Logistic Regression Analysis & Craniometric Study

In crime scenes and accidents, the standard operating protocols for personal identification is not difficult when the entire body is found. As a result, the investigators can directly collect the sample of the decrease such as facial photograph, DNA, fingerprint and dental record in order to compare to possible relatives or with ante-mortem profile. However, the investigators are not always lucky. In severe accidents such aircraft crashes, only little information of the decrease is available, the skin and soft tissue may be completely burnt out and the skeleton can be broken into small pieces due to the impact. The skeleton examination in historical sites by archaeologists presents even more complication. The archaeologists need not only to identify general aspects of the skeleton, for instant age, sex, cause of death, stature and race, but also to estimate the period of death and the possibility to discover the particular person that might be significant in the history. Several techniques have been applied to assist the identification of the decrease ranging from the simplest technique which may acquire the evidence from the personal belonging until using the advance scientific techniques. These techniques can be generally categorized into two methods, invasive and non-invasive. The invasive method includes biochemical analysis, microscopy, accelerator mass spectrometry radiocarbon dating (with standard C-14), ancient DNA analysis, histology and endoscope whereas the non-invasive technique involved the aid of engineering technologies such as radiographic analysis and computed tomography (CT) examination. The archaeological researches had been increasingly conducted by means of non-invasive techniques which 112 of 245 researches have applied the non-invasive technique and the trend of investigation gradually moved from invasive to non-invasive examinations. One main advantage of radiography includes the ability to access general aspects of mummy without releasing the bandages which may be destroyed important features or contaminated. In the early 1900s, another non-invasive medical examination device, computed tomography scanner, has been invented by Alessandro Vallebona, but the technology has remained unpopular until the 1970s which modern era of computed tomography scanner began. Not too long, computed tomography scanner became an effective tool in examination the autopsy. The computed tomography generally relies on medical imaging processing combined with reverse engineering principles which the object is captured the profile and presented the virtual three-dimensional models in computer. With these advanced features, the perspective of archaeology and forensic medicine has changed into three-dimensional aspect. Consequently, The two-dimensional radiographic image occlusion and the problem such uncertainty from bias of investigator in direct measurements are eliminated. an effective clinical diagnosis device in many hospitals. The use of three-dimensional model allows the surgeon to examine the abnormality of organs in any configurations which the two-dimensional technique may be inaccessible. Moreover, the three-dimensional models can be used to simulate the surgical operation prior surgery subsequently reduce operating time and increase safety of patients. Alternative uses of computed tomography include morphometric study and the evaluation the risk of implant usage. Reverse engineering has been widely applied several years in clinical fields and forensic medicine. Initially, reverse engineering was first used in free-form product designs which the conventional “Forward Engineering” has limited drawing functions and time consumption. Product design based on “Forward Engineering”, the process involves turning the conceptual product design to physical product whereas reverse engineering is inversed. The process of reverse engineering involves turning the physical product back to the virtual models (normally three-dimension) From the three dimensional virtual models, the conceptual design can be obtained. Reverse engineering can be described as two phases which are digitization and reconstruction phase. The digitization phase involves the data acquisition of the physical model using various types of scanner. The initial geometry from the scanner is then obtained in three forms, point clouds, polygon model and series of image depending on the acquisition technique of each scanner. In the reconstruction phase, the obtained data is processed in

