频域阻抗法研究细胞介电特性

对生物细胞介电特性的研究是生物医学物理学公认的前沿重点课题之一.本文介绍如何采用宽频域交流阻抗技术研究细胞介电特性的原理和方法,以及在细胞介电谱的基础上,如何通过非线性数值计算建立细胞的数学模型和物理模型.本文以蛙骨骼肌细胞为例,在100Hz～100 MHz范围内,应用阻抗分析仪测量了细胞交流阻抗,通过细胞介电谱、Cole-Cole图、介电耗损因子频率谱、介电损耗角正切频率谱等方式,分析了骨骼肌细胞介电特性的数据特征;最后使用Cole-Cole模型和椭圆壳介电理论,建立了骨骼肌细胞的数学模型和物理模型,为今后利用数理模型方法分析骨骼肌疲劳、骨骼肌萎缩等奠定了基础.     

骨骼肌细胞的介电弛豫特性

在100Hz～100MHz频率范围内,利用非线性数值计算和曲线拟合分析,验证了蛙离体骨骼肌细胞的介电弛豫特性满足Cole-Cole公式(误差≤3.45%),通过频域介电谱、Cole-Cole图、介电损耗因子和介电损耗角正切频率谱的曲线拟合分析,确定了蛙骨骼肌细胞的Cole-Cole介电参数:高频段相对介电常数εh=78,第一相对介电增量△ε1=113000,第二相对介电增量△ε2=45000,第一特征频率fc1=9 kHz,第二特征频率fc2=158 kHz,第一相位角β1=0.881,第二相位角β2=0.984,低频段电导率κL=0.55mS/cm,常数A=35,常数m=1.08.     

应用Cole-Cole公式分析蛙血液细胞介电谱

利用Cole-Cole公式对10^4～10^8Hz频率段的蛙血液细胞介电谱进行了曲线拟合分析，建立了蛙血液细胞Cole-Cole参数：高频段相对介电常数εh=60，第一相对介电增量△εl=4900，第二相对介电增量△ε2=1200，第一特征频率fl=0．2MHz，第二特征频率f2=2．4MHz，第一相位角βl=0．92，第二相位角β2=0．93，低频段电导率εl=3．38ms／cm。     

蛙血细胞被动电生理特性的数据分析

在10^4-10^8Hz范围内,应用阻抗测量技术研究了蛙血液细胞的介电常数,电导率与电场频率的关系特性,利用细胞介电谱,Cole-Cole图,介电损失和损耗角正切分析了蛙血液细胞的被动电生理特性的数据特征,结果表明：蛙全血细胞具有两个特征频率,第一特征频率fci在10^5Hz范围内,第二特征频率fc2在10^6Hz范围内。     

蛙骨骼肌细胞的被动电特性

应用宽频域阻抗测量技术研究骨骼肌纤维走行与电场呈垂直和平行两个方向的蛙离体骨骼肌的被动电特性。采用Cole-Cole数学模型的非线性数值计算,经过频域介电谱、Cole-Cole图、介电损耗因子和介电损耗角正切频率谱的曲线拟合分析,建立了蛙骨骼肌细胞在垂直和平行两个方向的介电参数：在垂直方向,高频段介电常数εh=78,第一介电常数增量△ε1=113000,第二介电常数增量△ε2=45000,第一特征频率,fc1=9kHz,第二特征频率fc2=158kHz,第一相位角β1=0．881,第二相位角β2=0．984,低频段电导率κL=0．55mS／cm;在平行方向,εh=78,△ε1=550000,△ε2=140000,fc1=1．12kHz,fc2=19．9kHz,β1=0．92,β2=0．99,κL=4．5mS／cm。     

