Partial correlation analyses of global diffusion tensor imaging-derived metrics in glioblastoma multiforme: Pilot study

Table 1 Diffusion tensor imaging-derived tensor metric formulas

MD

MD = D = (λ1 + λ2 + λ3)/3

FA

FA = [(3/2) × (q/L)]1/2 = (3/2)1/2{[(λ1 - D)2+(λ2 - D)2+(λ3 - D)2]/(λ12 + λ22 + λ32)}1/2

RA

RA = q/p = {[(λ1 - D)2 + (λ2 - D)2+(λ3 - D)2]1/2}/[31/2D]

RD

RD = (λ2 + λ3)/2

AD

AD = λ1

Cs

Cs = 3λ3/(λ1 + λ2 + λ3)

p

p = 31/2D = (λ1 + λ2 + λ3)/31/2

q

q = [(λ1 - D)2 + (λ2 - D)2 + (λ3 - D)2]1/2

L

L = (p2 + q2)1/2 = (λ12 + λ22 + λ32)1/2

Cl

Cl = (λ1 - λ2)/(λ1 + λ2 + λ3)

Cp

Cp = 2(λ2 - λ3)/(λ1 + λ2 + λ3)

MD: Mean diffusivity; FA: Fractional anisotropy; RA: Relative anisotropy; RD: Radial diffusivity; AD: Axial diffusivity; Cs: Spherical tensor; p: Pure isotropic diffusion; q: Pure anisotropic diffusion; L: Total magnitude of the diffusion tensor; Cl: Linear tensor; Cp: Planar tensor.

Table 2 Means, SD and correlations (controlled for the effect of age and gender) in healthy brains

Tensor metric													Mean	SD
		Cs											0.756690	0.032259
FA	Pearson’s R	-0.456	FA										0.284317	0.018917
	P-value	0.029
RA	Pearson’s R	-0.992	0.434	RA									0.224873	0.029523
	P-value	0.000	0.039
Cp	Pearson’s R	-0.979	0.460	0.938	Cp								0.133346	0.017086
	P-value	0.000	0.031	0.000
Cl	Pearson’s R	-0.946	0.442	0.978	0.855	Cl							0.111574	0.016583
	P-value	0.000	0.024	0.000	0.000
L	Pearson’s R	0.372	-0.115	-0.416	-0.317	-0.186	L						0.002275	0.000100
	P-value	0.117	0.578	0.076	0.200	0.408
p	Pearson’s R	0.179	-0.095	-0.214	-0.020	-0.014	0.945	p					0.002096	0.000087
	P-value	0.477	0.652	0.395	0.938	0.953	0.000
AD	Pearson’s R	0.322	-0.012	-0.348	-0.287	0.019	0.804	0.761	AD				0.001553	0.000056
	P-value	0.179	0.952	0.144	0.249	0.933	0.000	0.000
MD	Pearson’s R	0.181	-0.096	-0.215	-0.022	-0.014	0.945	1.000	0.762	MD			0.001210	0.000050
	P-value	0.473	0.649	0.391	0.934	0.953	0.000	0.000	0.000
RD	Pearson’s R	0.053	-0.297	-0.119	0.426	-0.131	0.877	0.954	0.628	0.954	RD		0.001046	0.000072
	P-value	0.821	0.132	0.606	0.054	0.542	0.000	0.000	0.001	0.000
q	Pearson’s R	-0.077	0.698	0.019	0.257	0.138	0.138	0.153	0.393	0.152	0.406	q	0.000445	0.000055
	P-value	0.721	0.000	0.929	0.225	0.492	0.502	0.466	0.047	0.467	0.029

FA: Fractional anisotropy; RA: Relative anisotropy; Cp: Planar tensor; p: Pure isotropic diffusion; q: Pure anisotropic diffusion; L: Total magnitude of the diffusion tensor; Cl: Linear tensor; MD: Mean diffusivity; RD: Radial diffusivity; AD: Axial diffusivity.

