Medical & Biological Engineering & Computing

, Volume 51, Issue 1–2, pp 197–205 | Cite as

Local property characterization of prostate glands using inhomogeneous modeling based on tumor volume and location analysis

  • Yeongjin Kim
  • Bummo Ahn
  • Jae Won Lee
  • Koon Ho Rha
  • Jung Kim
Original Article


Mechanical property characterization of prostate tumors can enhance the results obtained by palpation by providing quantitative and precise diagnostic information to surgeons. The multi-focal characteristics of prostate tumors cause inhomogeneity and local property variance in the prostate glands, which is one reason for inaccurate property characterizations of the tumors. Therefore, biomechanical models should include inhomogeneity and local property variance by taking into consideration the anatomical information (location and volume) of the tumors. We developed six inhomogeneous local prostate models using the finite element method, which takes into account the location and volume information of prostate tumors. The models were divided into six different sections: lateral apex, lateral mid, lateral base, medial apex, medial mid and medial base tumors. Information on the location and volume of prostate tumors was obtained using pathological analysis. The mechanical properties of prostate tumors were estimated using the developed model simulation and the ex vivo indentation experiment results from the human resected prostates. The results showed that the mean elastic moduli of the normal and tumoral regions were 14.7 and 41.6 kPa, respectively. Our models provided more reliable estimates of the elastic moduli than the conventionally used Hertz–Sneddon model, and the results from our model were more closely correlated with previous studies due to the inclusion of the anatomical information via inhomogeneous modeling. These six local models provide baseline property criteria for the diagnosis and localization of prostate tumors using the optimized elastic moduli of normal prostate tissues.


Local mechanical properties FEM Prostate 

1 Introduction

The mechanical properties of biological tissues are important indicators of the tissues’ pathological states. For instance, prostate adenocarcinomas have higher cellular densities than normal tissue, and the pathological findings from prostate adenocarcinoma demonstrate that these tumors have well-defined gland patterns and are denser than normal tissue. Thus, these changes in the tissue increase the mechanical properties of the tumor [13, 21]. Mechanical diagnosis is one possible approach for detecting tumors using the mechanical property differences between normal and tumor tissues. Palpation is the most frequently used clinical diagnostic method used by urologists to distinguish between malignant and benign tumors. However, the success rate of this technique is low [19], and it is not able to provide quantitative and precise information due to its dependence on the clinician’s skill. Mechanical characterization, based on well-defined biomechanical models, could address these limitations and provide more accurate and significant information to clinicians.

A great deal of research on mechanical characterization has been performed. Krouskop et al. [15] measured the mechanical properties of prostate tissue and showed that the elastic modulus of prostate tumor tissue is greater than that of normal tissue. Yang et al. [28] performed in vitro macro- and micro-indentation tests to measure the dynamic mechanical properties of human prostate tissue. Fearing et al. [27] used a probing system in silicone phantoms with inclusions and conducted a statistical analysis with the existence of these inclusions. Ahn et al. [5] localized the inclusions within silicone phantoms using the sweeping palpation system and the FEM-based mechanical property characterization. Tanaka et al. performed in vivo tests with human prostates, and the results were characterized according to three different firmness levels (soft, firm, and hard) to distinguish between cancerous and normal tissues [7, 25, 26]. Liu et al. used the internal structure of the prostate with rolling mechanical imaging to determine the approximate location, shape, and size of cancerous nodules [16, 22]. Ahn et al. [2, 4] and Carson et al. [6] characterized the mechanical properties of human prostate tissue in ex vivo experiments. The property characterization methods suggested by the previous studies were built on overly simplified assumptions that prostate tissue is linear and homogeneous, which limits the validity of mechanical property characterization. The inhomogeneous characteristics of normal and tumor tissues should be statistically analyzed for tumor location and volume, and this information should be incorporated into tissue modeling to more accurately characterize the tissue properties. Therefore, we obtained pathological information (location and volume) from prostate tumors and developed a novel, tumor-containing tissue model. Another important issue that should be included in modeling is the local property variance due to the multi-focal nodules of prostate tumors. Previous models did not consider boundary conditions and surface geometry in local mechanical stimulation experiments and thus do not include the local property variance of prostate glands. It is, therefore, necessary to develop local inhomogeneous prostate models that cover all sections of the prostate. For each local section, the location and volume information of each prostate tumor was determined by uro-pathologist and was statistically analyzed. Based on this information, six local inhomogeneous prostate models were developed as an enhanced numerical model strategy that included the inhomogeneous nature of the internal prostate structure.