细胞外灌流对骨骼肌细胞介电谱的影响

通过灌流的方法,探讨细胞外液对骨骼肌细胞介电谱的影响,应用非线性Co le-Co le公式的曲线拟合与数值计算,比较灌流后骨骼肌细胞介电谱参数,结果表明:(1)低频段介电常数Lε和高频段电导率hκ随着细胞外灌流液电导率的降低而减少;(2)细胞外灌流对骨骼肌细胞介电谱的特征频率(fC 1,fC 2)影响不大;(3)细胞外灌流主要影响骨骼肌细胞Δε″和tgδ的峰值。     

垂直和平行方向的骨骼肌介电谱的比较研究

在10Hz-100MHz频率范围内，应用阻抗分析仪测量了骨骼肌纤维走行与测量电场呈垂直和平行两个方向上的蛙离体骨骼肌的介电谱。比较了平行和垂直于外施电场方向的骨骼肌细胞介电谱的区别：（1）在低频低，平行方向电导率（K1，∥）高于垂直方向电导率（K1，⊥）近10倍；（2）在高频段，平行方向电导率（Kh,∥）与垂直方向电导率（Kh,⊥）不相等，存在着约0.8mS/cm的差值；（3）在电导率Cole-Cole图上，平行方向电导率增量（△k∥)低于垂直方向电导率增量（△k⊥);(4)在介电损失（ε“)方面，平行方向介电损失（ε“∥）主峰明显高于垂直方向介电损失（ε“⊥)主峰；（5）在介电损耗角正切（tgδ）方面，平行介电损耗正切（tgδ∥）主峰的频率滞后于垂直方向介电损耗角正切（tgδ⊥）主峰的频率，但是tgδ∥峰值高于tgδ⊥峰值。     

0.1 MHz～100 MHz大鼠血液细胞的介电响应

目的：确立正常大鼠血液细胞对0．1MHz-100MHz交流电场的介电响应的数据特征。材料与方法：取10只雄性Sprague-Dawley大鼠全血，利用Agilent4294A阻抗分析仪测量了26个全血细胞悬浮液样本的交流阻抗，通过频域介电谱和Cole-Cole图的数据分析，确立了正常大鼠血液细胞对交流电场的介电响应的数据特征。结果：在0．1MHz-100MHz频率范围内，大鼠血液细胞的介电常数和电导率具有电场频率的依赖关系，主要表现在具有两个中心特征频率的介电弛豫：第一介电弛豫约发生在fc1=2MHz，第二介电弛豫约产生在fc2=3MHz。结论：交流阻抗技术可以观察血液细胞的介电响应特性。     

细胞悬浮液介电谱检测与应用研究进展

细胞悬浮液介电谱是一种快速、实时、无损进行细胞物理特性定量研究的方法,在研究细胞构成和细胞生命活动过程中具有重要意义。细胞的结构和组成使其成为介电谱研究最适合的体系之一。细胞悬浮液介电谱随着检测频率的增加呈现α、β和γ三个典型的弛豫,对弛豫类型的解析有助于了解细胞组分和活动的信息。而细胞电参数模型的发展将细胞介电特性的研究深化到亚细胞层面,有助于了解更加细致的细胞组分和生命活动的信息。本文对细胞的介电行为,细胞悬浮液介电谱的检测、解析以及应用进行简要综述。     

人血液细胞介电谱的实验研究

在0．01～100MHz范围内，测量人血液细胞的介电谱，确立人血液细胞对交流电场的介电响应的数据特征。利用频域阻抗技术测量了正常人血液细胞交流阻抗，绘制细胞的介电常数和电导率与电场频率的关系曲线。建立了人血液细胞的介电谱和Cole—Cole图，明确了人血细胞的介电频响的数据特征。在射频电场中，人血液细胞的介电常数和电导率具有频率依赖性，表现为具有两个特征频率的介电弛豫：第一介电弛豫发生在fc。为1．42MHz，第二介电弛豫产生在fcz为3．32MHz。     

