe o
poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=12∙104)
ashould_ene gy_ab =
6.8328786710-10 K
uashould_ene gy_ab =
1.4661182210-12 K
bshould_ene gy_ab =
0.00184608 K/J
ubshould_ene gy_ab =
2.7250765010-6 K/J
ua,bshould_ene gy_ab =
-3,2404823110-18 K2/J
Rshould_ene gy_ab2 =
0,79272417
sshould_ene gy_ab =
2.9707816110-10 K
𝑘2,0,975,0,9,120 000=1,6449
Uy,con should_ene gy_ab =
4,8866410-10 K
21NRM05 STASIS
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3.5 All implan s oge he
As a sample, e alua ion o all da a coming om all ou implan s a 30 minu es exposu e we e e alua ed
and he o e all pa ame e s we e calcula ed.
3.5.1 Fo he linea eg ession in he o m o 𝒀=𝜷 𝑿
1. Linea eg ession
𝑌=𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e o
30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=16∙104)
ball30m_b =
2,40313060 K/W
uball30m_b =
0,00067089 K/W
Rall30m_b2 =
0,97086364
sall30m_b =
5,6976766210-10 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con all30m_b =
9,3721110-10 K
2. Linea eg ession
𝑌=𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe di ided by he
implan su ace, exposu e o 30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=16∙104)
ball30m_bS =
0,05714077 K/Wm2
uball30m_bS =
0,00001001 K/Wm2
Rall30m_bS2 =
0,98843460
sall30m_bS =
3,5897194210-10 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con all30m_bS =
5,9047310-10 K
3.5.2 Fo he linea eg ession in he o m o 𝒀=𝜶 + 𝜷 𝑿
1. Linea eg ession 𝑌=𝛼+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe , exposu e
o 30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=16∙104)
aall30m_ab =
4,4545298510-10 K
uaall30m_ab =
1,9013836710-12 K
ball30m_ab =
2,25120807 K/W
uball30m_ab =
0,00089554 K/W
ua,ball30m_ab =
-1,2329907810-15 K2/W
Rall30m_ab2 =
0.99231007
sall30m_ab =
2.9883168010-11 K
𝑘2,0,975,0,9,40 000=1,6449
Uy,con all30m_ab =
8,6282310-10 K
2. Linea eg ession
𝑌=𝑎+ 𝛽 𝑋 o empe a u e inc ease depending on he deposi ed powe di ided
by he implan su ace, exposu e o 30 minu es (n – numbe o poin s)
(1−𝛼=0,95,𝑝=0,9,𝑛=16∙104)
aall30m_abS =
6.8328786710-10 K
uaall30m_abS =
1.3583111110-12 K
ball30m_abS =
0.05640815 K/W
uball30m_abS =
1.5142550810-5 K/W
ua,ball30m_abS =
-1.5525632510-18 K2/W
Rall30m_abS2 =
0.98860143
sall30m_abS =
3.5637560710-10 K
𝑘2,0,975,0,9,120 000=1,6449
Uy,con all30m_abS =
5,8620210-10 K
21NRM05 STASIS
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4 SUMMARY OF THE TASK
4.1 Summa i izing he esul s
The ollowing ables compa e he esul s o he wo app oaches:
a. wi h a linea eg ession in he o m o 𝑌=𝛽 𝑋
b. wi h a linea eg ession in he o m o 𝑌=𝛼+ 𝛽 𝑋
The main idea is compa ing he declina ion o he eg ession line, i.e. he pa ame e b, ega dless he shi
o he line ( ep esen ed by a pa ame e a) is conside ed. To do so, he deposi ed powe in W was
ans e ed o ene gy in J. Fou cases we e compa ed - h ee ela ed o he ime (5, 15, and 30 minu es),
and one o he whole se o 120000 poin s ( o any combina ion o he angles