2 Materials and methods

2.1 Indentation experiments [3]

Experimental specimens were prepared from the resected prostates of 46 patients who underwent a radical prostatectomy at Severance Hospital, Yonsei University, in Seoul, Korea, between April 2009 and July 2009. We excluded the specimens of patients who had undergone prostate-related surgery and patients with clinically insignificant small cancer (<0.5 ml) or preoperative hormonal/radiation therapy. The mean age was 63 years (range 44–69), and the mean PSA level was 12.9 ng/ml (range 2.8–120.9). The mean preoperative volume of the specimens was 41.5 ml (range 18.27–115.9 ml). The pathological stages of prostate cancer specimens were classified according to the TNM (tumor, node, and metastasis) stage. The clinical stages of the prostate cancer samples in this system were T1c in 31 patients, T2a in 6 patients, T2b in 5 patients, T2c in 1 patient, T3a in 1 patient, and T3b in 2 patients. All the patients provided written informed consent, and the study was approved by the Institutional Review Board (IRB No. 1-2009-0012). The indentation experiments were conducted using a minimally motorized indenter [3]. The pathological information was disclosed during the experiments. The indenter was brought into contact with the posterior surface of the prostate and used to induce a 3-mm deep indentation (position control) at a speed of 1 mm/s. For each prostate specimen, the indentation experiments were performed at 12 sites along the posterior surface of the prostate (see Fig. 1a). These sites are related to those sampled in double sextant needle biopsies. The original diagnostic scheme for prostate tumors consists of six core examinations: lateral apex (LA), lateral mid (LM), lateral base (LB), medial apex (MA), medial mid (MM) and medial base (MB) on both the left and right sides [6].
Fig. 1

a The 12 sections of the prostate used in the double sextant biopsy scheme. b Experimental setup. c Depth (location) and diameter information from the pathological analysis

2.2 Pathological location and volume analyses of tumor lesions

The geometry of prostate glands and the volume and location of tumor lesions were incorporated into the prostate tissue model. After performing the indentation experiments, the pathology experts submitted tissue samples for histological examination. A single uro-pathologist, who was blind to the results of the mechanical testing, analyzed all of the specimens. The volume of each tumor lesion and the depth (location) relative to the posterior surface were documented for each section (see Fig. 1c). We assumed that the tumor lesion was shaped like a sphere to simplify the tumor volume estimates. Therefore, the tumor volumes could be estimated using the following equation:
$$ {\text{Volume}}\, = \,4/3\, \times \,\left( {\text{radius}} \right)^{3} $$