Anisotropy in the dielectric properties of skeletal muscle

The dielectric permittivity and conductivity of freshly excised dog skeletal muscle were measured at frequencies between 20 Hz and 1 MHz, with the tissue samples oriented either parallel or perpendicular to the applied electric field. At frequencies below 100 kHz a four-electrode technique was employed; at frequencies above 100 kHz a conventional two-electrode technique was used in conjunction with a commercial admittance bridge. All measurements were performed with the tissue sample at body temperature. Over the entire frequency range of the study, the dielectric properties of the muscle were found to be significantly anisotropic. At audio frequencies, the conductivity of the muscle measured in a direction parallel to the fibre orientation was typically found to be ten times higher than that measured perpendicular to the fibre axis; at frequencies approaching 1 MHz the conductivities measured in both directions approached a common value, near 8 ms cm^?1. The dielectric permittivity in both orientations is strongly dependent on frequency. These data are analysed using the suspension equation, and comments are made on the mechanisms that are responsible for the observed properties. In an Appendix these results are related to some of the very early work on the subject.     

In vivo and in vitro dielectric properties of feline tissues at low radiofrequencies

The dielectric constant and conductivity of muscle, liver, spleen and kidney of cats in vivo and in situ immediately following the animal's death were measured at frequencies from 10 kHz to 100 MHz. A novel multi-ring capacitive sensor and a computer-controlled automatic network analyser (ANA) were employed. The results were compared with the data available from literature for the same species in the frequency range between 10 and 100 MHz. It was found that at frequencies from 10 to 100 kHz the in vitro dielectric constant for all tissues except spleen was smaller than the in vivo one. In contrast, in the range from 1 to 100 MHz the in vitro dielectric constant was larger than the in vivo one. At intermediate frequencies from 0.1 to 1 MHz both the dielectric constant in vivo and in vitro were the same within the experimental uncertainty. The dielectric constant of the spleen in vivo was quite similar to that in vitro. The in vivo conductivity of all tissues appeared to be higher than in vitro from 10 kHz to 10 MHz, while at frequencies above 10 MHz the two conductivities were within the experimental uncertainty.     

大鼠腓肠肌细胞介电谱测量和Cole-Cole数学模型分析

测量大鼠腓肠肌细胞介电谱,利用Cole-Cole方程的曲线拟合建立Cole-Cole数学模型参数.在100 Hz～100 MHz频率范围,使用Agilent 4294A阻抗分析仪对电场与肌纤维方向呈平行和垂直的大鼠腓肠肌进行了阻抗测量,并利用Cole-Cole方程的数值计算,对细胞介电谱、Cole-Cole图、介电损耗因子频谱、电导率虚部频谱和损耗角正切频谱进行曲线拟合分析和残差分析,比较电场与肌纤维方向呈平行或垂直两种情况的介电行为区别.结果表明:骨骼肌细胞的介电弛豫具有两个特征频率,其平行方向的特征频率低于垂直方向;平行方向的介电增量高于垂直方向的介电增量;平行方向的低频极限量高于垂直方向的低频极限量;平行方向和垂直方向的介电常数高频极限量相等;平行方向和垂直方向的电导率高频极限量存在一定差距.平行方向的电导率虚部频谱和损耗角正切分别高于垂直方向的值,但是,平行方向的电导率虚部最大值低于其垂直方向的值.腓肠肌细胞的介电常数和电导率存在频率依存性和各向异性,其介电行为存在α和β两个介电散射,并满足Cole-Cole数学模型.     

Dielectric properties of Co-gamma-irradiated and microwave-heated rat tumour and skin measured in vivo between 0.2 and 2.4 GHz

The dielectric properties of a rat tumour (rhabdomyosarcoma R1H), skin and muscle were measured in vivo with an open-ended coaxial line and a computer-controlled system based on a network analyser. The permittivity of the tumour R1H and of the normal tissues in anaesthetised rats was determined at frequencies between 0.2 and 2.4 GHz. No significant differences were observed either between rat tumour and muscle or between normal and 15 Gy irradiated rat tumour and skin. However, after a hyperthermia treatment at 43 degrees C for 60 min the dielectric properties, especially of the rat skin, changed due to the hyperthermic induced oedema which is related to an increase in tissue water content. The process of the oedema modifies the dielectric properties of the skin to a higher degree than those of the tumour.     