and

i is one da a poin ).
Fo he deposi ed powe
Table 4.1 Fo he linea eg ession in he o m o 𝑌=𝛽 𝑋
Pa ame e
5 minu es
15 minu es
30 minu es
Ankle Pla e
bankpla_b / K/W
1,4712125
2,115517798
2,552769599
Hip
bhip_b / K/W
1,133156432
1,897958636
2,49762561
Knee
bknee_b / K/W
1,145453
1,777887961
2,278559419
Shoulde
bshould_b / K/W
2,28773545
3,56581087
4,45101618
Table 4.2 Fo he linea eg ession in he o m o 𝑌=𝛼+ 𝛽 𝑋
Pa ame e
5 minu es
15 minu es
30 minu es
Ankle Pla e
aankpla_ab / K
2.2983610-11
3.11163310-11
3.5856610-11
bankpla_ab / K/W
1.230235528
1.788778401
2.17682236
Hip
ahip_ab / K
1.2057610-10
1.1376910-9
1.387910-9
bhip_ab / K/W
1.09149561
1.504872446
2.018085947
Knee
aknee_ab / K
3.365910-11
-9.1403910-12
-3.2243210-11
bknee_ab / K/W
1.135547694
1.780577858
2.288048166
Shoulde
ashould_ab / K
-7.3825577710-11
-1.1529653510-10
-1.3627949110-10
bshould_ab / K/W
2.44132357
3.80567595
4.73453459
Fo ene gy
Table 4.3 Fo he linea eg ession in he o m o 𝑌=𝛽 𝑋
Pa ame e
Value
Ankle Pla e
bankpla_ene gy_b / K/J
0.00167640
Hip
bhip_ene gy_b / K/J
0.001580637
Knee
bknee_ene gy_b / K/J
0.00146018
Shoulde
bshould_ene gy_b / K/J
0.00287617
Table 4.4 Fo he linea eg ession in he o m o 𝑌=𝛼+ 𝛽 𝑋
Pa ame e
Value
Ankle Pla e
aankpla_ene gy_ab / K
5.4104990110-11
bankpla_ene gy_ab / K/J
0.00126533
Hip
ahip_ene gy_ab / K
2.5969710-9
21NRM05 STASIS
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bhip_ene gy_ab / K/J
0.000930428
Knee
aknee_ene gy_ab / K
1.9700352010-9
bknee_ene gy_ab / K/J
0.00104006
Shoulde
ashould_ene gy_ab / K
6.8328786710-10
bshould_ene gy_ab / K/J
0.00184608
Example
As an example, he ollowing able compa es esul s o one case o exposu e ime and he same
eg ession model. The las line ep esen s he esul s o deposi ed ene gy di ided by he su ace.
Table 4.5 Compa ison o pa ame e s o 30 minu es exposu e ime and a model 𝑌=𝛽 𝑋
Implan
Model
∆𝑇×10−8/ K
𝑈(∆𝑇)×10−8/ K
𝑏
Deposi ed powe
×10−9
Ankle pla e
∆𝑇=𝑏 𝑃
0,003 – 0,06
0,006
2,55 K/W
0,01 – 0,09 W
Hip
∆𝑇=𝑏 𝑃
0,5 - 1
0,138
2,50 K/W
2 – 4 W
Knee
∆𝑇=𝑏 𝑃
0,06 – 1,1
0,072
2,28 K/W
0,5 – 5 W
Shoulde
∆𝑇=𝑏 𝑃
0,018 – 0,35
0,009
4,45 K/W
0 – 1 W
All 4 implan s
∆𝑇=𝑏 𝑃
0,05– 1,1
0,094
2,40 K/W
(0,5 – 5) ×10−9 W
All 4 implan s
∆𝑇=𝑏 𝑃𝑆
0,1– 1,1
0,0013
0,057 Km2
W
(1,1 – 19) ×10−8
W/m2
I is wo h no ing om a physical poin o iew, one can obse e a na u al p ocess o hea ing and hea
ans e o he en i onmen - he non-linea sec ion o he g aph indica es he hea ing o he implan i sel
om he momen he g adien coil is u ned on, and he linea sec ion demons a es he ans e o hea
om he implan o he su ounding issues.
Wi h inc easing ime, he di ec ion o he magne ic ield o maximum empe a u e ise app oaches he
di ec ion o maximum ene gy s o age in he implan . A he ime o 30 minu es, hey a e al eady close.
4.2 Wha we lea ned so a ? Ques ions and answe s
Following is a sho summa y o ac s, wha we lea ned so a by p ocessing he ob ained da a, and wha is
s ill needed o do.
Wha we ob ained in gene al?
The linea ela ionship be ween he deposi ed powe
(ene gy, powe di ided by su ace) and he empe a u e
ise.
Which o m ge s his ela ionship?
This ela ionship we can app oxima e by linea eg ession
in he o m Y = b X (o a line c ossing h ough he ze o
poin ) o Y = a + b X (a line shi ed om he ze o poin )
Wi h which es ic ions?
Fo each implan , we ook all in o ma ion on powe and he
espec i e empe a u e inc ease as da a poin s, ega dless
o he combina ion o angles and also he ime o exposu e.
In o he wo ds, we did no in es iga e he way da a we e
ob ained, and pu ely s a is ical me hods we e applied
Wha is he use ulness o ob ained
ela ionship?
We can selec he maximum empe a u e inc ease and we
can de i e he deposi ed powe ela ed o ha empe a u e
inc ease
Wha we canno say om he ob ained
ela ionship?
We canno say
a) he way he deposi ed powe was b ough o he
implan . In o he wo ds, we know he ela ionship