order to reconstruct the three-dimensional model. with “At this step, the elimination of noise data and filtering of unnecessary data may also be performed. For the production phases, it may be added as a final step in reverse engineering. This phase employs various manufacturing processes to fabricate the three-dimensional virtual model. However, this phase may not be mandatory, because sometime the geometry is only stored in database without any further processing. The characteristic of tactile approach is relatively simple. Touch probe is used in conjunction with robotic mechanism such as coordinate measurement machine (CMM), articulated arm or computer numerical control (CNC) devices to determine the position of the object (Cartesian coordinate). The accuracy is considered to be a main advantage of tactile approach, nevertheless the digitization process is quite slow and difficult to digitize complex geometry. A wide range of object can be applied with this approach regardless of color, shininess and transparency, this approach is not appropriate for deformable materials. In non-contact approach, the medium is used to measure the physical object using the principle of reflection or penetration. Laser beam and white light are medium sources commonly found in many three-dimensional scanners and they rely on the principle of reflection. The medium travels from the generator to the object before reflects and transmits to the receiver unit. The determination of geometry can be processed using at least one two-dimensional images combined with some optical parameters such as reflection angle, distance and time of flight. The initial geometry is presented in form of cloud point or of polygon model. Use of laser beam and white light has advantage in fast digitization and continuous data, but too shiny and transparent object present complication. The digitization process initializes the transmission of the X-ray through the object. A set of data acquisitions is performed with the constant interval throughout entire object which subsequently give a series of slice image (Hounsfield, 1980). Each slice contains the information of object’s position and the value of Hounsfield unit (HU). The density of object is proportional to the Hounsfield value. The higher Hounsfield value indicates high-density object such as enameled and cortical bone whereas the lower Hounsfield value indicates low-density object such as cancellous bone, fat and soft tissue. Various Hounsfield values of various substances are given in Table 1. In order to reconstruct the three-dimensional model, the optimal Hounsfield values must be selected (threshold). After that the threshold regions of each slice are combined to construct the volumetric model. For the computed tomography device, the speed of digitization and ability to examine the internal topology are considered to be superior, but the artifact (noise data) caused by metallic structure is drawback. The anatomical landmarks in craniometric study are categorized in to median and bilateral landmarks. The median landmarks are approximately located on sagittal plane. Each of them has only one location. There are 13 median landmarks which the specific definitions can be described as follows:

· Glabella (GL) - the most anterior point of frontal bone between supraorbital in the sagittal plane.

·  Bregma (BR) - the crossing of the coronal and sagittal sutures on the top of the skull.

·  Opisthocranium (OPC) - the most posterior point in midline of inion bone which length of the skull is maximum when measure from Galbella point.

·   Nasion (NA) - the intersection point of the internasal and frontonasal sutures in the sagittal plane.

·   Opistion (OPS) - the most posterior midsagittal point on the posterior margin of the foramen magnum.

·    Basion (BA) - the most anterior point of the great foramen magnum in the sagittal plane.

·  Orale (OR) - the midpoint on the intersection of posterior alveolar sockets rim of the cavities of two upper central incisors.

· Prosthion (PR) - the lowest, most anterior point on the alveolar portion of the premaxilla,

in the median plane, between the upper central incisors.

·   Staphylion (STA) - point in the medial line (interpalatal suture) of the posterior part of the hard palate where it is crossed by a line drawn tangent to the curves of the posterior margins of the palate.

·    Nasospinale (NAS) - the lowest point of lower anterior nasal aperture in mid-sagittal plane.

·    Gnathion (GN) - The midpoint on the lower border of the mandible in the sagittal plane.

·    Pogonion (PG) - The most projecting point of the chin in the standard sagittal plane.

·    Infradentale (ID) - The anterior superior point on the mandible at its labial contact between mandibular central incisors.

·    For the bilateral landmarks, each of them is located on both sides of skull. There are 17 bilateral landmarks which the specific definitions can be described as follows:

· Euryon (EU) - the lateral point on either side of the greatest transverse diameter of the skull.

·    Staphanion (ST) - the intersection of the superior temporal line and the coronal suture.

· Frontotemporale (FT) - the most anterior point on either side of temporal crest of the minimum transverse breadth of frontal bone.

· Bolton (BO) - The superior point of the curvature between occipital condyle and posterior margin of foramen magnum.

·    Orbitale (ORB) - the most inferior point of each infraorbital rim .

·    Ectoconchion (EC) - the most lateral point on each orbital's margin where a line running parallel to upper orbital border cut the lateral orbital margin.

·    Maxillo-frontale (MF) - the intersection point on anterior lacrimal crest and frontomaxillary sutures.

·    Supraorbitale (SOR) - the most superior point of each superior orbital rim.

· Zygonion (ZG) - The most lateral point on the outline of each zygomatic arch.

· Zygomaxillare (ZM) - The most interior point on each zygomatico-axillary sutures.