In vitro dielectric properties of human tissues at radiofrequencies

In vitro permittivity measurements of excised human liver, spleen, kidney and cardiac muscle at frequencies from 10 kHz to 100 MHz are described. An end-of-the-line capacitive sensor and a computer-controlled network analyser HP 3577 were employed. The results were compared with human data reported by other investigators as well as with the animal (cat) data obtained earlier in this laboratory. It was found that the conductivity of most of the human tissues tested was significantly higher than that of the animal tissues for the test frequencies. The dielectric constants for human kidney and spleen are higher than the corresponding animal (cat) tissues at frequencies from 10 kHz to approximately 1 MHz and at around 100 MHz. However, the values for liver do not differ significantly between the two species in the same frequency range.     

正常人血小板介电谱的实验研究

在100KHz～110MHz范围内,测量人血小板的介电谱,分析了人血小板对交流电场的介电响应的数据特征。利用频域阻抗技术首次测量了正常人血小板交流阻抗,绘制血小板的介电常数和电导率与电场频率的关系曲线。建立了人血小板的介电谱和Cole-Cole图,明确了人血小板的介电频响的数据特征。在射频电场中,人血小板的介电常数和电导率具有频率依赖性,血小板介电谱具有两个特征频率:第一特征频率fC1为6.66MHz,第二特征频率fC2为9.81MHz。     

Dielectric properties of rat embryo and foetus as a function of gestation

The dielectric properties of rat embryos/foetuses have been acquired at several stages of gestation at 37 °C and in the frequency range of 40 MHz-20 GHz. Measurements were carried out on homogenized tissues, as trial experiments did not show any systematic difference between the dielectric data of intact and homogenized tissues at microwave frequencies. The results showed that dielectric properties of the foetus are generally higher than adult muscle and brain. The measured data also showed some decline for both permittivity and conductivity as the foetus grew from 18 to 20 days old; however, these changes were not statistically significant. Data were also collected for placenta and amniotic fluid which were in good agreement with those recently obtained from human tissues. Finally, tabulated numerical dielectric data for rat foetal tissues are presented for a wide range of medical and telecommunication frequencies.     

Sensitivity and specificity analysis of fringing-field dielectric spectroscopy applied to a multi-layer system modelling the human skin

The sensitivity and specificity of dielectric spectroscopy for the detection of dielectric changes inside a multi-layered structure is investigated. We focus on providing a base for sensing physiological changes in the human skin, i.e. in the epidermal and dermal layers. The correlation between changes of the human skin's effective permittivity and changes of dielectric parameters and layer thickness of the epidermal and dermal layers is assessed using numerical simulations. Numerical models include fringing-field probes placed directly on a multi-layer model of the skin. The resulting dielectric spectra in the range from 100 kHz up to 100 MHz for different layer parameters and sensor geometries are used for a sensitivity and specificity analysis of this multi-layer system. First, employing a coaxial probe, a sensitivity analysis is performed for specific variations of the parameters of the epidermal and dermal layers. Second, the specificity of this system is analysed based on the roots and corresponding sign changes of the computed dielectric spectra and their first and second derivatives. The transferability of the derived results is shown by a comparison of the dielectric spectra of a coplanar probe and a scaled coaxial probe. Additionally, a comparison of the sensitivity of a coaxial probe and an interdigitated probe as a function of electrode distance is performed. It is found that the sensitivity for detecting changes of dielectric properties in the epidermal and dermal layers strongly depends on frequency. Based on an analysis of the dielectric spectra, changes in the effective dielectric parameters can theoretically be uniquely assigned to specific changes in permittivity and conductivity. However, in practice, measurement uncertainties may degrade the performance of the system.