21NRM05 STASIS
22 o 51
be ween he empe a u e inc ease and he magni ude o
he incoming powe , bu we do no know he ime o
exposu e and pa ame e s o he magne ic ield which
gene a ed he incoming powe
b) he in luence o angles
c) he in luence o implan geome y wi h one excep ion,
when we di ided he incoming powe by he su ace o
indi idual implan s
d) he maximum empe a u e a any gi en pa icula poin
o he implan . In o he wo ds, we know he gene al
empe a u e ise in dependence on he ac ing powe ,
ei he a one pa icula ime o in a ime in e al, bu
no he empe a u e a any poin o he implan
e) he in luence o ime o exposu e
Wha is needed in u u e in es iga ions?
Fo u he use o he model and i s be e complexi y, he
ollowing in o ma ion needs o be ob ained and
implemen ed:
a) A model ela ionship be ween he measu ed MRI
machine inpu pa ame e s and he gene a ed powe ,
ac ing on he implan
b) In luence o implan geome y on he mal dis ibu ion
c) Limi s o pe missible empe a u e inc ease, ime limi s,
and o he limi a ions o implan exposu e (wha is he
longes exposu e o he implan )
d) O he
21NRM05 STASIS
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5 GRAPHICAL RESULTS
5.1 Ankle pla e
5.1.1 Ankle pla e - linea eg ession in he o m o 𝒀=𝜷 𝑿
21NRM05 STASIS
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21NRM05 STASIS
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5.1.2 Ankle pla e - linea eg ession in he o m o Y =

+

X
21NRM05 STASIS
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5.3 Knee
5.3.1 Knee - linea eg ession in he o m o 𝒀=𝜷 𝑿

21NRM05 STASIS
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21NRM05 STASIS
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5.3.2 Knee - linea eg ession in he o m o Y =

+

X
21NRM05 STASIS
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21NRM05 STASIS
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5.4 Shoulde
5.4.1 Shoulde - linea eg ession in he o m o 𝒀=𝜷 𝑿
Figu es o indi idual imes a e missing
21NRM05 STASIS
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5.4.2 Shoulde - linea eg ession in he o m o Y =