2.3 Finite element model

Finite element (FE) models, which take into account the geometries of the prostate glands and the indenter, were constructed and further optimized with the experimental data. Three-dimensional geometries of normal prostate and tumor-containing prostate (TCP) were reconstructed using the AMIRA software (Template Graphics Software, Inc., USA). The prostate segmentation was performed by urologists. The size of normal prostate gland is known to be ~3 cm in diameter [18]. Thus, normal prostate (NP) models and TCP models with width of 30 mm, height of 30 mm, and thickness of 20 mm are developed and an indenter is located for each section (LB, MB, LM, MM, LA, and MA) as shown in Fig. 2. While the NP model only has homogeneous normal tissue region, the TCP model includes two distinct regions: normal tissue and tumor. From the anatomical information, the tumor lesion was modeled as a sphere with a diameter of ~1 cm (see Table 1; Fig. 2). The displacement boundary conditions were applied to the indenter and to the anterior side of prostate (Fig. 2). The rigid spherical tip indenter with 3-mm diameter was given a 3 mm vertical displacement (indentation depth) for six sections. The anterior side was constrained to assume perfect contact with the substrate. Finite element method (FEM) simulations were performed using the commercial software ABAQUS/Standard 6.5.1 (SIMULIA, USA). The developed FE model consists of 33,743 nodes with a total of 203,316 linear elements (C3D4). The normal and tangential contact conditions between the indenter and tissues were assumed to be hard contacts and frictionless. The Young’s modulus and the Poisson’s ratio were used to represent material parameters of both normal tissue and tumor lesion. The NP and TCP models were assumed to be incompressible materials. The material parameter estimation for normal tissue and tumor lesion was performed using a numerical approach, which includes an algorithm coupled with NP and TCP model simulations that minimize the errors between the simulation and ex vivo experimental results in Fig. 3b. The models are used to simulate the indentation experiment, which depends on elastic material parameters. To estimate the Young’s modulus, E, we employed the Levenberg–Marquardt method [1, 14, 20, 29]. The estimated Young’s modulus after iteration is defined as the value that yields an optimal fit of simulated results to the experiment results. For each section, the mean value of force displacement curves is used for the estimation. The estimation process consists of two steps. In step 1, the Young’s modulus of normal tissue region in NP models were determined assuming that the results from the normal prostate indentation experiments correspond to the behavior of the normal prostate for each section (LB, MB, LM, MM, LA, and MA). In step 2, based on the Young’s modulus of normal tissue region from step 1, the Young’s modulus of tumor in TCP models for six sections were estimated with the results from the tumor region indentation experiments (see Fig. 3a) (Table 2).
Fig. 2

Six TCP models for tumors containing prostate tissues from six sections (LB, MB, LM, MM, LA and MA)

Table 1

Tumor depth and diameter analysis results for six sections

Cancer region







Depth (mm)

0 ± 0

1 ± 1.29

1.61 ± 1.75

0.64 ± 0.93

0.4 ± 0.89

1 ± 1.15

Diameter (cm)

1.14 ± 0.89

1.20 ± 0.92

1.03 ± 0.89

1.12 ± 1.06

1.08 ± 0.96

1.08 ± 1.03

Fig. 3

a Steps for generating and optimizing the TCP model from tumor location and volume analysis and estimating the normal tissue and tumor properties. b Optimization process

Table 2

Case number according to tumor location, tumor volume and Gleason score








Normal tissue (n)







Cancer tissue (n)







Gleason score












Tumor volume










2.4 Quantitative parameter analysis

In the TCP model, the mechanical property estimation can be affected by tumor location and volume. For a clearer demonstration, we carried out an FEM simulation and also performed a quantitative analysis of the results while varying the following simulation conditions: (1) tumor diameter and (2) tumor depth, as shown in Fig. 4. The FE models were designed with geometries, boundary conditions and material properties identical to those of the TCP models. To establish a relationship between the tissue behavior and the parameters related to the tumor, the simulation results of different parameters were fitted by the curve-fitting tool in MATLAB (MathWorks, USA). The first-order equation (Ax + B) was used to establish a relationship between the tissue behavior and the parameters related to the tumor.
Fig. 4

Peak force ratio example of MM section due to depth and diameter changes of the tumor region. The first-order linear modeling was fit to the peak force ratio changes for the parameter study

3 Results

The data from 72 regions from six patients were excluded because of mechanical or clinical data corresponding to the exclusion criteria. A total of 206 sites of the 480 regions (40 prostate specimens) revealed cancer tissues on histopathological examination. The results of the tumor volume and location analysis are shown in Table 1. The tumors are also distributed as spheres with a diameter of about 1 cm near the surface of posterior side (0–2 mm). Figure 5 shows the stress distributions of the TCP models obtained by the FEM simulation. The estimated elastic moduli of each section from the TCP models and Hertz–Sneddon model are presented in Table 3. The cancers were the most frequently distributed at the base of the prostate (36.4 %), followed by the mid-gland (34.5 %) and then the apex of the prostate (29.1 %). From the parameter study, the relationship between the relative peak force and the equation parameters (A and B) are shown in Table 4. The typical peak force ratio depending on the parameters related to the tumor (diameter and depth) show linearity as shown in Fig. 4.
Fig. 5

a Stress distributions of the six TCP models for six sections (LB, MB, LM, MM, LA and MA). b The estimated elastic moduli for the six sections. c Young’s modulus from the Hertz–Sneddon model estimation