· Nasal (NS) - The most lateral point on each nasal's margin where maximum nasal breadth.

·    Endomolare (ENM) - the most medial point of internal curvature surface of alveolar ridge corresponding to second molar tooth.

·    Coronion (CO) - The most superior point on each coroniod process.

·    Condylion superior (CS) - the most superior point on each mandibular condyle.

·    Conlylion laterale (CDL) - the most lateral point on each mandibular condyle.

·    Gonion (GO) - the point at each mandibular angle that is defined by dropping a perpendicular from the intersection point of the tangent lines to the posterior margin of the mandibular vertical ramus and inferior margin of the mandibular body or horizontal ramus.

·    Laterla infradentale (LID) - the midpoint of a line tangent to the outer margins of the cavities of the lateral incisor of each lower canine teeth.

The determination of sex from skeleton is one of the critical components in forensic medicine as well as archaeology. The determination can be interpreted based on the average data from craniometric parameters of certain population. The accuracy of sex determination depends on several factors which one of them is osteological elements. Various osteological elements have been used to predict sex of skeleton which includes femur, tibia, pelvis, skull, humerus, hyoid, talus, and calcaneus. However, among aforementioned elements, the best for prediction is pelvis, follow by skull and long bone.  Logistic regression analysis is a method to analysis multi-variate analysis which aims to predict the probability of occurrence of an event under consideration by fitting the raw data using to a logit function logistic curve. The advantage of logistic regression is less of parameter restrictions than discriminant analysis and regression analysis. The output from the logistic regression analysis can only be “Yes” or “No” which normally designated as “0” and “1”, respectively. Basically, logistic regression function (Z) is written in form of

Z = β0 + β1x1 + β2x2 + β3x3 + β4x4 + … +βnxn + βn+1xn+1

where β0 is called intercept and β1, β2, β3 ,β4, …,βn and βn+1 are regression coefficients of x1, x2, x3, x4, …,xn and xn+1 variable, respectively. From the following logistic model of Z, the probability of event (P.E.) under consideration can be calculate through

P.E. = eZ / (1 + eZ)

In equation (2)  is a natural logarithm, its value is approximately 2.71828. The probability of event varies from “0” to “1”. The near “1” value means the independent variables influences the probability of event whereas the value close to “0” means the independent variables have little effect to probability of event. In this study, a binary logistic regression using forward stepwise is applied to determine sex based on average data of craniometric parameters in previous section. The fitting process excludes the measurement with high co-linearity. The probability from logistic regression function, “0” indicates male whereas “1” indicates female, respectively.

Since there is possibility to find skull as fragment bone in forensics and archaeology, then the assessment of necessary craniometric parameters becomes complex. Although the missing craniometric parameters can be predicted using correlation. Some correlation coefficients among these craniometric parameters are mostly inferior. With low correlation coefficient, the equation may not be an appropriate solution to determine those missing craniometric parameters. As a result, a purposed alternative is to reconstruct defected skull surface based on the mirror surface topology of normal side with aids.

Generally, in forensic medicine and archaeological researches, the study relies on direct measurement and other two-dimensional techniques which may not be accurate. The measurement errors can be influenced by human error, instrumental error, image magnification and image occlusion. The advantage of three-dimensional computed tomography technique includes the analysis of specimen without destruction or damage of specimens as well as the ability to analyze the specimens in configuration which the conventional technique cannot provide. Comparing to the other reverse engineering technologies, computed tomography presents the superior ability in accessing the internal geometry which the other tools find the difficulty in data capturing. Logistic regression is used to derive functions for sex determination based on average numerical values which obtained from craniometric parameters. Three models are purposed, Model A is based on cranial parameters, Model B is based on mandible parameters and Model C is based on both cranial and mandibular parameters. From the result, Model C provides the best accuracy among other models which is 94.2%. The prediction equation relies on four parameters which are Coronion height-left, Nasion-basion length, Palatal length, and Upper facial height which subsequently produce logistic regression.

Acknowledgements:

The Police Department;

www.politie.nl and a Chief Inspector – Mr. Erik Akerboom     ©

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