+

X

21NRM05 STASIS
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21NRM05 STASIS
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5.5 All ou implan s oge he
5.5.1 All ou implan s oge he - linea eg ession in he o m o 𝒀=𝜷 𝑿
21NRM05 STASIS
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5.5.2 All ou implan s oge he - linea eg ession in he o m o 𝒀=𝜶 + 𝜷 𝑿
21NRM05 STASIS
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Task B: Pe o ming a s a is ical analysis o he ag eemen be ween
he expe imen al and nume ical esul s.
1. DEFINITION OF THE TASK
The STASIS p ojec p oposal eads
Resul s om A3.1.6 and A3.2.2 we e collec ed by INRIM. These co espond o empe a u e inc ease
expe imen s oge he wi h he ele an esul s ob ained om nume ical simula ions.
Bo h expe imen al and nume ical da a a e associa ed wi h an unce ain y alue.
The ask is o pe o m a s a is ical analysis in o de o es ablish how much expe imen al esul s ma ch
wi h he nume ical esul s also accoun ing o he ele an unce ain ies.
In o he wo ds, ollowing da a a e a ailable (see Fig. B1)
a. Tempe a u e ise in K o a pa icula implan , simula ion poin , ob ained by simula ion in disc e e
samples o he exposi ion ime (g een line, unce a in y limi s a e also illus a ed),
b. The co esponding empe a u e ise in K o he same implan , he same measu emen poin and an
o e all expe imen al se up, ob ained by expe imen in disc e e samples o he exposi ion ime (o ange
line, unce ain y limi s a e also illus a ed).
Figu e B1. G aphical ep esen a ion o he ask
(Shown a e da a o Hip(RE), column 1 (measu emen poin 1))
The ollowing implan s we e conside ed o he analysis: emu , hip, knee, shoulde , ibia. A o al o 21
.ma iles we e ecei ed o analysis. Each .ma ile e e s o a speci ic expe imen (expe imen al da a +
ele an simula ion da a). The ilename epo s he implan in ol ed in he expe imen , he ype o
expe imen , he implan posi ion (when ele an ) and he used MR sequence. Each single Ma lab ile
con ains 6 a ays:
1. Expe imen al da a:
ime_ esampled(:,1)
Column ec o wi h ime samples
ch_ esampled(:,1:nc)
Column ec o wi h empe a u e samples; Each column e e s o a
empe a u e channel (measu emen poin )
21NRM05 STASIS
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Table B.1 Resul s o he s aigh -line unc ion o he da a se ob ained
a
b
u(a)
u(b)
Co a iance u(a,b)
Task 1
All da a
-0.004907905185139
0.924327743761982
0.002693956867838
0.025767880339540
-3.054564128133216e-05
16.356225461292260
Task 2
Femu
200 s
-0.004730217587454
0.764718356179748
0.008910662518204
0.054692237926329
-3.943972340959600e-04
12.628808844127024
400 s
0.005484039284024
0.794856667329768
0.016632775139442
0.057877198517401
-7.891698747274929e-04
6.153752039199373
600 s
0.008816646973441
0.846492742818379
0.023261674414261
0.060293704812444
-0.001143871188974
2.934548380175607
900 s
0.019996056335162
0.902026680656433
0.032540845293747
0.063432356664473
-0.001668952276106
1.518828987277543
Hip
200 s
0.032811974462212
0.675617192505557
0.007072946246634
0.026867613797268
-1.478000675677771e-04
71.048007289867640
400 s
0.084510037995691
0.706981615857333
0.012459134533751
0.029064187803765
-2.818537343583272e-04
43.416643501154084
600 s
0.111144500822584
0.734546879023881
0.037975359708094
0.039849506044676
-0.001234784942520
9.852844269361958
900 s
0.142266773037649
0.770801042214080
0.051051413169259
0.042812645885891
-0.001806335746488
9.384097184437433
Knee
200 s
-0.032700997000726
1.363775029442935
0.014226073886945
0.100974986207993
-0.001258899417226
56.425459240637615
400 s
-0.086568159309177
1.599471865771367
0.031151828999689
0.132949206001708
-0.003777865631926
47.715613021277810
600 s
-0.016167458845686
0.948402139155403
0.068575618419529
0.176310022995135
-0.010795593998282
1.398042607547288
900 s
-0.008410344367889
0.975509217870057
0.101381672501821
0.202210521678653
-0.018725419437812
0.937575813899910
Shoulde
200 s
0.092348790812444
0.605476218531904
0.021853895529061
0.044989454137160
-8.810759574447535e-04
63.192080641849046
400 s
0.135806389583340
0.664324351155069
0.035654762816244
0.049739998863051
-0.001602071216622
38.862364904973470
600 s
-6.942268151502020
6.662260323516325
5.259269630098430
4.422615337265153
-23.252142515793548
6.609665129465449
900 s
-8.448816378108440
6.852350502801359
7.111394417175920
5.045863739893506
-35.872930040495824
5.012914868532930
Tibial
200 s
0.007981113298991
0.747216771432548
0.018756384837045
0.032845168480118
-5.036758959273508e-04
15.039333715460039
400 s
-0.012373094230415
0.851839266200256
0.028255461147689
0.036981250849329
-8.595562018906676e-04
9.990926533472772
600 s
-0.043726806293060
0.925261632810579
0.035578652206837
0.039586481317741
-0.001160989179935
4.878173260086101
900 s
-0.058557238649261
0.972882215768814
0.043985242614225
0.041628823001058
-0.001513425989819
3.502485857130775
All
implan s
200 s
0.019404360162885
0.747732444719381
0.004004268972022
0.014975736364059
-4.409892159967782e-05
3.298069621031615e+02
400 s
0.047282489207037
0.797156939505872
0.007333200626946
0.016940397573535
-9.519947247492448e-05
2.630251338560409e+02