Table 3 Means, SD and correlations (controlled for the effect of age and gender) in brains with glioblastoma multiforme

Tensor metric													Mean	SD
		Cs											0.771562	0.066812
FA	Pearson’s R	-0.570	FA										0.253531	0.028425
	P-value	0.003
RA	Pearson’s R	-1.000	0.592	RA									0.201778	0.053287
	P-value	0.000	0.002
Cp	Pearson’s R	-0.936	0.576	0.901	Cp								0.133265	0.043503
	P-value	0.000	0.003	0.000
Cl	Pearson’s R	-0.904	0.819	0.969	0.803	Cl							0.098462	0.011929
	P-value	0.000	0.000	0.000	0.000
L	Pearson’s R	0.096	0.151	0.009	-0.159	0.182	L						0.002111	0.000140
	P-value	0.648	0.472	0.967	0.446	0.469
p	Pearson’s R	0.156	-0.129	-0.094	-0.216	-0.177	0.834	p					0.001961	0.000123
	P-value	0.456	0.540	0.664	0.299	0.482	0.000
AD	Pearson’s R	-0.111	0.343	0.191	0.053	0.173	0.871	0.881	AD				0.001397	0.000080
	P-value	0.596	0.094	0.372	0.803	0.492	0.000	0.000
MD	Pearson’s R	0.154	-0.125	-0.090	-0.215	-0.173	0.837	1.000	0.883	MD			0.001132	0.000071
	P-value	0.462	0.550	0.675	0.303	0.491	0.000	0.000	0.000
RD	Pearson’s R	0.305	-0.411	-0.260	-0.360	-0.395	0.706	0.954	0.699	0.953	RD		0.000999	0.000073
	P-value	0.139	0.041	0.219	0.077	0.105	0.000	0.000	0.000	0.000
q	Pearson’s R	-0.484	0.928	0.539	0.466	0.736	0.430	0.187	0.629	0.191	-0.114	q	0.000363	0.000048
	P-value	0.014	0.000	0.007	0.019	0.001	0.032	0.371	0.001	0.361	0.588

MD: Mean diffusivity; FA: Fractional anisotropy; RA: Relative anisotropy; RD: Radial diffusivity; AD: Axial diffusivity; Cs: Spherical tensor; p: Pure isotropic diffusion; q: Pure anisotropic diffusion; L: Total magnitude of the diffusion tensor; Cl: Linear tensor; Cp: Planar tensor.

Table 4 Estimated marginal means SE and CI of diffusion tensor imaging-derived tensor metrics (the effect of age was controlled at the value of 43.92 yr)

Tensor metric	Healthy brains				Brains with GBM
	Mean	SE	95%CI		Mean	SE	95%CI
			Lower	Upper			Lower	Upper
Cs	0.739511	0.009798	0.719577	0.759446	0.766043	0.007824	0.750126	0.781960
FA	0.290160	0.005721	0.278520	0.301799	0.255660	0.004568	0.246366	0.264954
RA	0.241025	0.008008	0.224734	0.257317	0.211498	0.006394	0.198490	0.224506
Cp	0.141366	0.007941	0.125210	0.157522	0.137961	0.006341	0.125061	0.150860
Cl	0.119041	0.003243	0.112443	0.125638	0.099495	0.002589	0.094227	0.104763
L	0.002287	0.000029	0.002227	0.002347	0.002103	0.000024	0.002055	0.002151
p	0.002122	0.000027	0.002068	0.002177	0.001946	0.000021	0.001903	0.001990
AD	0.001558	0.000020	0.001518	0.001598	0.001395	0.000016	0.001363	0.001426
MD	0.001225	0.000015	0.001194	0.001257	0.001124	0.000012	0.001099	0.001149
RD	0.001059	0.000015	0.001029	0.001089	0.000988	0.000012	0.000964	0.001012
q	0.000454	0.000011	0.000432	0.000476	0.000371	0.000009	0.000354	0.000389

MD: Mean diffusivity; FA: Fractional anisotropy; RA: Relative anisotropy; RD: Radial diffusivity; AD: Axial diffusivity; Cs: Spherical tensor; p: Pure isotropic diffusion; q: Pure anisotropic diffusion; L: Total magnitude of the diffusion tensor; Cl: Linear tensor; Cp: Planar tensor; GBM: Glioblastoma multiforme.