Delineation of potential hot spots for hyperthermia treatment planning optimisation

Figures & data

Figure 1. Delineated potential hot spots in muscle tissue at a selection level of (a) six, (b) four and (c) three times the OST.

Figure 2. Delineated potential hot spots in fat tissue at a selection level of (a) six, (b) four and (c) three times the OST.

Table I.  Overview of number of delineated potential hot spots per selection level and tissue type.

		Number of potential hot spots (PHsps)
	Selection level (multiple of the OST)	PHsp vol.  ≤ 5 cm^3	5 cm^3 < PHsp vol. ≤ 10 cm^3	10 cm^3 < PHsp vol. ≤ Vmax	Total number of PHsps	Vmax (cm^3)
Muscle	6	12	2	–	14	6
	4	15	2	4	21	44
	3	28	4	7	39	110
Fat	6	15	–	6	21	201
	4	30	6	12	48	385
	3	55	5	11	71	786

Table II.  Optimisation results for patient case 1.

Setup label	Optimised objective function	Power load applied to the patient at a SAR of 50 W/kg in the target	Π1	Π2	Π3	RPHS constraint
A11	Π1	831	0.186	0.0116	0.0004181	None
A12	Π1	836	0.181	0.0120	0.0004040	8
A13	Π1	893	0.165	0.0118	0.0003714	7
A14	Π1	1038	0.134	0.0105	0.0003508	6
A21	Π2	920	0.162	0.0131	0.0003407	None
A22	Π2	920	0.162	0.0131	0.0003407	8
A23	Π2	970	0.149	0.0129	0.0003242	7
A24	Π2	1102	0.127	0.0118	0.0003200	6
A30	Π3	3152	0.045	0.0041	0.0008157	None
A31	Π3	1569	0.088	0.0068	0.0006930	10
A32	Π3	1453	0.093	0.0075	0.0005596	8
A33	Π3	1404	0.095	0.0084	0.0004653	7
A34	Π3	1342	0.102	0.0084	0.0003838	6
B11	Π1	831	0.186	0.0098	0.0002547	None
B12	Π1	828	0.185	0.0098	0.0002536	6
B13	Π1	876	0.169	0.0094	0.0002358	5
B14	Π1	1121	0.124	0.0078	0.0002096	4.1
B21	Π2	835	0.178	0.0101	0.0002418	None
B22	Π2	835	0.178	0.0101	0.0002418	6
B23	Π2	882	0.164	0.0096	0.0002268	5
B24	Π2	1121	0.124	0.0078	0.0002096	4.1
B30	Π2	1330	0.105	0.0057	0.0003278	None
B31	Π2	1330	0.105	0.0057	0.0003278	7
B32	Π2	1194	0.116	0.0065	0.0003148	6
B33	Π2	1195	0.115	0.0068	0.0002766	5
B34	Π2	1147	0.121	0.0075	0.0002135	4.1
C11	Π1	831	0.186	0.0087	0.0001924	None
C12	Π1	852	0.175	0.0083	0.0001844	4
C13	Π1	1099	0.117	0.0062	0.0001439	3.58
C21	Π2	837	0.181	0.0088	0.0001830	None
C22	Π2	855	0.169	0.0084	0.0001771	4
C23	Π2	1099	0.117	0.0062	0.0001439	3.58
C31	Π2	972	0.147	0.0063	0.0002176	None
C32	Π3	963	0.145	0.0064	0.0002049	4
C33	Π3	1099	0.117	0.0062	0.0001439	3.58

Π₁: the SAR in the target at a normalised feed vector, Π₂: maximal SAR in the target at minimal summed SAR in a selected set of potential hot spots, Π₃: maximal SAR in the target at minimal weighed summed SAR in a selected set of potential hot spots.

Figure 3. RPHS value distribution of the potential hot spots for the maximised objective functions. Patient case 1, selection level of six times the OST.

Figure 4. RPHS value distribution of the potential hot spots for the maximised objective functions. Patient case 1, selection level of four times the OST.

Figure 5. RPHS value distribution of the potential hot spots for the maximised objective functions. Patient case 1, selection level of three times the OST.

Table III.  Optimisation results for patient case 2.

Setup label	Optimised Objective function	Power load applied to the patient at a SAR of 50 W/kg in the target	Π1	Π2	Π3	RPHS constraint
A11	Π1	581	1.007	0.0336	0.0103	None
A21	Π2	588	0.819	0.0376	0.0082	None
A31	Π3	608	0.665	0.0277	0.0152	None
A32	Π3	603	0.677	0.0280	0.0152	8
A33	Π3	585	0.730	0.0295	0.0150	7
A34	Π3	567	0.788	0.0314	0.0144	6
B11	Π1	581	1.007	0.0175	0.00283	None
B12	Π1	581	1.007	0.0175	0.00283	5
B13	Π1	595	0.993	0.0174	0.00275	4
B21	Π2	597	0.701	0.0191	0.00243	None
B22	Π2	597	0.701	0.0191	0.00243	5
B23	Π2	617	0.726	0.0188	0.00232	4
B31	Π3	550	0.863	0.0176	0.00308	None
B32	Π3	555	0.881	0.0177	0.00306	5
B33	Π3	574	0.913	0.0175	0.00291	4
C11	Π1	581	1.007	0.01248	0.00129	None
C12	Π1	596	0.675	0.01346	0.00121	3
C21	Π2	554	0.710	0.01406	0.00132	None
C22	Π2	596	0.666	0.01347	0.00120	3
C31	Π3	559	0.816	0.01339	0.00144	None
C32	Π3	553	0.878	0.01359	0.00142	4
C33	Π3	596	0.675	0.01346	0.00121	3

Π₁: the SAR in the target at a normalised feed vector, Π₂: maximal SAR in the target at minimal summed SAR in a selected set of potential hot spots, Π₃: maximal SAR in the target at minimal weighed summed SAR in a selected set of potential hot spots.

Figure 6. Delineated potential hot spots in fat tissue at a selection level of (a) six, (b) four and (c) three times the OST.

Figure 7. Delineated potential hot spots in muscle tissue at a selection level of (a) six, (b) four and (c) three times the OST.

Figure 8. RPHS value Distribution of the potential hot spots for the maximised objective functions. Patient case 2, selection level of six times the OST.

Figure 9. RPHS value Distribution of the potential hot spots for the maximised objective functions. Patient case 2, selection level of four times the OST.

Figure 10. RPHS value Distribution of the potential hot spots for the maximised objective functions. Patient case 2, selection level of three times the OST.

Figure 11. The feed vector homogeneity index for the potential hot spots found at the different selection levels defined for both patient case 1 and patient case 2.

Table IV.  Grid points added by the post processing step for patient case 1.

Setup label	Optimised objective function	Power load applied to the patient at a SAR of 50 W/kg in the target	Π1	Grid points added by the post processing step	Grid points delineated in initial step
A30	Π3	3152	0.045	1561	763
A31	Π3	1569	0.088	16
A32	Π3	1453	0.093	2
A33	Π3	1404	0.095	2
A34	Π3	1342	0.102	70
B30	Π3	1330	0.105	10	1691
B31	Π3	1330	0.105	10
B32	Π3	1194	0.116	1
B33	Π3	1195	0.115	2
B34	Π3	1147	0.121	130
C31	Π3	972	0.147	0	3176
C32	Π3	963	0.145	0
C33	Π3	1099	0.117	0