21NRM05 STASIS
49 o 51
600 s
0.012029267473151
0.843408051415499
0.014173075703090
0.020017327043491
-2.192219973245130e-04
57.266271836093990
900 s
0.023309698882737
0.879474979322333
0.019556198278792
0.021759148159872
-3.371221376833681e-04
51.079917132521660
Task 3
Femu
All da a
-0.006232712451246
0.974316799768952
0.002636770831267
0.015137320761821
-1.785595462315558e-05
22.031284019898187
Hip
All da a
-0.010127130291883
0.981961439309857
0.003091733874135
0.037031500592081
-8.783850728521455e-05
8.663269118337070
Knee
All da a
-0.025655599242253
0.635730970788776
0.004724296366429
0.025062916742844
-8.769111124247974e-05
40.491842193596625
Shoulde
All da a
-0.007870851702194
0.602963188245692
0.002278225200328
0.019661337835525
-2.033082567756539e-05
28.873495789406000
Tibial
All da a
-0.029140236234364
0.846196607619542
0.003503254322056
0.013505486922342
-3.597166595319500e-05
53.408775848999454
Task 4
Femu
(RE) Column 1
-0.006232718194965
0.974316840921663
0.002636770204518
0.015137311789100
-1.785593812292627e-05
22.031284019276782
(RE) Column 2
-0.008476106084576
1.094590662635126
0.002057347855561
0.027751097606440
-4.055233576945168e-05
7.523012472448466
(RE) Column 3
-0.005898772150929
0.934139807147304
0.001142507077300
0.022498232107492
-1.583725406549432e-05
16.890858701944012
(WO) Column 1
-0.014480766272367
0.819962538854963
0.003120426729800
0.007300288348353
-6.840082202684264e-06
2.157251420955415e+02
(WO) Column 2
-0.025935624908013
0.882618375809857
0.001865718639896
0.009087580699284
-1.200322437929293e-05
1.277057052346939e+02
(WO) Column 3
-0.017089974693584
0.801482938072242
0.001096810204045
0.010254121944293
-7.193855497312013e-06
1.493173819253223e+02
Hip
(RE) Column 1
-0.016743859722609
1.105160605337667
0.002636829337239
0.019618394120527
-3.627700103513687e-05
26.234347983448260
(RE) Column 2
-0.057813095789869
0.771213156107088
0.003902334649557
0.009282837603295
-2.421292971189638e-05
2.036805548965392e+02
(RE) Column 3
-0.023709808684009
0.707954247349384
0.001870730219673
0.007596874347081
-7.300274677495872e-06
1.333386488648540e+02
(WO) Column 1
-0.018073454641214
1.236555055376612
0.001919757451050
0.017692451049411
-2.034602034536907e-05
74.326988493140850
(WO) Column 2
-0.052194553032637
0.835559397697266
0.004194794132810
0.005473999054752
-1.473461300988362e-05
1.616714292884419e+02
(WO) Column 3
-0.033560775212565
0.838425625804233
0.002162951775858
0.005504634667619
-6.080451653533217e-06
2.057898045903108e+02
Knee
(RE) Column 1
-0.043192999226446