Table 3

The optimized Young’s moduli from the TCP model estimation and the Hertz–Sneddon model estimation [3]

Cancer region







Overall region

TCP model estimate

 Normal prostate region








 Cancer region








Hertz–Sneddon model estimate

 Normal prostate region








 Cancer region








Table 4

Parameter study of simulations using different diameters, depths, and property ratios of tumors



R2 value


R2 value

Property ratio

R2 value


0.0739 × (diameter) + 0.6306


−0.1765 × (depth) + 1.0197


0.1483 × (property ratio) + 0.8756



0.0337 × (diameter) + 0.6767


−0.0182 × (depth) + 0.9997


0.1597 × (property ratio) + 0.8547



0.0287 × (diameter) + 0.7993


−0.0193 × (depth) + 0.9902


0.0905 × (property ratio) + 0.9095



0.1019 × (diameter) + 0.9226


−0.0133 × (depth) + 1.0082


0.1363 × (property ratio) + 0.9423



0.0555 × (diameter) + 0.7223


−0.0692 × (depth) + 1.0141


0.0847 × (property ratio) + 0.9953



0.0127 × (diameter) + 0.9182


−0.0253 × (depth) + 1.0242


0.1437 × (property ratio) + 0.8625


For each section, a first-order linear model was fit to the peak force ratio change graphs, as in Fig. 5

4 Discussion

This paper presents the TCP models to obtain more precise mechanical properties of normal tissue and tumor lesion. The models include prostate geometries reconstructed by sequential CT images and inhomogeneous structure based on the tumor volume and location information. Ahn et al. estimated the elastic moduli of the normal and tumor-contained tissues of the human prostate using the Hertz–Sneddon model whose elastic moduli of normal tissue and tumor are 17.0 and 24.1 kPa, respectively [3]. In our research, we consider the volume and location information of tumor lesion statistically and develop the TCP models to estimate more precise elastic moduli of local sections. The estimated elastic moduli of the normal tissue and tumor were 14.7 and 41.6 kPa, respectively. These results are supported by the previous research that the elasticity of the cancerous cell and tissue is reported to be about 2–3 times higher than that of the normal cells and tissues [9, 12]. A recent study by Zhang et al. reported that the elastic moduli of normal prostate tissue and prostate tissue with greater than 60 % of the total prostate volume being cancerous were 15.9 and 40.4 kPa, respectively. Therefore, we assert that the estimated properties of normal tissue and cancerous tissue used in this model are more precise than those obtained by other researchers.

Although we obtained more precise measurements of the properties of prostates, our model still has some limitations. It assumes homogeneity and isotropicity within both regions and neglects the detailed network of biological tissue structures [8, 11]. The prostate is ~70 % glandular elements and 30 % fibromuscular stroma. The relative proportions of glandular elements and fibromuscular stroma differs between individuals and might indicate different elasticities. Therefore, consideration of the structural characteristics of each region is required for more accurate analyses.

Moreover, in addition to the tumor, many diseases and the prostate parenchyma could have influenced the mechanical properties of the prostate tissues. The presence of prostate hyperplasia, prostatic calcification, cysts and inflammatory granuloma might have induced changes in the mechanical property of the prostate in this study [10], although patients who had undergone preoperative hormonal/radiation therapy or prostate-related surgery and patients with clinically insignificant small cancer (<0.5 ml) were excluded in this model. In our model, each region is assumed to be homogeneous and isotropic and does not take into account the unique structural characteristics within the regions. When using the estimated properties of the prostate in the clinic, the more accurate boundary conditions of in vivo experiments should be used. The human prostate is suspended by the pubo-urethral ligaments and pubo-prostatic ligaments. The dorsal midline fibrous raphe dorsally anchors the prostate with Denonvilliers’ fascia, and the prostate is supported by the pelvic bones [23]. In addition, a layer of fat covers the prostate. These anatomical features and in vivo experimental conditions should be taken into consideration to obtain more precise properties of the prostate. In the case that the tumor tissue located in the boundary area of any two neighboring areas, the behavior of the model should be affected. During the diagnosis of prostate cancer, the physicians performed a needle biopsy at six regions (apex, mid, base and bilaterally) and suspicious regions detected by DRE. Recently, the physicians attempted needle biopsy from a sextant to extended or double sextant protocol to increase the cancer detection rate (reduce the boundary area of any two neighboring areas) [24]. The palpation does not cause any side effects according to the number of palpations, but the increase in the number of needle biopsies causes side effects, such as pain, post-biopsy infection, hematuria, hematochezia, hematospermia, vasovagal reflex, voiding difficulty and acute urinary retention [17]. Therefore, we could enhance the diagnostic accuracy by increasing the number of palpations. The local models of the six sections that were developed can be used to establish clinical diagnosis criteria. Based on the estimated prostate tissue properties of the six sections, we were able to provide the location of the prostate tumors. Due to the multi-focal characteristics of prostate tumors, the original diagnostic scheme for prostate tumor was divided into six section examinations (LA, LM, LB, MA, MM, and MB) [6]. Single palpation and models do not take into account the surface geometry and boundary conditions, and so cannot cover the entire prostate or distinguish multi-focal tumors. Therefore, a single TCP model cannot represent the mechanical properties of entire sections of the prostate and is not clinically valid for diagnosis and localization of prostate tumors. It is necessary to develop local prostate models that can cover all six sections (LB, MB, LM, MM, LA, and MA). Based on the pathological location and volume information, six local prostate models were developed to characterize prostate tumor tissues. The steps used to localize and differentiate tumors are shown in Fig. 6. Local characteristics from newly performed robotic palpation experiments were obtained and then compared with the estimated elastic moduli of the TCP models in Fig. 6a. The localization was completed to determine suspicious tumor regions (Fig. 6c). For diagnostic applications based on the mechanical properties of human organs, normal property criteria are important to detect suspicious regions. In contrast, due to personal variation and other diseases that affect the mechanical properties, comparisons between the obtained specimen properties and the cancer property criteria could not lead to the identification of the presence of cancer nodules. Therefore, an accurate estimation of the normal property criteria is required for detecting suspicious regions. To better represent the prostate glands, the model should reflect the geometric factors related to morphologies and actual experimental conditions, including the indentation depth and its relative magnitude to the sample thickness, to rule out the undesired effects from the underlying substrates. The Hertz–Sneddon model is based on numerous assumptions, including a flat surface, non-frictional contact, infinitesimal deformation, infinite sample thickness, and isotropic and linear elastic properties. Therefore, it is less suitable than the FEM model, which takes a more realistic approach to tissue–material interactions due to the complex geometries and boundary conditions of the prostate.
Fig. 6

Steps for localizing and differentiating tissue abnormalities using the optimized elastic modulus database and case study results. a Local prostate tissue criteria from the TCP model database. b Local property estimations from robotic palpation. c Localization using the comparison of robotic palpation results and local normal criteria

In this research, we developed the six section TCP models based on prostate geometries (tumor volume and location information). In addition, these models were used to estimate more precise properties of prostate normal tissue and tumor lesion, which can provide the quantitative and precise diagnostic information to surgeons. The obtained results can also be used as the baseline property criteria for the diagnosis and localization of prostate tumors.



This work was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MEST) (No. 2012-0001007).


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Copyright information

© International Federation for Medical and Biological Engineering 2012

Authors and Affiliations

  • Yeongjin Kim
    • 1
  • Bummo Ahn
    • 2
  • Jae Won Lee
    • 3
  • Koon Ho Rha
    • 4
  • Jung Kim
    • 1
  1. 1.Division of Mechanical Engineering, School of Mechanical, Aerospace and Systems EngineeringKorea Advanced Institute of Science and TechnologyDaejeonRepublic of Korea
  2. 2.The Simulation Group, Department of Radiology, Center for Integration of Medicine and Innovative TechnologyHarvard Medical SchoolCambridgeUSA
  3. 3.Department of UrologyJesaeng General HospitalSoengnamRepublic of Korea
  4. 4.Department of Urology, Urological Science InstituteYonsei University College of MedicineSeoulRepublic of Korea

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