0.825570125801035
0.004467118540836
0.016276953256501
-4.994158398155970e-05
1.135774387648894e+02
(RE) Column 2
-0.034538552005863
1.017801716943328
0.005382778567051
0.018862084421613
-6.719419224789433e-05
57.858114601268085
(RE) Column 3
-0.004030894372869
0.931333152977411
0.001772915161297
0.022608818513522
-2.505432986681995e-05
15.584181236160006
Shoulde
(RE) Column 1
-0.011368711127394
0.700416319819935
0.002232891632581
0.012204125617612
-1.017234028905895e-05
64.443861744462030
(RE) Column 2
-0.014974527951590
0.869540334505379
0.003651757261737
0.013406528752676
-1.909794711220192e-05
47.972676598516190
(RE) Column 3
-0.007459415085771
0.930055126903404
0.002330648427774
0.012099748784110
-9.194749181638742e-06
29.768809127857107
(WO) Column 1
-0.030981907741031
0.615641030688305
0.002055573339668
0.005539338887334
-6.254061891484881e-06
3.316615129318416e+02
21NRM05 STASIS
50 o 51
(WO) Column 2
-0.056188927881634
0.791370820236438
0.003103801211024
0.006036364482795
-1.185521993983736e-05
4.079458835598822e+02
(WO) Column 3
-0.015783600211746
0.962898933063130
0.001961545555037
0.006200481008795
-5.628324898417632e-06
1.049761210610379e+02
Tibial
(RE) Column 1
-0.029140148368575
0.846196270801262
0.003503268711441
0.013505577273523
-3.597206005349667e-05
53.408775893887970
(RE) Column 2
-0.036696178580039
0.828405139241780
0.003857732286419
0.014700399118551
-4.213683677797982e-05
92.797142743558070
(RE) Column 3
-0.017247590112678
0.909471049544661
0.002918067420570
0.014883774207750
-3.251342842190504e-05
22.514565823455534
(WO) Column 1
-0.084158194884998
0.864489155796940
0.004431159689568
0.005524489017350
-1.703726454715574e-05
6.613607628106338e+02
(WO) Column 2
-0.079704878088096
0.839609160589047
0.004164139515233
0.005569931423752
-1.504637522552644e-05
6.559714187593834e+02
(WO) Column 3
-0.044828414879061
0.965986355332829
0.003549813677295
0.006034187194786
-1.347092352156828e-05
2.381353580279230e+02
51 o 51
CONCLUSION
In summa y, an open-sou ce e e ence ha dwa e consis ing o an 8-channel 3T pTx body coil, pe o man pa allel
ansmission RF exposu e ha dwa e and ope a ing so wa e ha e been de eloped, which is sui able, amongs
o he s, o o line implan es ing by manu ac u e s o es houses.
Mo e de ailed in o ma ion on he e e ence ha dwa e and so wa e can be ound in he public eposi o ies, and i s
applica ion is u he de ailed in deli e able D1 o he STASIS p ojec .
The aims o he STASIS p ojec deli e able ha e been success ully achie ed, ul illing Objec i e 2 o he p ojec .